<p class="course-title-kicker">CS103 · Lecture 19</p> # Inheritance: Base and Derived Classes <p class="course-title-tagline">A derived class is a base class, with more</p> <p class="course-title-instructor">Dr. Debasish Pattanayak · <a href="https://drdebmath.github.io">drdebmath.github.io</a></p>

## Where Lecture 18 ended · A class owns what it creates A class can own its data and release it (Lecture 18). Give Lecture 14's node two links, `left` and `right`, and a `BinaryTree` owns a whole tree of them. A **search tree** needs everything a binary tree has, plus an ordered `insert`. **Today's question.** Copy the class, or reuse it? Plan: derive one class from another, see the order of construction, control access, and learn when not to inherit.

## Inheritance · A SearchTree is a BinaryTree ~~~cpp class BinaryTree { // base class public: int size() const; // counts the nodes protected: std::unique_ptr<Node> root; // Node: value, left, right }; class SearchTree : public BinaryTree { // derived class public: void insert(int v); // smaller left, larger right bool contains(int v) const; }; void report(const BinaryTree& t) { std::cout << "size " << t.size() << '\n'; } int main() { SearchTree t; for (int v : {50, 30, 70, 20}) t.insert(v); std::cout << t.size() << ' ' << t.contains(20) << '\n'; // 4 1 report(t); // size 4 } ~~~ <figure class="course-stepper" data-course-stepper> <svg class="course-array-address-figure course-l19base-figure" viewBox="0 0 900 380" role="img" aria-label="A step-by-step trace of the program that builds a SearchTree object t, in 8 frames. The object t is drawn as an outer box that contains a BinaryTree part holding the root pointer; SearchTree adds only functions. Frame 1: t is created and root is a null pointer. Frame 2: insert(50) makes 50 the root node. Frame 3: insert(30) makes 30 the left child of 50. Frame 4: insert(70) makes 70 the right child of 50. Frame 5: insert(20) makes 20 the left child of 30, so each node is owned by its parent. Frame 6: t.size() runs the inherited BinaryTree::size and returns 4. Frame 7: t.contains(20) returns 1 and the output shows 4 1. Frame 8: report(t) binds a const BinaryTree reference to the BinaryTree part of t, size gives 4, and the output adds size 4." xmlns="http://www.w3.org/2000/svg"> <style> .course-l19base-figure text{font-family:ui-monospace,Menlo,Consolas,monospace;fill:currentColor} .course-l19base-figure .cell{fill:none;stroke:currentColor;stroke-width:2} .course-l19base-figure .cell.obj{fill:rgba(142,232,216,.18)} .course-l19base-figure .cell.heap{fill:rgba(255,214,102,.22)} .course-l19base-figure .cell.dead{fill:rgba(255,120,120,.22);stroke-dasharray:6 5} .course-l19base-figure .cell.pend{stroke-dasharray:3 6} .course-l19base-figure .hl{fill:rgba(110,170,255,.35);stroke:none} .course-l19base-figure .arrow{fill:none;stroke:currentColor;stroke-width:2.5} .course-l19base-figure .head{fill:currentColor} </style> <g data-step="0"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 build the tree</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 call inherited functions</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 base reference</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="78" font-size="18" font-weight="700">SearchTree t</text><rect class="cell obj" x="36" y="88" width="548" height="196"/><text x="52" y="110" font-size="18" font-weight="700">BinaryTree part</text><rect class="cell heap" x="52" y="124" width="110" height="36"/><text x="107" y="149" font-size="18" text-anchor="middle">root</text><text x="172" y="148" font-size="16">= nullptr</text><text x="52" y="200" font-size="16">SearchTree adds</text><text x="52" y="222" font-size="16">functions only</text><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">SearchTree t;</text><text x="450" y="362" font-size="16" text-anchor="middle">t holds one BinaryTree part; root is a null pointer</text></g> <g data-step="1"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 build the tree</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 call inherited functions</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 base reference</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="78" font-size="18" font-weight="700">SearchTree t</text><rect class="cell obj" x="36" y="88" width="548" height="196"/><text x="52" y="110" font-size="18" font-weight="700">BinaryTree part</text><rect class="cell heap" x="52" y="124" width="110" height="36"/><text x="107" y="149" font-size="18" text-anchor="middle">root</text><text x="52" y="200" font-size="16">SearchTree adds</text><text x="52" y="222" font-size="16">functions only</text><circle class="hl" cx="390" cy="142" r="26"/><circle class="cell obj" cx="390" cy="142" r="18"/><text x="390" y="148" font-size="16" text-anchor="middle">50</text><line class="arrow" x1="162.0" y1="142.0" x2="361.0" y2="142.0"/><polygon class="head" points="372.0,142.0 361.0,147.0 361.0,137.0"/><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">t.insert(50);</text><text x="450" y="362" font-size="16" text-anchor="middle">The first value becomes the root node, owned by root</text></g> <g data-step="2"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 build the tree</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 call inherited functions</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 base reference</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="78" font-size="18" font-weight="700">SearchTree t</text><rect class="cell obj" x="36" y="88" width="548" height="196"/><text x="52" y="110" font-size="18" font-weight="700">BinaryTree part</text><rect class="cell heap" x="52" y="124" width="110" height="36"/><text x="107" y="149" font-size="18" text-anchor="middle">root</text><text x="52" y="200" font-size="16">SearchTree adds</text><text x="52" y="222" font-size="16">functions only</text><circle class="cell obj" cx="390" cy="142" r="18"/><text x="390" y="148" font-size="16" text-anchor="middle">50</text><circle class="hl" cx="310" cy="196" r="26"/><circle class="cell obj" cx="310" cy="196" r="18"/><text x="310" y="202" font-size="16" text-anchor="middle">30</text><line class="arrow" x1="375.1" y1="152.1" x2="334.0" y2="179.8"/><polygon class="head" points="324.9,185.9 331.2,175.6 336.8,183.9"/><line class="arrow" x1="162.0" y1="142.0" x2="361.0" y2="142.0"/><polygon class="head" points="372.0,142.0 361.0,147.0 361.0,137.0"/><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">t.insert(30);</text><text x="450" y="362" font-size="16" text-anchor="middle">30 < 50, so it becomes the left child of 50</text></g> <g data-step="3"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 build the tree</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 call inherited functions</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 base reference</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="78" font-size="18" font-weight="700">SearchTree t</text><rect class="cell obj" x="36" y="88" width="548" height="196"/><text x="52" y="110" font-size="18" font-weight="700">BinaryTree part</text><rect class="cell heap" x="52" y="124" width="110" height="36"/><text x="107" y="149" font-size="18" text-anchor="middle">root</text><text x="52" y="200" font-size="16">SearchTree adds</text><text x="52" y="222" font-size="16">functions only</text><circle class="cell obj" cx="390" cy="142" r="18"/><text x="390" y="148" font-size="16" text-anchor="middle">50</text><circle class="cell obj" cx="310" cy="196" r="18"/><text x="310" y="202" font-size="16" text-anchor="middle">30</text><line class="arrow" x1="375.1" y1="152.1" x2="334.0" y2="179.8"/><polygon class="head" points="324.9,185.9 331.2,175.6 336.8,183.9"/><circle class="hl" cx="470" cy="196" r="26"/><circle class="cell obj" cx="470" cy="196" r="18"/><text x="470" y="202" font-size="16" text-anchor="middle">70</text><line class="arrow" x1="404.9" y1="152.1" x2="446.0" y2="179.8"/><polygon class="head" points="455.1,185.9 443.2,183.9 448.8,175.6"/><line class="arrow" x1="162.0" y1="142.0" x2="361.0" y2="142.0"/><polygon class="head" points="372.0,142.0 361.0,147.0 361.0,137.0"/><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">t.insert(70);</text><text x="450" y="362" font-size="16" text-anchor="middle">70 > 50, so it becomes the right child of 50</text></g> <g data-step="4"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 build the tree</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 call inherited functions</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 base reference</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="78" font-size="18" font-weight="700">SearchTree t</text><rect class="cell obj" x="36" y="88" width="548" height="196"/><text x="52" y="110" font-size="18" font-weight="700">BinaryTree part</text><rect class="cell heap" x="52" y="124" width="110" height="36"/><text x="107" y="149" font-size="18" text-anchor="middle">root</text><text x="52" y="200" font-size="16">SearchTree adds</text><text x="52" y="222" font-size="16">functions only</text><circle class="cell obj" cx="390" cy="142" r="18"/><text x="390" y="148" font-size="16" text-anchor="middle">50</text><circle class="cell obj" cx="310" cy="196" r="18"/><text x="310" y="202" font-size="16" text-anchor="middle">30</text><line class="arrow" x1="375.1" y1="152.1" x2="334.0" y2="179.8"/><polygon class="head" points="324.9,185.9 331.2,175.6 336.8,183.9"/><circle class="cell obj" cx="470" cy="196" r="18"/><text x="470" y="202" font-size="16" text-anchor="middle">70</text><line class="arrow" x1="404.9" y1="152.1" x2="446.0" y2="179.8"/><polygon class="head" points="455.1,185.9 443.2,183.9 448.8,175.6"/><circle class="hl" cx="250" cy="250" r="26"/><circle class="cell obj" cx="250" cy="250" r="18"/><text x="250" y="256" font-size="16" text-anchor="middle">20</text><line class="arrow" x1="296.6" y1="208.0" x2="271.6" y2="230.6"/><polygon class="head" points="263.4,238.0 268.2,226.9 274.9,234.3"/><line class="arrow" x1="162.0" y1="142.0" x2="361.0" y2="142.0"/><polygon class="head" points="372.0,142.0 361.0,147.0 361.0,137.0"/><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">t.insert(20);</text><text x="450" y="362" font-size="16" text-anchor="middle">20 < 50, then 20 < 30: the left child of 30</text></g> <g data-step="5"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 build the tree</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">2 call inherited functions</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 base reference</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="78" font-size="18" font-weight="700">SearchTree t</text><rect class="hl" x="32" y="84" width="556" height="204"/><rect class="cell obj" x="36" y="88" width="548" height="196"/><text x="52" y="110" font-size="18" font-weight="700">BinaryTree part</text><rect class="cell heap" x="52" y="124" width="110" height="36"/><text x="107" y="149" font-size="18" text-anchor="middle">root</text><text x="52" y="200" font-size="16">size() is found</text><text x="52" y="222" font-size="16">in BinaryTree</text><circle class="cell obj" cx="390" cy="142" r="18"/><text x="390" y="148" font-size="16" text-anchor="middle">50</text><circle class="cell obj" cx="310" cy="196" r="18"/><text x="310" y="202" font-size="16" text-anchor="middle">30</text><line class="arrow" x1="375.1" y1="152.1" x2="334.0" y2="179.8"/><polygon class="head" points="324.9,185.9 331.2,175.6 336.8,183.9"/><circle class="cell obj" cx="470" cy="196" r="18"/><text x="470" y="202" font-size="16" text-anchor="middle">70</text><line class="arrow" x1="404.9" y1="152.1" x2="446.0" y2="179.8"/><polygon class="head" points="455.1,185.9 443.2,183.9 448.8,175.6"/><circle class="cell obj" cx="250" cy="250" r="18"/><text x="250" y="256" font-size="16" text-anchor="middle">20</text><line class="arrow" x1="296.6" y1="208.0" x2="271.6" y2="230.6"/><polygon class="head" points="263.4,238.0 268.2,226.9 274.9,234.3"/><line class="arrow" x1="162.0" y1="142.0" x2="361.0" y2="142.0"/><polygon class="head" points="372.0,142.0 361.0,147.0 361.0,137.0"/><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">t.size()</text><text x="450" y="362" font-size="16" text-anchor="middle">The inherited BinaryTree::size() counts the 4 nodes and returns 4</text></g> <g data-step="6"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 build the tree</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">2 call inherited functions</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 base reference</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="78" font-size="18" font-weight="700">SearchTree t</text><rect class="cell obj" x="36" y="88" width="548" height="196"/><text x="52" y="110" font-size="18" font-weight="700">BinaryTree part</text><rect class="cell heap" x="52" y="124" width="110" height="36"/><text x="107" y="149" font-size="18" text-anchor="middle">root</text><text x="52" y="200" font-size="16">contains() is</text><text x="52" y="222" font-size="16">from SearchTree</text><circle class="cell obj" cx="390" cy="142" r="18"/><text x="390" y="148" font-size="16" text-anchor="middle">50</text><circle class="cell obj" cx="310" cy="196" r="18"/><text x="310" y="202" font-size="16" text-anchor="middle">30</text><line class="arrow" x1="375.1" y1="152.1" x2="334.0" y2="179.8"/><polygon class="head" points="324.9,185.9 331.2,175.6 336.8,183.9"/><circle class="cell obj" cx="470" cy="196" r="18"/><text x="470" y="202" font-size="16" text-anchor="middle">70</text><line class="arrow" x1="404.9" y1="152.1" x2="446.0" y2="179.8"/><polygon class="head" points="455.1,185.9 443.2,183.9 448.8,175.6"/><circle class="cell obj" cx="250" cy="250" r="18"/><text x="250" y="256" font-size="16" text-anchor="middle">20</text><line class="arrow" x1="296.6" y1="208.0" x2="271.6" y2="230.6"/><polygon class="head" points="263.4,238.0 268.2,226.9 274.9,234.3"/><line class="arrow" x1="162.0" y1="142.0" x2="361.0" y2="142.0"/><polygon class="head" points="372.0,142.0 361.0,147.0 361.0,137.0"/><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><text x="636" y="104" font-size="16">4 1</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">t.contains(20)</text><text x="450" y="362" font-size="16" text-anchor="middle">SearchTree::contains() walks 50, 30, 20 and returns 1; both values print as 4 1</text></g> <g data-step="7"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 build the tree</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 call inherited functions</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">3 base reference</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="78" font-size="18" font-weight="700">SearchTree t</text><rect class="hl" x="32" y="84" width="556" height="204"/><rect class="cell obj" x="36" y="88" width="548" height="196"/><text x="52" y="110" font-size="18" font-weight="700">BinaryTree part</text><rect class="cell heap" x="52" y="124" width="110" height="36"/><text x="107" y="149" font-size="18" text-anchor="middle">root</text><text x="52" y="200" font-size="16">report(t): the</text><text x="52" y="222" font-size="16">parameter refers</text><text x="52" y="244" font-size="16">to this part</text><circle class="cell obj" cx="390" cy="142" r="18"/><text x="390" y="148" font-size="16" text-anchor="middle">50</text><circle class="cell obj" cx="310" cy="196" r="18"/><text x="310" y="202" font-size="16" text-anchor="middle">30</text><line class="arrow" x1="375.1" y1="152.1" x2="334.0" y2="179.8"/><polygon class="head" points="324.9,185.9 331.2,175.6 336.8,183.9"/><circle class="cell obj" cx="470" cy="196" r="18"/><text x="470" y="202" font-size="16" text-anchor="middle">70</text><line class="arrow" x1="404.9" y1="152.1" x2="446.0" y2="179.8"/><polygon class="head" points="455.1,185.9 443.2,183.9 448.8,175.6"/><circle class="cell obj" cx="250" cy="250" r="18"/><text x="250" y="256" font-size="16" text-anchor="middle">20</text><line class="arrow" x1="296.6" y1="208.0" x2="271.6" y2="230.6"/><polygon class="head" points="263.4,238.0 268.2,226.9 274.9,234.3"/><line class="arrow" x1="162.0" y1="142.0" x2="361.0" y2="142.0"/><polygon class="head" points="372.0,142.0 361.0,147.0 361.0,137.0"/><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><text x="636" y="104" font-size="16">4 1</text><text x="636" y="126" font-size="16">size 4</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">report(t); // const BinaryTree& t</text><text x="450" y="362" font-size="16" text-anchor="middle">The base reference binds to the BinaryTree part of t; its size() gives 4, printed as size 4</text></g> </svg> </figure>

## Public inheritance: the general form | Part | Meaning | | --- | --- | | `class Derived : public Base { ... };` | **Public inheritance**: `Derived` is the **derived class**, `Base` is the **base class**. | | Inherited members | Every public member of `Base` is a public member of `Derived`; the derived object contains a `Base` part. | | `Derived(args) : Base(args), member(x) { }` | The **initializer list** constructs the base class first, then the data members. | | `protected:` | Visible to the class, its derived classes, and its friends; not to other code. | | `friend` | A friend function may use private and protected members; friendship is not inherited. | | Private base members | They are in the derived object, but the derived class cannot name them. |

## How `size()` works · Recursion over both subtrees ~~~cpp class BinaryTree { public: int size() const { return count(root.get()); } // start at the root protected: std::unique_ptr<Node> root; private: int count(const Node* n) const { // nodes in the subtree at n if (n == nullptr) return 0; // base case: empty subtree return 1 + count(n->left.get()) + count(n->right.get()); } }; // tree 50, 30, 70, 20: t.size() returns 4 ~~~ <figure class="course-stepper" data-course-stepper> <svg class="course-array-address-figure course-l19size-figure" viewBox="0 0 900 380" role="img" aria-label="A step-by-step trace, in 9 frames, of how BinaryTree::size() counts the nodes of the tree 50, 30, 70, 20, where 50 is the root, 30 its left child, 70 its right child, and 20 the left child of 30, with a call stack beside the tree. Frame 1: t.size() runs the inherited size(), which calls count(root.get()). Frame 2: count(50) is pushed; root.get() gives the node pointer without taking ownership. Frame 3: count(50) first counts its left subtree, pushing count(30). Frame 4: count(30) counts its left subtree, pushing count(20). Frame 5: both children of 20 are null, the base case returns 0 for each, so count(20) is 1 plus 0 plus 0, which is 1. Frame 6: count(20) is popped; the right child of 30 is null, so count(30) is 1 plus 1 plus 0, which is 2. Frame 7: count(30) is popped and count(50) counts its right subtree; count(70) is pushed and returns 1 because 70 has no children. Frame 8: count(50) returns 1 plus 2 plus 1, which is 4. Frame 9: size() returns 4 and the call stack is empty again." xmlns="http://www.w3.org/2000/svg"> <style> .course-l19size-figure text{font-family:ui-monospace,Menlo,Consolas,monospace;fill:currentColor} .course-l19size-figure .cell{fill:none;stroke:currentColor;stroke-width:2} .course-l19size-figure .cell.frame{fill:rgba(142,232,216,.18)} .course-l19size-figure .cell.frame.top{fill:rgba(110,170,255,.35)} .course-l19size-figure .node{fill:rgba(142,232,216,.18);stroke:currentColor;stroke-width:2} .course-l19size-figure .node.done{fill:rgba(255,214,102,.30)} .course-l19size-figure .hl{fill:rgba(110,170,255,.35);stroke:none} .course-l19size-figure .edge{stroke:currentColor;stroke-width:2} .course-l19size-figure .head{fill:currentColor} </style> <g data-step="0"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 start</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 go down</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 return</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 result</tspan></text><rect class="cell" x="20" y="48" width="560" height="262" style="stroke-dasharray:3 6"/><text x="36" y="74" font-size="17" font-weight="700">t (BinaryTree part)</text><line class="edge" x1="279.3" y1="104.1" x2="210.2" y2="144.4"/><polygon class="head" points="200.7,149.9 207.5,139.6 213.0,149.1"/><line class="edge" x1="320.7" y1="104.1" x2="389.8" y2="144.4"/><polygon class="head" points="399.3,149.9 387.0,149.1 392.5,139.6"/><line class="edge" x1="163.0" y1="179.0" x2="134.7" y2="207.3"/><polygon class="head" points="127.0,215.0 130.9,203.4 138.6,211.1"/><circle class="node" cx="300" cy="92" r="24"/><text x="300" y="98" font-size="17" text-anchor="middle">50</text><circle class="node" cx="180" cy="162" r="24"/><text x="180" y="168" font-size="17" text-anchor="middle">30</text><circle class="node" cx="420" cy="162" r="24"/><text x="420" y="168" font-size="17" text-anchor="middle">70</text><circle class="node" cx="110" cy="232" r="24"/><text x="110" y="238" font-size="17" text-anchor="middle">20</text><rect class="cell" x="600" y="48" width="280" height="262"/><text x="616" y="74" font-size="17" font-weight="700">call stack</text><rect class="cell frame top" x="616" y="260" width="248" height="36"/><text x="630" y="284" font-size="17" font-weight="700">t.size()</text><text x="450" y="340" font-size="18" text-anchor="middle" font-weight="700">t.size();</text><text x="450" y="366" font-size="16" text-anchor="middle">size() is inherited from BinaryTree; it calls count(root.get())</text></g> <g data-step="1"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 start</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 go down</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 return</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 result</tspan></text><rect class="cell" x="20" y="48" width="560" height="262" style="stroke-dasharray:3 6"/><text x="36" y="74" font-size="17" font-weight="700">t (BinaryTree part)</text><line class="edge" x1="279.3" y1="104.1" x2="210.2" y2="144.4"/><polygon class="head" points="200.7,149.9 207.5,139.6 213.0,149.1"/><line class="edge" x1="320.7" y1="104.1" x2="389.8" y2="144.4"/><polygon class="head" points="399.3,149.9 387.0,149.1 392.5,139.6"/><line class="edge" x1="163.0" y1="179.0" x2="134.7" y2="207.3"/><polygon class="head" points="127.0,215.0 130.9,203.4 138.6,211.1"/><circle class="hl" cx="300" cy="92" r="31"/><circle class="node" cx="300" cy="92" r="24"/><text x="300" y="98" font-size="17" text-anchor="middle">50</text><circle class="node" cx="180" cy="162" r="24"/><text x="180" y="168" font-size="17" text-anchor="middle">30</text><circle class="node" cx="420" cy="162" r="24"/><text x="420" y="168" font-size="17" text-anchor="middle">70</text><circle class="node" cx="110" cy="232" r="24"/><text x="110" y="238" font-size="17" text-anchor="middle">20</text><rect class="cell" x="600" y="48" width="280" height="262"/><text x="616" y="74" font-size="17" font-weight="700">call stack</text><rect class="cell frame" x="616" y="260" width="248" height="36"/><text x="630" y="284" font-size="17">t.size()</text><rect class="cell frame top" x="616" y="216" width="248" height="36"/><text x="630" y="240" font-size="17" font-weight="700">count(50)</text><text x="450" y="340" font-size="18" text-anchor="middle" font-weight="700">count(root.get())</text><text x="450" y="366" font-size="16" text-anchor="middle">root.get() gives the node pointer without taking ownership</text></g> <g data-step="2"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 start</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">2 go down</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 return</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 result</tspan></text><rect class="cell" x="20" y="48" width="560" height="262" style="stroke-dasharray:3 6"/><text x="36" y="74" font-size="17" font-weight="700">t (BinaryTree part)</text><line class="edge" x1="279.3" y1="104.1" x2="210.2" y2="144.4"/><polygon class="head" points="200.7,149.9 207.5,139.6 213.0,149.1"/><line class="edge" x1="320.7" y1="104.1" x2="389.8" y2="144.4"/><polygon class="head" points="399.3,149.9 387.0,149.1 392.5,139.6"/><line class="edge" x1="163.0" y1="179.0" x2="134.7" y2="207.3"/><polygon class="head" points="127.0,215.0 130.9,203.4 138.6,211.1"/><circle class="node" cx="300" cy="92" r="24"/><text x="300" y="98" font-size="17" text-anchor="middle">50</text><circle class="hl" cx="180" cy="162" r="31"/><circle class="node" cx="180" cy="162" r="24"/><text x="180" y="168" font-size="17" text-anchor="middle">30</text><circle class="node" cx="420" cy="162" r="24"/><text x="420" y="168" font-size="17" text-anchor="middle">70</text><circle class="node" cx="110" cy="232" r="24"/><text x="110" y="238" font-size="17" text-anchor="middle">20</text><rect class="cell" x="600" y="48" width="280" height="262"/><text x="616" y="74" font-size="17" font-weight="700">call stack</text><rect class="cell frame" x="616" y="260" width="248" height="36"/><text x="630" y="284" font-size="17">t.size()</text><rect class="cell frame" x="616" y="216" width="248" height="36"/><text x="630" y="240" font-size="17">count(50)</text><rect class="cell frame top" x="616" y="172" width="248" height="36"/><text x="630" y="196" font-size="17" font-weight="700">count(30)</text><text x="450" y="340" font-size="18" text-anchor="middle" font-weight="700">count(n->left.get())</text><text x="450" y="366" font-size="16" text-anchor="middle">count(50) first counts its left subtree: a new call for 30</text></g> <g data-step="3"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 start</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">2 go down</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 return</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 result</tspan></text><rect class="cell" x="20" y="48" width="560" height="262" style="stroke-dasharray:3 6"/><text x="36" y="74" font-size="17" font-weight="700">t (BinaryTree part)</text><line class="edge" x1="279.3" y1="104.1" x2="210.2" y2="144.4"/><polygon class="head" points="200.7,149.9 207.5,139.6 213.0,149.1"/><line class="edge" x1="320.7" y1="104.1" x2="389.8" y2="144.4"/><polygon class="head" points="399.3,149.9 387.0,149.1 392.5,139.6"/><line class="edge" x1="163.0" y1="179.0" x2="134.7" y2="207.3"/><polygon class="head" points="127.0,215.0 130.9,203.4 138.6,211.1"/><circle class="node" cx="300" cy="92" r="24"/><text x="300" y="98" font-size="17" text-anchor="middle">50</text><circle class="node" cx="180" cy="162" r="24"/><text x="180" y="168" font-size="17" text-anchor="middle">30</text><circle class="node" cx="420" cy="162" r="24"/><text x="420" y="168" font-size="17" text-anchor="middle">70</text><circle class="hl" cx="110" cy="232" r="31"/><circle class="node" cx="110" cy="232" r="24"/><text x="110" y="238" font-size="17" text-anchor="middle">20</text><rect class="cell" x="600" y="48" width="280" height="262"/><text x="616" y="74" font-size="17" font-weight="700">call stack</text><rect class="cell frame" x="616" y="260" width="248" height="36"/><text x="630" y="284" font-size="17">t.size()</text><rect class="cell frame" x="616" y="216" width="248" height="36"/><text x="630" y="240" font-size="17">count(50)</text><rect class="cell frame" x="616" y="172" width="248" height="36"/><text x="630" y="196" font-size="17">count(30)</text><rect class="cell frame top" x="616" y="128" width="248" height="36"/><text x="630" y="152" font-size="17" font-weight="700">count(20)</text><text x="450" y="340" font-size="18" text-anchor="middle" font-weight="700">count(n->left.get())</text><text x="450" y="366" font-size="16" text-anchor="middle">count(30) counts its left subtree: a new call for 20</text></g> <g data-step="4"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 start</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 go down</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">3 return</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 result</tspan></text><rect class="cell" x="20" y="48" width="560" height="262" style="stroke-dasharray:3 6"/><text x="36" y="74" font-size="17" font-weight="700">t (BinaryTree part)</text><line class="edge" x1="279.3" y1="104.1" x2="210.2" y2="144.4"/><polygon class="head" points="200.7,149.9 207.5,139.6 213.0,149.1"/><line class="edge" x1="320.7" y1="104.1" x2="389.8" y2="144.4"/><polygon class="head" points="399.3,149.9 387.0,149.1 392.5,139.6"/><line class="edge" x1="163.0" y1="179.0" x2="134.7" y2="207.3"/><polygon class="head" points="127.0,215.0 130.9,203.4 138.6,211.1"/><circle class="node" cx="300" cy="92" r="24"/><text x="300" y="98" font-size="17" text-anchor="middle">50</text><circle class="node" cx="180" cy="162" r="24"/><text x="180" y="168" font-size="17" text-anchor="middle">30</text><circle class="node" cx="420" cy="162" r="24"/><text x="420" y="168" font-size="17" text-anchor="middle">70</text><circle class="hl" cx="110" cy="232" r="31"/><circle class="node done" cx="110" cy="232" r="24"/><text x="110" y="238" font-size="17" text-anchor="middle">20</text><text x="140" y="256" font-size="16" font-weight="700">= 1</text><text x="40" y="292" font-size="15">left, right: nullptr → 0</text><rect class="cell" x="600" y="48" width="280" height="262"/><text x="616" y="74" font-size="17" font-weight="700">call stack</text><rect class="cell frame" x="616" y="260" width="248" height="36"/><text x="630" y="284" font-size="17">t.size()</text><rect class="cell frame" x="616" y="216" width="248" height="36"/><text x="630" y="240" font-size="17">count(50)</text><rect class="cell frame" x="616" y="172" width="248" height="36"/><text x="630" y="196" font-size="17">count(30)</text><rect class="cell frame top" x="616" y="128" width="248" height="36"/><text x="630" y="152" font-size="17" font-weight="700">count(20)</text><text x="450" y="340" font-size="18" text-anchor="middle" font-weight="700">if (n == nullptr) return 0;</text><text x="450" y="366" font-size="16" text-anchor="middle">Both children of 20 are null: base case, 0 each, so count(20) is 1 + 0 + 0</text></g> <g data-step="5"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 start</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 go down</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">3 return</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 result</tspan></text><rect class="cell" x="20" y="48" width="560" height="262" style="stroke-dasharray:3 6"/><text x="36" y="74" font-size="17" font-weight="700">t (BinaryTree part)</text><line class="edge" x1="279.3" y1="104.1" x2="210.2" y2="144.4"/><polygon class="head" points="200.7,149.9 207.5,139.6 213.0,149.1"/><line class="edge" x1="320.7" y1="104.1" x2="389.8" y2="144.4"/><polygon class="head" points="399.3,149.9 387.0,149.1 392.5,139.6"/><line class="edge" x1="163.0" y1="179.0" x2="134.7" y2="207.3"/><polygon class="head" points="127.0,215.0 130.9,203.4 138.6,211.1"/><circle class="node" cx="300" cy="92" r="24"/><text x="300" y="98" font-size="17" text-anchor="middle">50</text><circle class="hl" cx="180" cy="162" r="31"/><circle class="node done" cx="180" cy="162" r="24"/><text x="180" y="168" font-size="17" text-anchor="middle">30</text><text x="210" y="186" font-size="16" font-weight="700">= 2</text><circle class="node" cx="420" cy="162" r="24"/><text x="420" y="168" font-size="17" text-anchor="middle">70</text><circle class="node done" cx="110" cy="232" r="24"/><text x="110" y="238" font-size="17" text-anchor="middle">20</text><text x="140" y="256" font-size="16" font-weight="700">= 1</text><text x="240" y="216" font-size="15">right: nullptr → 0</text><rect class="cell" x="600" y="48" width="280" height="262"/><text x="616" y="74" font-size="17" font-weight="700">call stack</text><rect class="cell frame" x="616" y="260" width="248" height="36"/><text x="630" y="284" font-size="17">t.size()</text><rect class="cell frame" x="616" y="216" width="248" height="36"/><text x="630" y="240" font-size="17">count(50)</text><rect class="cell frame top" x="616" y="172" width="248" height="36"/><text x="630" y="196" font-size="17" font-weight="700">count(30)</text><text x="450" y="340" font-size="18" text-anchor="middle" font-weight="700">return 1 + count(left) + count(right);</text><text x="450" y="366" font-size="16" text-anchor="middle">count(20) returned 1; the right of 30 is null (0); count(30) is 1 + 1 + 0 = 2</text></g> <g data-step="6"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 start</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 go down</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">3 return</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 result</tspan></text><rect class="cell" x="20" y="48" width="560" height="262" style="stroke-dasharray:3 6"/><text x="36" y="74" font-size="17" font-weight="700">t (BinaryTree part)</text><line class="edge" x1="279.3" y1="104.1" x2="210.2" y2="144.4"/><polygon class="head" points="200.7,149.9 207.5,139.6 213.0,149.1"/><line class="edge" x1="320.7" y1="104.1" x2="389.8" y2="144.4"/><polygon class="head" points="399.3,149.9 387.0,149.1 392.5,139.6"/><line class="edge" x1="163.0" y1="179.0" x2="134.7" y2="207.3"/><polygon class="head" points="127.0,215.0 130.9,203.4 138.6,211.1"/><circle class="node" cx="300" cy="92" r="24"/><text x="300" y="98" font-size="17" text-anchor="middle">50</text><circle class="node done" cx="180" cy="162" r="24"/><text x="180" y="168" font-size="17" text-anchor="middle">30</text><text x="210" y="186" font-size="16" font-weight="700">= 2</text><circle class="hl" cx="420" cy="162" r="31"/><circle class="node done" cx="420" cy="162" r="24"/><text x="420" y="168" font-size="17" text-anchor="middle">70</text><text x="450" y="186" font-size="16" font-weight="700">= 1</text><circle class="node done" cx="110" cy="232" r="24"/><text x="110" y="238" font-size="17" text-anchor="middle">20</text><text x="140" y="256" font-size="16" font-weight="700">= 1</text><text x="420" y="216" font-size="15" text-anchor="middle">left, right: nullptr → 0</text><rect class="cell" x="600" y="48" width="280" height="262"/><text x="616" y="74" font-size="17" font-weight="700">call stack</text><rect class="cell frame" x="616" y="260" width="248" height="36"/><text x="630" y="284" font-size="17">t.size()</text><rect class="cell frame" x="616" y="216" width="248" height="36"/><text x="630" y="240" font-size="17">count(50)</text><rect class="cell frame top" x="616" y="172" width="248" height="36"/><text x="630" y="196" font-size="17" font-weight="700">count(70)</text><text x="450" y="340" font-size="18" text-anchor="middle" font-weight="700">count(n->right.get())</text><text x="450" y="366" font-size="16" text-anchor="middle">Back in count(50): now the right subtree; 70 has no children, so 1</text></g> <g data-step="7"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 start</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 go down</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 return</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">4 result</tspan></text><rect class="cell" x="20" y="48" width="560" height="262" style="stroke-dasharray:3 6"/><text x="36" y="74" font-size="17" font-weight="700">t (BinaryTree part)</text><line class="edge" x1="279.3" y1="104.1" x2="210.2" y2="144.4"/><polygon class="head" points="200.7,149.9 207.5,139.6 213.0,149.1"/><line class="edge" x1="320.7" y1="104.1" x2="389.8" y2="144.4"/><polygon class="head" points="399.3,149.9 387.0,149.1 392.5,139.6"/><line class="edge" x1="163.0" y1="179.0" x2="134.7" y2="207.3"/><polygon class="head" points="127.0,215.0 130.9,203.4 138.6,211.1"/><circle class="hl" cx="300" cy="92" r="31"/><circle class="node done" cx="300" cy="92" r="24"/><text x="300" y="98" font-size="17" text-anchor="middle">50</text><text x="330" y="82" font-size="16" font-weight="700">= 4</text><circle class="node done" cx="180" cy="162" r="24"/><text x="180" y="168" font-size="17" text-anchor="middle">30</text><text x="210" y="186" font-size="16" font-weight="700">= 2</text><circle class="node done" cx="420" cy="162" r="24"/><text x="420" y="168" font-size="17" text-anchor="middle">70</text><text x="450" y="186" font-size="16" font-weight="700">= 1</text><circle class="node done" cx="110" cy="232" r="24"/><text x="110" y="238" font-size="17" text-anchor="middle">20</text><text x="140" y="256" font-size="16" font-weight="700">= 1</text><rect class="cell" x="600" y="48" width="280" height="262"/><text x="616" y="74" font-size="17" font-weight="700">call stack</text><rect class="cell frame" x="616" y="260" width="248" height="36"/><text x="630" y="284" font-size="17">t.size()</text><rect class="cell frame top" x="616" y="216" width="248" height="36"/><text x="630" y="240" font-size="17" font-weight="700">count(50)</text><text x="450" y="340" font-size="18" text-anchor="middle" font-weight="700">return 1 + 2 + 1;</text><text x="450" y="366" font-size="16" text-anchor="middle">count(50) adds itself to both subtree counts: 1 + 2 + 1 = 4</text></g> <g data-step="8"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 start</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 go down</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 return</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">4 result</tspan></text><rect class="cell" x="20" y="48" width="560" height="262" style="stroke-dasharray:3 6"/><text x="36" y="74" font-size="17" font-weight="700">t (BinaryTree part)</text><line class="edge" x1="279.3" y1="104.1" x2="210.2" y2="144.4"/><polygon class="head" points="200.7,149.9 207.5,139.6 213.0,149.1"/><line class="edge" x1="320.7" y1="104.1" x2="389.8" y2="144.4"/><polygon class="head" points="399.3,149.9 387.0,149.1 392.5,139.6"/><line class="edge" x1="163.0" y1="179.0" x2="134.7" y2="207.3"/><polygon class="head" points="127.0,215.0 130.9,203.4 138.6,211.1"/><circle class="node done" cx="300" cy="92" r="24"/><text x="300" y="98" font-size="17" text-anchor="middle">50</text><text x="330" y="82" font-size="16" font-weight="700">= 4</text><circle class="node done" cx="180" cy="162" r="24"/><text x="180" y="168" font-size="17" text-anchor="middle">30</text><text x="210" y="186" font-size="16" font-weight="700">= 2</text><circle class="node done" cx="420" cy="162" r="24"/><text x="420" y="168" font-size="17" text-anchor="middle">70</text><text x="450" y="186" font-size="16" font-weight="700">= 1</text><circle class="node done" cx="110" cy="232" r="24"/><text x="110" y="238" font-size="17" text-anchor="middle">20</text><text x="140" y="256" font-size="16" font-weight="700">= 1</text><rect class="cell" x="600" y="48" width="280" height="262"/><text x="616" y="74" font-size="17" font-weight="700">call stack</text><rect class="cell frame top" x="616" y="260" width="248" height="36"/><text x="630" y="284" font-size="17" font-weight="700">t.size()</text><text x="450" y="340" font-size="18" text-anchor="middle" font-weight="700">std::cout << t.size(); // 4</text><text x="450" y="366" font-size="16" text-anchor="middle">size() returns 4; every call has returned and the stack is empty again</text></g> </svg> </figure>

## Order of construction · Base first, derived last ~~~cpp // Tag(n) prints "construct n"; ~Tag() prints "destroy n" (Lecture 18) class BinaryTree { public: BinaryTree() { std::cout << "BinaryTree()\n"; } ~BinaryTree() { std::cout << "~BinaryTree()\n"; } }; class SearchTree : public BinaryTree { public: SearchTree() : label("label") { std::cout << "SearchTree()\n"; } ~SearchTree() { std::cout << "~SearchTree()\n"; } private: Tag label; // data member of the derived class }; int main() { SearchTree t; std::cout << "end of main\n"; } // BinaryTree(), construct label, SearchTree(), end of main, // ~SearchTree(), destroy label, ~BinaryTree() ~~~

## Construction order step by step <figure class="course-stepper" data-course-stepper> <svg class="course-array-address-figure course-l19order-figure" viewBox="0 0 900 380" role="img" aria-label="A step-by-step trace of lecture-19-construction-order.cpp, in 8 frames. A SearchTree object t is drawn as an outer box with three layers: the BinaryTree part, the data member label of class Tag, and the SearchTree constructor body, next to an output panel. Frame 1: t is declared and nothing is built yet. Frame 2: the BinaryTree part is built first and the output shows BinaryTree(). Frame 3: the data member label is built second and the output adds construct label. Frame 4: the body of the SearchTree constructor runs third and the output adds SearchTree(). Frame 5: main prints end of main while t is alive. Frame 6: at the closing brace the SearchTree destructor body runs first and prints ~SearchTree(). Frame 7: the data member label is destroyed second and prints destroy label. Frame 8: the BinaryTree part is destroyed last and prints ~BinaryTree(); destruction is the exact reverse of construction, giving 7 output lines." xmlns="http://www.w3.org/2000/svg"> <style> .course-l19order-figure text{font-family:ui-monospace,Menlo,Consolas,monospace;fill:currentColor} .course-l19order-figure .cell{fill:none;stroke:currentColor;stroke-width:2} .course-l19order-figure .cell.obj{fill:rgba(142,232,216,.18)} .course-l19order-figure .cell.heap{fill:rgba(255,214,102,.22)} .course-l19order-figure .cell.dead{fill:rgba(255,120,120,.22);stroke-dasharray:6 5} .course-l19order-figure .cell.pend{stroke-dasharray:3 6} .course-l19order-figure .hl{fill:rgba(110,170,255,.35);stroke:none} .course-l19order-figure .arrow{fill:none;stroke:currentColor;stroke-width:2.5} .course-l19order-figure .head{fill:currentColor} </style> <g data-step="0"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 construct</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 run</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 destroy</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="78" font-size="18" font-weight="700">SearchTree t</text><rect class="cell pend" x="44" y="90" width="512" height="52"/><text x="60" y="122" font-size="18" opacity="0.5">BinaryTree part</text><rect class="cell pend" x="44" y="154" width="512" height="52"/><text x="60" y="186" font-size="18" opacity="0.5">data member label (Tag)</text><rect class="cell pend" x="44" y="218" width="512" height="52"/><text x="60" y="250" font-size="18" opacity="0.5">SearchTree body</text><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">SearchTree t;</text><text x="450" y="362" font-size="16" text-anchor="middle">Nothing is built yet; the base part is constructed first</text></g> <g data-step="1"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 construct</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 run</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 destroy</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="78" font-size="18" font-weight="700">SearchTree t</text><rect class="hl" x="39" y="85" width="522" height="62"/><rect class="cell obj" x="44" y="90" width="512" height="52"/><text x="60" y="122" font-size="18">BinaryTree part</text><text x="540" y="122" font-size="16" text-anchor="end">built 1st</text><rect class="cell pend" x="44" y="154" width="512" height="52"/><text x="60" y="186" font-size="18" opacity="0.5">data member label (Tag)</text><rect class="cell pend" x="44" y="218" width="512" height="52"/><text x="60" y="250" font-size="18" opacity="0.5">SearchTree body</text><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><text x="636" y="104" font-size="16">BinaryTree()</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">BinaryTree() // base class constructor</text><text x="450" y="362" font-size="16" text-anchor="middle">The base part is built first and prints BinaryTree()</text></g> <g data-step="2"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 construct</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 run</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 destroy</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="78" font-size="18" font-weight="700">SearchTree t</text><rect class="cell obj" x="44" y="90" width="512" height="52"/><text x="60" y="122" font-size="18">BinaryTree part</text><text x="540" y="122" font-size="16" text-anchor="end">built 1st</text><rect class="hl" x="39" y="149" width="522" height="62"/><rect class="cell obj" x="44" y="154" width="512" height="52"/><text x="60" y="186" font-size="18">data member label (Tag)</text><text x="540" y="186" font-size="16" text-anchor="end">built 2nd</text><rect class="cell pend" x="44" y="218" width="512" height="52"/><text x="60" y="250" font-size="18" opacity="0.5">SearchTree body</text><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><text x="636" y="104" font-size="16">BinaryTree()</text><text x="636" y="126" font-size="16">construct label</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">: label("label") // member initializer</text><text x="450" y="362" font-size="16" text-anchor="middle">Next the data member label is constructed and prints construct label</text></g> <g data-step="3"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 construct</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 run</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 destroy</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="78" font-size="18" font-weight="700">SearchTree t</text><rect class="cell obj" x="44" y="90" width="512" height="52"/><text x="60" y="122" font-size="18">BinaryTree part</text><text x="540" y="122" font-size="16" text-anchor="end">built 1st</text><rect class="cell obj" x="44" y="154" width="512" height="52"/><text x="60" y="186" font-size="18">data member label (Tag)</text><text x="540" y="186" font-size="16" text-anchor="end">built 2nd</text><rect class="hl" x="39" y="213" width="522" height="62"/><rect class="cell obj" x="44" y="218" width="512" height="52"/><text x="60" y="250" font-size="18">SearchTree body</text><text x="540" y="250" font-size="16" text-anchor="end">built 3rd</text><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><text x="636" y="104" font-size="16">BinaryTree()</text><text x="636" y="126" font-size="16">construct label</text><text x="636" y="148" font-size="16">SearchTree()</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">SearchTree() { ... } // body</text><text x="450" y="362" font-size="16" text-anchor="middle">Last the body of the derived constructor runs and prints SearchTree()</text></g> <g data-step="4"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 construct</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">2 run</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 destroy</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="78" font-size="18" font-weight="700">SearchTree t</text><rect class="cell obj" x="44" y="90" width="512" height="52"/><text x="60" y="122" font-size="18">BinaryTree part</text><rect class="cell obj" x="44" y="154" width="512" height="52"/><text x="60" y="186" font-size="18">data member label (Tag)</text><rect class="cell obj" x="44" y="218" width="512" height="52"/><text x="60" y="250" font-size="18">SearchTree body</text><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><text x="636" y="104" font-size="16">BinaryTree()</text><text x="636" y="126" font-size="16">construct label</text><text x="636" y="148" font-size="16">SearchTree()</text><text x="636" y="170" font-size="16">end of main</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">std::cout << "end of main\n";</text><text x="450" y="362" font-size="16" text-anchor="middle">The object is complete and alive; the program prints end of main</text></g> <g data-step="5"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 construct</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 run</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">3 destroy</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="78" font-size="18" font-weight="700">SearchTree t</text><rect class="cell obj" x="44" y="90" width="512" height="52"/><text x="60" y="122" font-size="18">BinaryTree part</text><rect class="cell obj" x="44" y="154" width="512" height="52"/><text x="60" y="186" font-size="18">data member label (Tag)</text><rect class="hl" x="39" y="213" width="522" height="62"/><rect class="cell dead" x="44" y="218" width="512" height="52"/><text x="60" y="250" font-size="18">SearchTree body</text><text x="540" y="250" font-size="16" text-anchor="end">destroyed 1st</text><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><text x="636" y="104" font-size="16">BinaryTree()</text><text x="636" y="126" font-size="16">construct label</text><text x="636" y="148" font-size="16">SearchTree()</text><text x="636" y="170" font-size="16">end of main</text><text x="636" y="192" font-size="16">~SearchTree()</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">~SearchTree() { ... } // body</text><text x="450" y="362" font-size="16" text-anchor="middle">The closing brace of main: the derived destructor body runs first</text></g> <g data-step="6"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 construct</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 run</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">3 destroy</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="78" font-size="18" font-weight="700">SearchTree t</text><rect class="cell obj" x="44" y="90" width="512" height="52"/><text x="60" y="122" font-size="18">BinaryTree part</text><rect class="hl" x="39" y="149" width="522" height="62"/><rect class="cell dead" x="44" y="154" width="512" height="52"/><text x="60" y="186" font-size="18">data member label (Tag)</text><text x="540" y="186" font-size="16" text-anchor="end">destroyed 2nd</text><rect class="cell dead" x="44" y="218" width="512" height="52"/><text x="60" y="250" font-size="18">SearchTree body</text><text x="540" y="250" font-size="16" text-anchor="end">destroyed 1st</text><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><text x="636" y="104" font-size="16">BinaryTree()</text><text x="636" y="126" font-size="16">construct label</text><text x="636" y="148" font-size="16">SearchTree()</text><text x="636" y="170" font-size="16">end of main</text><text x="636" y="192" font-size="16">~SearchTree()</text><text x="636" y="214" font-size="16">destroy label</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">label is destroyed</text><text x="450" y="362" font-size="16" text-anchor="middle">The data member label is destroyed next and prints destroy label</text></g> <g data-step="7"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 construct</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 run</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">3 destroy</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="78" font-size="18" font-weight="700">SearchTree t</text><rect class="hl" x="39" y="85" width="522" height="62"/><rect class="cell dead" x="44" y="90" width="512" height="52"/><text x="60" y="122" font-size="18">BinaryTree part</text><text x="540" y="122" font-size="16" text-anchor="end">destroyed 3rd</text><rect class="cell dead" x="44" y="154" width="512" height="52"/><text x="60" y="186" font-size="18">data member label (Tag)</text><text x="540" y="186" font-size="16" text-anchor="end">destroyed 2nd</text><rect class="cell dead" x="44" y="218" width="512" height="52"/><text x="60" y="250" font-size="18">SearchTree body</text><text x="540" y="250" font-size="16" text-anchor="end">destroyed 1st</text><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><text x="636" y="104" font-size="16">BinaryTree()</text><text x="636" y="126" font-size="16">construct label</text><text x="636" y="148" font-size="16">SearchTree()</text><text x="636" y="170" font-size="16">end of main</text><text x="636" y="192" font-size="16">~SearchTree()</text><text x="636" y="214" font-size="16">destroy label</text><text x="636" y="236" font-size="16">~BinaryTree()</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">~BinaryTree() // base destructor</text><text x="450" y="362" font-size="16" text-anchor="middle">Last the base part is destroyed: the reverse of construction order</text></g> </svg> </figure>

## Poll 1: What does main print? <div class="course-poll-layout"> <div> ~~~cpp class A { public: A() { std::cout << "A"; } ~A() { std::cout << "a"; } }; class B : public A { public: B() { std::cout << "B"; } ~B() { std::cout << "b"; } }; int main() { B x; } ~~~ **A)** `ABba` · **B)** `BAab`<br>**C)** `ABab` · **D)** `BAba` </div> <figure class="course-slido-qr"><img src="assets/slido-lecture19.svg" alt="QR code that opens the Lecture 19 Slido event." width="360" height="360"><figcaption>📊 sli.do · #2413622</figcaption></figure> </div>

## Access in a derived class · protected and friend ~~~cpp class BinaryTree { public: int size() const; // public: everyone friend void printRoot(const BinaryTree& t); protected: std::unique_ptr<Node> root; // protected: derived classes private: int count(const Node* n) const; // private: BinaryTree only }; class SearchTree : public BinaryTree { public: void insert(int v); }; // in insert: root OK, count error · in main: t.size() OK, t.root error // printRoot(t) prints "root 50": a friend may use root ~~~ <div class="course-access-table"> | Access | In `BinaryTree` | Own members | Derived class | Friends | `main` | |---|---|---|---|---|---| | `public` | `size()` | yes | yes | yes | yes | | `protected` | `root` | yes | yes | yes | no | | `private` | `count()` | yes | no | yes | no | </div> <figure class="course-stepper" data-course-stepper> <svg class="course-array-address-figure course-l19agraph-figure" viewBox="0 0 900 380" role="img" aria-label="A step-by-step graph in 5 frames of which code may name which member of BinaryTree. On the left are four kinds of code: BinaryTree member functions, the friend function printRoot, SearchTree member functions, and main. On the right are the members public size(), protected root, and private count(). An arrow means access is allowed; a cross means a compile error. Frame 1: BinaryTree member functions have arrows to all three members. Frame 2: the friend printRoot also has arrows to all three. Frame 3: SearchTree member functions have arrows to size() and root, and a cross to the private count(). Frame 4: main has an arrow only to size(), and crosses to root and count(). Frame 5: all allowed arrows together: public size() is reached by 4 kinds of code, protected root by 3, private count() by 2." xmlns="http://www.w3.org/2000/svg"> <style> .course-l19agraph-figure text{font-family:ui-monospace,Menlo,Consolas,monospace;fill:currentColor} .course-l19agraph-figure .box{fill:rgba(142,232,216,.18);stroke:currentColor;stroke-width:2} .course-l19agraph-figure .box.focus{fill:rgba(110,170,255,.35)} .course-l19agraph-figure .box.off{fill:none;stroke-dasharray:4 5;opacity:.45} .course-l19agraph-figure .box.mem.public{fill:rgba(142,232,216,.30)} .course-l19agraph-figure .box.mem.protected{fill:rgba(255,214,102,.28)} .course-l19agraph-figure .box.mem.private{fill:rgba(255,120,120,.22)} .course-l19agraph-figure .edge{stroke:currentColor;stroke-width:1.5;opacity:.35} .course-l19agraph-figure .edge.bold{stroke-width:2.5;opacity:1} .course-l19agraph-figure .edge.blocked{stroke-dasharray:6 6;opacity:.8} .course-l19agraph-figure .head{fill:currentColor;opacity:.35} .course-l19agraph-figure .head.bold{opacity:1} </style> <g data-step="0"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 the class</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 a friend</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 derived class</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 other code</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">5 all</tspan></text><text x="30" y="62" font-size="16" font-weight="700">code that names a member</text><text x="600" y="62" font-size="16" font-weight="700">members of BinaryTree</text><line class="edge bold" x1="300" y1="100.0" x2="588.0" y2="109.6"/><polygon class="head bold" points="600,110.0 587.8,115.6 588.2,103.6"/><line class="edge bold" x1="300" y1="100.0" x2="588.5" y2="188.5"/><polygon class="head bold" points="600,192.0 586.8,194.2 590.3,182.7"/><line class="edge bold" x1="300" y1="100.0" x2="589.6" y2="268.0"/><polygon class="head bold" points="600,274.0 586.6,273.2 592.6,262.8"/><rect class="box focus" x="30" y="76" width="270" height="48" rx="8"/><text x="44" y="97" font-size="17" font-weight="700">BinaryTree members</text><text x="44" y="116" font-size="15">size(), count()</text><rect class="box off" x="30" y="134" width="270" height="48" rx="8"/><text x="44" y="155" font-size="17" font-weight="700" opacity=".45">friend printRoot</text><text x="44" y="174" font-size="15" opacity=".45">declared in BinaryTree</text><rect class="box off" x="30" y="192" width="270" height="48" rx="8"/><text x="44" y="213" font-size="17" font-weight="700" opacity=".45">SearchTree members</text><text x="44" y="232" font-size="15" opacity=".45">insert()</text><rect class="box off" x="30" y="250" width="270" height="48" rx="8"/><text x="44" y="271" font-size="17" font-weight="700" opacity=".45">main</text><text x="44" y="290" font-size="15" opacity=".45">any other code</text><rect class="box mem public" x="600" y="86" width="270" height="48" rx="8"/><text x="614" y="116" font-size="17" font-weight="700">public: size()</text><rect class="box mem protected" x="600" y="168" width="270" height="48" rx="8"/><text x="614" y="198" font-size="17" font-weight="700">protected: root</text><rect class="box mem private" x="600" y="250" width="270" height="48" rx="8"/><text x="614" y="280" font-size="17" font-weight="700">private: count()</text><text x="450" y="340" font-size="18" text-anchor="middle" font-weight="700">class BinaryTree { ... }</text><text x="450" y="366" font-size="16" text-anchor="middle">Its own member functions may name every member, even private count()</text></g> <g data-step="1"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 the class</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">2 a friend</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 derived class</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 other code</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">5 all</tspan></text><text x="30" y="62" font-size="16" font-weight="700">code that names a member</text><text x="600" y="62" font-size="16" font-weight="700">members of BinaryTree</text><line class="edge" x1="300" y1="100.0" x2="588.0" y2="109.6"/><polygon class="head" points="600,110.0 587.8,115.6 588.2,103.6"/><line class="edge" x1="300" y1="100.0" x2="588.5" y2="188.5"/><polygon class="head" points="600,192.0 586.8,194.2 590.3,182.7"/><line class="edge" x1="300" y1="100.0" x2="589.6" y2="268.0"/><polygon class="head" points="600,274.0 586.6,273.2 592.6,262.8"/><line class="edge bold" x1="300" y1="158.0" x2="588.2" y2="111.9"/><polygon class="head bold" points="600,110.0 589.1,117.8 587.2,106.0"/><line class="edge bold" x1="300" y1="158.0" x2="588.1" y2="190.6"/><polygon class="head bold" points="600,192.0 587.4,196.6 588.8,184.7"/><line class="edge bold" x1="300" y1="158.0" x2="588.8" y2="269.7"/><polygon class="head bold" points="600,274.0 586.6,275.3 591.0,264.1"/><rect class="box" x="30" y="76" width="270" height="48" rx="8"/><text x="44" y="97" font-size="17" font-weight="700">BinaryTree members</text><text x="44" y="116" font-size="15">size(), count()</text><rect class="box focus" x="30" y="134" width="270" height="48" rx="8"/><text x="44" y="155" font-size="17" font-weight="700">friend printRoot</text><text x="44" y="174" font-size="15">declared in BinaryTree</text><rect class="box off" x="30" y="192" width="270" height="48" rx="8"/><text x="44" y="213" font-size="17" font-weight="700" opacity=".45">SearchTree members</text><text x="44" y="232" font-size="15" opacity=".45">insert()</text><rect class="box off" x="30" y="250" width="270" height="48" rx="8"/><text x="44" y="271" font-size="17" font-weight="700" opacity=".45">main</text><text x="44" y="290" font-size="15" opacity=".45">any other code</text><rect class="box mem public" x="600" y="86" width="270" height="48" rx="8"/><text x="614" y="116" font-size="17" font-weight="700">public: size()</text><rect class="box mem protected" x="600" y="168" width="270" height="48" rx="8"/><text x="614" y="198" font-size="17" font-weight="700">protected: root</text><rect class="box mem private" x="600" y="250" width="270" height="48" rx="8"/><text x="614" y="280" font-size="17" font-weight="700">private: count()</text><text x="450" y="340" font-size="18" text-anchor="middle" font-weight="700">friend void printRoot(const BinaryTree&);</text><text x="450" y="366" font-size="16" text-anchor="middle">A friend has the same access as a member: all three</text></g> <g data-step="2"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 the class</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 a friend</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">3 derived class</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 other code</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">5 all</tspan></text><text x="30" y="62" font-size="16" font-weight="700">code that names a member</text><text x="600" y="62" font-size="16" font-weight="700">members of BinaryTree</text><line class="edge" x1="300" y1="100.0" x2="588.0" y2="109.6"/><polygon class="head" points="600,110.0 587.8,115.6 588.2,103.6"/><line class="edge" x1="300" y1="100.0" x2="588.5" y2="188.5"/><polygon class="head" points="600,192.0 586.8,194.2 590.3,182.7"/><line class="edge" x1="300" y1="100.0" x2="589.6" y2="268.0"/><polygon class="head" points="600,274.0 586.6,273.2 592.6,262.8"/><line class="edge" x1="300" y1="158.0" x2="588.2" y2="111.9"/><polygon class="head" points="600,110.0 589.1,117.8 587.2,106.0"/><line class="edge" x1="300" y1="158.0" x2="588.1" y2="190.6"/><polygon class="head" points="600,192.0 587.4,196.6 588.8,184.7"/><line class="edge" x1="300" y1="158.0" x2="588.8" y2="269.7"/><polygon class="head" points="600,274.0 586.6,275.3 591.0,264.1"/><line class="edge bold" x1="300" y1="216.0" x2="588.7" y2="114.0"/><polygon class="head bold" points="600,110.0 590.7,119.7 586.7,108.3"/><line class="edge bold" x1="300" y1="216.0" x2="588.0" y2="193.0"/><polygon class="head bold" points="600,192.0 588.5,198.9 587.6,187.0"/><line class="edge bold blocked" x1="300" y1="216.0" x2="588.2" y2="271.7"/><text x="486.0" y="258.0" font-size="20" font-weight="700" text-anchor="middle">✗</text><rect class="box" x="30" y="76" width="270" height="48" rx="8"/><text x="44" y="97" font-size="17" font-weight="700">BinaryTree members</text><text x="44" y="116" font-size="15">size(), count()</text><rect class="box" x="30" y="134" width="270" height="48" rx="8"/><text x="44" y="155" font-size="17" font-weight="700">friend printRoot</text><text x="44" y="174" font-size="15">declared in BinaryTree</text><rect class="box focus" x="30" y="192" width="270" height="48" rx="8"/><text x="44" y="213" font-size="17" font-weight="700">SearchTree members</text><text x="44" y="232" font-size="15">insert()</text><rect class="box off" x="30" y="250" width="270" height="48" rx="8"/><text x="44" y="271" font-size="17" font-weight="700" opacity=".45">main</text><text x="44" y="290" font-size="15" opacity=".45">any other code</text><rect class="box mem public" x="600" y="86" width="270" height="48" rx="8"/><text x="614" y="116" font-size="17" font-weight="700">public: size()</text><rect class="box mem protected" x="600" y="168" width="270" height="48" rx="8"/><text x="614" y="198" font-size="17" font-weight="700">protected: root</text><rect class="box mem private" x="600" y="250" width="270" height="48" rx="8"/><text x="614" y="280" font-size="17" font-weight="700">private: count()</text><text x="450" y="340" font-size="18" text-anchor="middle" font-weight="700">class SearchTree : public BinaryTree</text><text x="450" y="366" font-size="16" text-anchor="middle">A derived class gets public and protected, not private</text></g> <g data-step="3"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 the class</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 a friend</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 derived class</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">4 other code</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">5 all</tspan></text><text x="30" y="62" font-size="16" font-weight="700">code that names a member</text><text x="600" y="62" font-size="16" font-weight="700">members of BinaryTree</text><line class="edge" x1="300" y1="100.0" x2="588.0" y2="109.6"/><polygon class="head" points="600,110.0 587.8,115.6 588.2,103.6"/><line class="edge" x1="300" y1="100.0" x2="588.5" y2="188.5"/><polygon class="head" points="600,192.0 586.8,194.2 590.3,182.7"/><line class="edge" x1="300" y1="100.0" x2="589.6" y2="268.0"/><polygon class="head" points="600,274.0 586.6,273.2 592.6,262.8"/><line class="edge" x1="300" y1="158.0" x2="588.2" y2="111.9"/><polygon class="head" points="600,110.0 589.1,117.8 587.2,106.0"/><line class="edge" x1="300" y1="158.0" x2="588.1" y2="190.6"/><polygon class="head" points="600,192.0 587.4,196.6 588.8,184.7"/><line class="edge" x1="300" y1="158.0" x2="588.8" y2="269.7"/><polygon class="head" points="600,274.0 586.6,275.3 591.0,264.1"/><line class="edge" x1="300" y1="216.0" x2="588.7" y2="114.0"/><polygon class="head" points="600,110.0 590.7,119.7 586.7,108.3"/><line class="edge" x1="300" y1="216.0" x2="588.0" y2="193.0"/><polygon class="head" points="600,192.0 588.5,198.9 587.6,187.0"/><line class="edge bold" x1="300" y1="274.0" x2="589.5" y2="115.8"/><polygon class="head bold" points="600,110.0 592.3,121.0 586.6,110.5"/><line class="edge bold blocked" x1="300" y1="274.0" x2="588.4" y2="195.2"/><text x="486.0" y="229.2" font-size="20" font-weight="700" text-anchor="middle">✗</text><line class="edge bold blocked" x1="300" y1="274.0" x2="588.0" y2="274.0"/><text x="486.0" y="280.0" font-size="20" font-weight="700" text-anchor="middle">✗</text><rect class="box" x="30" y="76" width="270" height="48" rx="8"/><text x="44" y="97" font-size="17" font-weight="700">BinaryTree members</text><text x="44" y="116" font-size="15">size(), count()</text><rect class="box" x="30" y="134" width="270" height="48" rx="8"/><text x="44" y="155" font-size="17" font-weight="700">friend printRoot</text><text x="44" y="174" font-size="15">declared in BinaryTree</text><rect class="box" x="30" y="192" width="270" height="48" rx="8"/><text x="44" y="213" font-size="17" font-weight="700">SearchTree members</text><text x="44" y="232" font-size="15">insert()</text><rect class="box focus" x="30" y="250" width="270" height="48" rx="8"/><text x="44" y="271" font-size="17" font-weight="700">main</text><text x="44" y="290" font-size="15">any other code</text><rect class="box mem public" x="600" y="86" width="270" height="48" rx="8"/><text x="614" y="116" font-size="17" font-weight="700">public: size()</text><rect class="box mem protected" x="600" y="168" width="270" height="48" rx="8"/><text x="614" y="198" font-size="17" font-weight="700">protected: root</text><rect class="box mem private" x="600" y="250" width="270" height="48" rx="8"/><text x="614" y="280" font-size="17" font-weight="700">private: count()</text><text x="450" y="340" font-size="18" text-anchor="middle" font-weight="700">int main() { ... }</text><text x="450" y="366" font-size="16" text-anchor="middle">Other code gets only the public interface</text></g> <g data-step="4"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 the class</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 a friend</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 derived class</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 other code</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">5 all</tspan></text><text x="30" y="62" font-size="16" font-weight="700">code that names a member</text><text x="600" y="62" font-size="16" font-weight="700">members of BinaryTree</text><line class="edge bold" x1="300" y1="100.0" x2="588.0" y2="109.6"/><polygon class="head bold" points="600,110.0 587.8,115.6 588.2,103.6"/><line class="edge bold" x1="300" y1="100.0" x2="588.5" y2="188.5"/><polygon class="head bold" points="600,192.0 586.8,194.2 590.3,182.7"/><line class="edge bold" x1="300" y1="100.0" x2="589.6" y2="268.0"/><polygon class="head bold" points="600,274.0 586.6,273.2 592.6,262.8"/><line class="edge bold" x1="300" y1="158.0" x2="588.2" y2="111.9"/><polygon class="head bold" points="600,110.0 589.1,117.8 587.2,106.0"/><line class="edge bold" x1="300" y1="158.0" x2="588.1" y2="190.6"/><polygon class="head bold" points="600,192.0 587.4,196.6 588.8,184.7"/><line class="edge bold" x1="300" y1="158.0" x2="588.8" y2="269.7"/><polygon class="head bold" points="600,274.0 586.6,275.3 591.0,264.1"/><line class="edge bold" x1="300" y1="216.0" x2="588.7" y2="114.0"/><polygon class="head bold" points="600,110.0 590.7,119.7 586.7,108.3"/><line class="edge bold" x1="300" y1="216.0" x2="588.0" y2="193.0"/><polygon class="head bold" points="600,192.0 588.5,198.9 587.6,187.0"/><line class="edge bold" x1="300" y1="274.0" x2="589.5" y2="115.8"/><polygon class="head bold" points="600,110.0 592.3,121.0 586.6,110.5"/><rect class="box" x="30" y="76" width="270" height="48" rx="8"/><text x="44" y="97" font-size="17" font-weight="700">BinaryTree members</text><text x="44" y="116" font-size="15">size(), count()</text><rect class="box" x="30" y="134" width="270" height="48" rx="8"/><text x="44" y="155" font-size="17" font-weight="700">friend printRoot</text><text x="44" y="174" font-size="15">declared in BinaryTree</text><rect class="box" x="30" y="192" width="270" height="48" rx="8"/><text x="44" y="213" font-size="17" font-weight="700">SearchTree members</text><text x="44" y="232" font-size="15">insert()</text><rect class="box" x="30" y="250" width="270" height="48" rx="8"/><text x="44" y="271" font-size="17" font-weight="700">main</text><text x="44" y="290" font-size="15">any other code</text><rect class="box mem public" x="600" y="86" width="270" height="48" rx="8"/><text x="614" y="116" font-size="17" font-weight="700">public: size()</text><text x="856" y="116" font-size="16" text-anchor="end">4 of 4</text><rect class="box mem protected" x="600" y="168" width="270" height="48" rx="8"/><text x="614" y="198" font-size="17" font-weight="700">protected: root</text><text x="856" y="198" font-size="16" text-anchor="end">3 of 4</text><rect class="box mem private" x="600" y="250" width="270" height="48" rx="8"/><text x="614" y="280" font-size="17" font-weight="700">private: count()</text><text x="856" y="280" font-size="16" text-anchor="end">2 of 4</text><text x="450" y="340" font-size="18" text-anchor="middle" font-weight="700">who may name it: public ⊃ protected ⊃ private</text><text x="450" y="366" font-size="16" text-anchor="middle">Count the arrows: public 4, protected 3, private 2 kinds of code</text></g> </svg> </figure> <figure class="course-stepper" data-course-stepper> <svg class="course-array-address-figure course-l19access-figure" viewBox="0 0 900 300" role="img" aria-label="A compact step-by-step diagram of who may name what in class BinaryTree, in 5 frames. The class box has three rows: public with size() and the friend printRoot, protected with root, and private with count(). Frame 1: a SearchTree member function insert uses root, which is protected, and this is allowed. Frame 2: insert names count, which is private, and the compiler reports that count is a private member of BinaryTree. Frame 3: main calls t.size(), which is public, allowed, and the output shows 1. Frame 4: main names t.root, which is protected, and the compiler reports that root is a protected member of BinaryTree. Frame 5: the friend function printRoot uses t.root, allowed, and the output adds root 50." xmlns="http://www.w3.org/2000/svg"> <style> .course-l19access-figure text{font-family:ui-monospace,Menlo,Consolas,monospace;fill:currentColor} .course-l19access-figure .cell{fill:none;stroke:currentColor;stroke-width:2} .course-l19access-figure .cell.obj{fill:rgba(142,232,216,.18)} .course-l19access-figure .cell.heap{fill:rgba(255,214,102,.22)} .course-l19access-figure .cell.dead{fill:rgba(255,120,120,.22);stroke-dasharray:6 5} .course-l19access-figure .cell.pend{stroke-dasharray:3 6} .course-l19access-figure .hl{fill:rgba(110,170,255,.35);stroke:none} .course-l19access-figure .arrow{fill:none;stroke:currentColor;stroke-width:2.5} .course-l19access-figure .head{fill:currentColor} </style> <g data-step="0"><text x="20" y="22" font-size="18"><tspan font-weight="700">1 derived class</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 outside code</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 friend</tspan></text><rect class="cell" x="20" y="36" width="400" height="200"/><text x="36" y="58" font-size="18" font-weight="700">class BinaryTree</text><rect class="cell obj" x="36" y="70" width="368" height="46"/><text x="48" y="99" font-size="16">public: size(), friend printRoot</text><rect class="hl" x="31" y="119" width="378" height="56"/><rect class="cell obj" x="36" y="124" width="368" height="46"/><text x="48" y="153" font-size="16">protected: root</text><rect class="cell obj" x="36" y="178" width="368" height="46"/><text x="48" y="207" font-size="16">private: count()</text><rect class="cell" x="470" y="121" width="190" height="52"/><text x="485" y="144" font-size="16" font-weight="700">SearchTree</text><text x="485" y="163" font-size="16">insert()</text><line class="arrow" x1="470.0" y1="147.0" x2="417.0" y2="147.0"/><polygon class="head" points="406.0,147.0 417.0,142.0 417.0,152.0"/><text x="437" y="139" font-size="20" text-anchor="middle" font-weight="700">✓</text><rect class="cell" x="680" y="36" width="200" height="200"/><text x="696" y="64" font-size="18" font-weight="700">output</text><text x="450" y="256" font-size="18" text-anchor="middle" font-weight="700">if (!root) root = make_unique<Node>(...);</text><text x="450" y="282" font-size="16" text-anchor="middle">A derived member function may name the protected member root</text></g> <g data-step="1"><text x="20" y="22" font-size="18"><tspan font-weight="700">1 derived class</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 outside code</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 friend</tspan></text><rect class="cell" x="20" y="36" width="400" height="200"/><text x="36" y="58" font-size="18" font-weight="700">class BinaryTree</text><rect class="cell obj" x="36" y="70" width="368" height="46"/><text x="48" y="99" font-size="16">public: size(), friend printRoot</text><rect class="cell obj" x="36" y="124" width="368" height="46"/><text x="48" y="153" font-size="16">protected: root</text><rect class="hl" x="31" y="173" width="378" height="56"/><rect class="cell dead" x="36" y="178" width="368" height="46"/><text x="48" y="207" font-size="16">private: count()</text><rect class="cell" x="470" y="175" width="190" height="52"/><text x="485" y="198" font-size="16" font-weight="700">SearchTree</text><text x="485" y="217" font-size="16">insert()</text><line class="arrow" x1="470.0" y1="201.0" x2="417.0" y2="201.0" style="stroke-dasharray:6 5"/><polygon class="head" points="406.0,201.0 417.0,196.0 417.0,206.0"/><text x="437" y="193" font-size="20" text-anchor="middle" font-weight="700">✗</text><rect class="cell" x="680" y="36" width="200" height="200"/><text x="696" y="64" font-size="18" font-weight="700">output</text><text x="450" y="256" font-size="18" text-anchor="middle" font-weight="700">count(root.get()); // in insert()</text><text x="450" y="282" font-size="16" text-anchor="middle">'count' is a private member of 'BinaryTree'</text></g> <g data-step="2"><text x="20" y="22" font-size="18"><tspan opacity=".5">1 derived class</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">2 outside code</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 friend</tspan></text><rect class="cell" x="20" y="36" width="400" height="200"/><text x="36" y="58" font-size="18" font-weight="700">class BinaryTree</text><rect class="hl" x="31" y="65" width="378" height="56"/><rect class="cell obj" x="36" y="70" width="368" height="46"/><text x="48" y="99" font-size="16">public: size(), friend printRoot</text><rect class="cell obj" x="36" y="124" width="368" height="46"/><text x="48" y="153" font-size="16">protected: root</text><rect class="cell obj" x="36" y="178" width="368" height="46"/><text x="48" y="207" font-size="16">private: count()</text><rect class="cell" x="470" y="67" width="190" height="52"/><text x="485" y="90" font-size="16" font-weight="700">main</text><text x="485" y="109" font-size="16">t.size()</text><line class="arrow" x1="470.0" y1="93.0" x2="417.0" y2="93.0"/><polygon class="head" points="406.0,93.0 417.0,88.0 417.0,98.0"/><text x="437" y="85" font-size="20" text-anchor="middle" font-weight="700">✓</text><rect class="cell" x="680" y="36" width="200" height="200"/><text x="696" y="64" font-size="18" font-weight="700">output</text><text x="696" y="90" font-size="16">1</text><text x="450" y="256" font-size="18" text-anchor="middle" font-weight="700">std::cout << t.size() << '\n';</text><text x="450" y="282" font-size="16" text-anchor="middle">Public: any code may call size(), so main prints 1</text></g> <g data-step="3"><text x="20" y="22" font-size="18"><tspan opacity=".5">1 derived class</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">2 outside code</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 friend</tspan></text><rect class="cell" x="20" y="36" width="400" height="200"/><text x="36" y="58" font-size="18" font-weight="700">class BinaryTree</text><rect class="cell obj" x="36" y="70" width="368" height="46"/><text x="48" y="99" font-size="16">public: size(), friend printRoot</text><rect class="hl" x="31" y="119" width="378" height="56"/><rect class="cell dead" x="36" y="124" width="368" height="46"/><text x="48" y="153" font-size="16">protected: root</text><rect class="cell obj" x="36" y="178" width="368" height="46"/><text x="48" y="207" font-size="16">private: count()</text><rect class="cell" x="470" y="121" width="190" height="52"/><text x="485" y="144" font-size="16" font-weight="700">main</text><text x="485" y="163" font-size="16">t.root</text><line class="arrow" x1="470.0" y1="147.0" x2="417.0" y2="147.0" style="stroke-dasharray:6 5"/><polygon class="head" points="406.0,147.0 417.0,142.0 417.0,152.0"/><text x="437" y="139" font-size="20" text-anchor="middle" font-weight="700">✗</text><rect class="cell" x="680" y="36" width="200" height="200"/><text x="696" y="64" font-size="18" font-weight="700">output</text><text x="696" y="90" font-size="16">1</text><text x="450" y="256" font-size="18" text-anchor="middle" font-weight="700">t.root = nullptr; // in main</text><text x="450" y="282" font-size="16" text-anchor="middle">'root' is a protected member of 'BinaryTree'</text></g> <g data-step="4"><text x="20" y="22" font-size="18"><tspan opacity=".5">1 derived class</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 outside code</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">3 friend</tspan></text><rect class="cell" x="20" y="36" width="400" height="200"/><text x="36" y="58" font-size="18" font-weight="700">class BinaryTree</text><rect class="cell obj" x="36" y="70" width="368" height="46"/><text x="48" y="99" font-size="16">public: size(), friend printRoot</text><rect class="hl" x="31" y="119" width="378" height="56"/><rect class="cell obj" x="36" y="124" width="368" height="46"/><text x="48" y="153" font-size="16">protected: root</text><rect class="cell obj" x="36" y="178" width="368" height="46"/><text x="48" y="207" font-size="16">private: count()</text><rect class="cell" x="470" y="121" width="190" height="52"/><text x="485" y="144" font-size="16" font-weight="700">friend</text><text x="485" y="163" font-size="16">printRoot(t)</text><line class="arrow" x1="470.0" y1="147.0" x2="417.0" y2="147.0"/><polygon class="head" points="406.0,147.0 417.0,142.0 417.0,152.0"/><text x="437" y="139" font-size="20" text-anchor="middle" font-weight="700">✓</text><rect class="cell" x="680" y="36" width="200" height="200"/><text x="696" y="64" font-size="18" font-weight="700">output</text><text x="696" y="90" font-size="16">1</text><text x="696" y="112" font-size="16">root 50</text><text x="450" y="256" font-size="18" text-anchor="middle" font-weight="700">printRoot(t); // a friend</text><text x="450" y="282" font-size="16" text-anchor="middle">A friend declared in BinaryTree may name root, so it prints root 50</text></g> </svg> </figure>

## Barbara Liskov · The substitution property <div class="course-story-layout"> <div> - 1987: Barbara Liskov (MIT), "Data Abstraction and Hierarchy", OOPSLA '87. - Her substitution property: S is a subtype of T if every program written in terms of T behaves the same when an S object is substituted for a T object. - 2008 ACM A.M. Turing Award. **Lesson:** derive only if every program written for the base class still works. </div> <figure class="course-story-figure"> <img src="assets/lecture-stories/barbara-liskov-2010.jpg" alt="Barbara Liskov in 2010." width="476" height="667" loading="lazy"> <figcaption>Barbara Liskov, 2010. Photo: Kenneth C. Zirkel, Wikimedia Commons, <a href="https://creativecommons.org/licenses/by-sa/3.0/deed.en">CC BY-SA 3.0</a>.</figcaption> </figure> </div>

## When substitution fails · A base operation breaks the invariant ~~~cpp class BinaryTree { public: void addLeftmost(int v) { // any binary tree may grow a leftmost leaf std::unique_ptr<Node>* p = &root; while (*p) p = &(*p)->left; *p = std::make_unique<Node>(Node{v, nullptr, nullptr}); } // ... size(), protected root }; class SearchTree : public BinaryTree { /* invariant: smaller left, larger right */ }; void grow(BinaryTree& t) { t.addLeftmost(99); } int main() { SearchTree t; for (int v : {50, 30, 70}) t.insert(v); grow(t); // compiles: a SearchTree is a BinaryTree std::cout << "size " << t.size() << ", contains(99) " << t.contains(99) << '\n'; } // size 4, contains(99) 0 ~~~

## Substitution step by step <figure class="course-stepper" data-course-stepper> <svg class="course-array-address-figure course-l19subst-figure" viewBox="0 0 900 380" role="img" aria-label="A step-by-step trace in 7 frames of a SearchTree t built by insert 50, 30, 70 and then passed to grow, which takes a BinaryTree reference. Frame 1: t holds 50 at the root, 30 on the left and 70 on the right, so the invariant smaller left, larger right holds. Frame 2: grow takes a BinaryTree reference that refers to t, and the compiler accepts it. Frame 3: addLeftmost(99) walks left from 50 to 30 to an empty left slot. Frame 4: 99 is attached as the left child of 30, drawn dashed and red: 99 is larger than 30 but on the left, which breaks the invariant. Frame 5: contains(99) compares 99 with 50 and goes right to 70. Frame 6: 99 is larger than 70, the right of 70 is empty, contains returns false, and the output panel shows size 4, contains(99) 0. Frame 7: summary: there is no compile error but the SearchTree invariant is broken, and a derived class is safe only if every base operation keeps its invariant." xmlns="http://www.w3.org/2000/svg"> <style> .course-l19subst-figure text{font-family:ui-monospace,Menlo,Consolas,monospace;fill:currentColor} .course-l19subst-figure .cell{fill:none;stroke:currentColor;stroke-width:2} .course-l19subst-figure .cell.obj{fill:rgba(142,232,216,.18)} .course-l19subst-figure .cell.heap{fill:rgba(255,214,102,.22)} .course-l19subst-figure .cell.dead{fill:rgba(255,120,120,.22);stroke-dasharray:6 5} .course-l19subst-figure .hl{fill:rgba(110,170,255,.35);stroke:none} .course-l19subst-figure .edge{fill:none;stroke:currentColor;stroke-width:2.5} .course-l19subst-figure .arrow{fill:none;stroke:currentColor;stroke-width:2.5} .course-l19subst-figure .head{fill:currentColor} </style> <g data-step="0"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 valid tree</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 base operation</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 search fails</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="80" font-size="18" font-weight="700">t (SearchTree)</text><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><line class="edge" x1="231" y1="114" x2="159" y2="166"/><line class="edge" x1="269" y1="114" x2="341" y2="166"/><circle class="cell obj" cx="250" cy="100" r="24"/><text x="250" y="106" font-size="18" text-anchor="middle">50</text><circle class="cell obj" cx="140" cy="180" r="24"/><text x="140" y="186" font-size="18" text-anchor="middle">30</text><circle class="cell obj" cx="360" cy="180" r="24"/><text x="360" y="186" font-size="18" text-anchor="middle">70</text><text x="170" y="240" font-size="16">invariant holds:</text><text x="170" y="262" font-size="16">smaller left,</text><text x="170" y="284" font-size="16">larger right</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">SearchTree t; insert 50, 30, 70</text><text x="450" y="362" font-size="16" text-anchor="middle">Three calls to insert build a valid search tree</text></g> <g data-step="1"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 valid tree</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 base operation</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 search fails</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="80" font-size="18" font-weight="700">t (SearchTree)</text><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><line class="edge" x1="231" y1="114" x2="159" y2="166"/><line class="edge" x1="269" y1="114" x2="341" y2="166"/><circle class="cell obj" cx="250" cy="100" r="24"/><text x="250" y="106" font-size="18" text-anchor="middle">50</text><circle class="cell obj" cx="140" cy="180" r="24"/><text x="140" y="186" font-size="18" text-anchor="middle">30</text><circle class="cell obj" cx="360" cy="180" r="24"/><text x="360" y="186" font-size="18" text-anchor="middle">70</text><text x="170" y="240" font-size="16">grow(BinaryTree& t):</text><text x="170" y="262" font-size="16">t refers to our tree;</text><text x="170" y="284" font-size="16">compiler accepts it</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">grow(t);</text><text x="450" y="362" font-size="16" text-anchor="middle">A SearchTree is a BinaryTree, so the call compiles</text></g> <g data-step="2"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 valid tree</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">2 base operation</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 search fails</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="80" font-size="18" font-weight="700">t (SearchTree)</text><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><line class="edge" x1="231" y1="114" x2="159" y2="166"/><line class="edge" x1="269" y1="114" x2="341" y2="166"/><circle class="hl" cx="250" cy="100" r="32"/><circle class="cell obj" cx="250" cy="100" r="24"/><text x="250" y="106" font-size="18" text-anchor="middle">50</text><circle class="hl" cx="140" cy="180" r="32"/><circle class="cell obj" cx="140" cy="180" r="24"/><text x="140" y="186" font-size="18" text-anchor="middle">30</text><circle class="cell obj" cx="360" cy="180" r="24"/><text x="360" y="186" font-size="18" text-anchor="middle">70</text><rect class="hl" x="50" y="240" width="40" height="40"/><rect class="cell" x="56" y="246" width="28" height="28" style="stroke-dasharray:4 4"/><text x="170" y="240" font-size="16">addLeftmost(99): walk</text><text x="170" y="262" font-size="16">left 50, 30, then an</text><text x="170" y="284" font-size="16">empty left slot</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">t.addLeftmost(99);</text><text x="450" y="362" font-size="16" text-anchor="middle">The base class walks left: 50, then 30, then an empty slot</text></g> <g data-step="3"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 valid tree</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">2 base operation</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 search fails</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="80" font-size="18" font-weight="700">t (SearchTree)</text><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><line class="edge" x1="231" y1="114" x2="159" y2="166"/><line class="edge" x1="269" y1="114" x2="341" y2="166"/><line class="edge" x1="124" y1="198" x2="86" y2="242" style="stroke-dasharray:6 5"/><circle class="cell obj" cx="250" cy="100" r="24"/><text x="250" y="106" font-size="18" text-anchor="middle">50</text><circle class="cell obj" cx="140" cy="180" r="24"/><text x="140" y="186" font-size="18" text-anchor="middle">30</text><circle class="cell obj" cx="360" cy="180" r="24"/><text x="360" y="186" font-size="18" text-anchor="middle">70</text><circle class="cell dead" cx="70" cy="260" r="24"/><text x="70" y="266" font-size="18" text-anchor="middle">99</text><text x="170" y="240" font-size="16">99 attached left of 30</text><text x="170" y="262" font-size="16">99 > 30 but on the left</text><text x="170" y="284" font-size="16">invariant broken</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">*p = make_unique<Node>(...)</text><text x="450" y="362" font-size="16" text-anchor="middle">99 > 30 but it sits on the left of 30: the invariant is broken</text></g> <g data-step="4"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 valid tree</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 base operation</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">3 search fails</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="80" font-size="18" font-weight="700">t (SearchTree)</text><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><line class="edge" x1="231" y1="114" x2="159" y2="166"/><line class="edge" x1="269" y1="114" x2="341" y2="166"/><line class="edge" x1="124" y1="198" x2="86" y2="242" style="stroke-dasharray:6 5"/><circle class="hl" cx="250" cy="100" r="32"/><circle class="cell obj" cx="250" cy="100" r="24"/><text x="250" y="106" font-size="18" text-anchor="middle">50</text><circle class="cell obj" cx="140" cy="180" r="24"/><text x="140" y="186" font-size="18" text-anchor="middle">30</text><circle class="hl" cx="360" cy="180" r="32"/><circle class="cell obj" cx="360" cy="180" r="24"/><text x="360" y="186" font-size="18" text-anchor="middle">70</text><circle class="cell dead" cx="70" cy="260" r="24"/><text x="70" y="266" font-size="18" text-anchor="middle">99</text><text x="170" y="240" font-size="16">contains(99):</text><text x="170" y="262" font-size="16">99 > 50: go right</text><text x="170" y="284" font-size="16">to 70</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">t.contains(99);</text><text x="450" y="362" font-size="16" text-anchor="middle">The search follows the ordering rule: 99 is larger than 50, go right</text></g> <g data-step="5"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 valid tree</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 base operation</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">3 search fails</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="80" font-size="18" font-weight="700">t (SearchTree)</text><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><text x="636" y="104" font-size="16">size 4, contains(99) 0</text><line class="edge" x1="231" y1="114" x2="159" y2="166"/><line class="edge" x1="269" y1="114" x2="341" y2="166"/><line class="edge" x1="124" y1="198" x2="86" y2="242" style="stroke-dasharray:6 5"/><circle class="cell obj" cx="250" cy="100" r="24"/><text x="250" y="106" font-size="18" text-anchor="middle">50</text><circle class="cell obj" cx="140" cy="180" r="24"/><text x="140" y="186" font-size="18" text-anchor="middle">30</text><circle class="hl" cx="360" cy="180" r="32"/><circle class="cell obj" cx="360" cy="180" r="24"/><text x="360" y="186" font-size="18" text-anchor="middle">70</text><circle class="cell dead" cx="70" cy="260" r="24"/><text x="70" y="266" font-size="18" text-anchor="middle">99</text><rect class="hl" x="410" y="240" width="40" height="40"/><rect class="cell" x="416" y="246" width="28" height="28" style="stroke-dasharray:4 4"/><text x="170" y="240" font-size="16">99 > 70: go right</text><text x="170" y="262" font-size="16">right of 70 is empty</text><text x="170" y="284" font-size="16">returns false</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">contains(99) returns 0</text><text x="450" y="362" font-size="16" text-anchor="middle">99 is in the tree but the search never looks left of 30</text></g> <g data-step="6"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 valid tree</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 base operation</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">3 search fails</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="80" font-size="18" font-weight="700">t (SearchTree)</text><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><text x="636" y="104" font-size="16">size 4, contains(99) 0</text><line class="edge" x1="231" y1="114" x2="159" y2="166"/><line class="edge" x1="269" y1="114" x2="341" y2="166"/><line class="edge" x1="124" y1="198" x2="86" y2="242" style="stroke-dasharray:6 5"/><circle class="cell obj" cx="250" cy="100" r="24"/><text x="250" y="106" font-size="18" text-anchor="middle">50</text><circle class="cell obj" cx="140" cy="180" r="24"/><text x="140" y="186" font-size="18" text-anchor="middle">30</text><circle class="cell obj" cx="360" cy="180" r="24"/><text x="360" y="186" font-size="18" text-anchor="middle">70</text><circle class="cell dead" cx="70" cy="260" r="24"/><text x="70" y="266" font-size="18" text-anchor="middle">99</text><text x="170" y="240" font-size="16">no compile error;</text><text x="170" y="262" font-size="16">the invariant of</text><text x="170" y="284" font-size="16">SearchTree is broken</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">Safe only if every base operation keeps the invariant</text><text x="450" y="362" font-size="16" text-anchor="middle">The compiler cannot check the derived class invariant</text></g> </svg> </figure>

## Has-a uses a data member · Composition ~~~cpp class Library { // has-a: composition public: explicit Library(const std::string& n) : name(n) {} void addBook(int id) { ids.insert(id); } bool hasBook(int id) const { return ids.contains(id); } private: std::string name; SearchTree ids; // data members, not a base class }; class BadLibrary : public SearchTree {}; // is-a: wrong here ~~~ **Takeaways:** has-a → a data member. `lib.insert(42)` is a compile error; `bad.insert(42)` compiles.

## Composition step by step <figure class="course-stepper" data-course-stepper> <svg class="course-array-address-figure course-l19compose-figure" viewBox="0 0 900 380" role="img" aria-label="A step-by-step trace in 6 frames of a Library class that has a SearchTree data member. Frame 1: the Library object lib is a box holding the data member name with value Central and the data member ids, an empty SearchTree. Frame 2: lib.addBook(1205) and lib.addBook(1101) forward to ids.insert, so ids holds 1205 at the root and 1101 on its left. Frame 3: hasBook(1101) forwards to ids.contains and returns 1, hasBook(9999) returns 0, and the output panel shows 1 0. Frame 4: lib.insert(42) is blocked because insert is not in the public interface of Library; the compile error is no member named insert in Library. Frame 5: BadLibrary bad inherits publicly from SearchTree, so its whole SearchTree interface is public, bad.insert(42) compiles, and the output adds 1. Frame 6: summary: has-a is a data member, which is composition, and is-a is public inheritance." xmlns="http://www.w3.org/2000/svg"> <style> .course-l19compose-figure text{font-family:ui-monospace,Menlo,Consolas,monospace;fill:currentColor} .course-l19compose-figure .cell{fill:none;stroke:currentColor;stroke-width:2} .course-l19compose-figure .cell.obj{fill:rgba(142,232,216,.18)} .course-l19compose-figure .cell.heap{fill:rgba(255,214,102,.22)} .course-l19compose-figure .cell.dead{fill:rgba(255,120,120,.22);stroke-dasharray:6 5} .course-l19compose-figure .hl{fill:rgba(110,170,255,.35);stroke:none} .course-l19compose-figure .edge{fill:none;stroke:currentColor;stroke-width:2.5} .course-l19compose-figure .arrow{fill:none;stroke:currentColor;stroke-width:2.5} .course-l19compose-figure .head{fill:currentColor} </style> <g data-step="0"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 forwarding</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 interface</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 inheritance</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="80" font-size="18" font-weight="700">lib (Library)</text><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><rect class="cell obj" x="40" y="96" width="370" height="184"/><text x="56" y="124" font-size="16">name</text><text x="56" y="148" font-size="16" font-weight="700">"Central"</text><rect class="cell heap" x="196" y="104" width="204" height="168"/><text x="206" y="126" font-size="16">ids (SearchTree)</text><text x="298" y="205" font-size="16" text-anchor="middle">(empty)</text><text x="425" y="150" font-size="16">data members:</text><text x="425" y="172" font-size="16">name, ids</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">Library lib("Central");</text><text x="450" y="362" font-size="16" text-anchor="middle">A Library object contains a string and a SearchTree as data members</text></g> <g data-step="1"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 forwarding</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 interface</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 inheritance</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="80" font-size="18" font-weight="700">lib (Library)</text><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><rect class="cell obj" x="40" y="96" width="370" height="184"/><text x="56" y="124" font-size="16">name</text><text x="56" y="148" font-size="16" font-weight="700">"Central"</text><rect class="cell heap" x="196" y="104" width="204" height="168"/><text x="206" y="126" font-size="16">ids (SearchTree)</text><line class="edge" x1="313" y1="187" x2="279" y2="219"/><circle class="cell obj" cx="330" cy="170" r="24"/><text x="330" y="176" font-size="18" text-anchor="middle">1205</text><circle class="cell obj" cx="262" cy="236" r="24"/><text x="262" y="242" font-size="18" text-anchor="middle">1101</text><line class="arrow" x1="560" y1="170" x2="424" y2="170"/><polygon class="head" points="412,170 426,163 426,177"/><text x="425" y="200" font-size="16">addBook forwards</text><text x="425" y="222" font-size="16">to ids.insert</text><text x="425" y="150" font-size="16">addBook(1101)</text><text x="425" y="128" font-size="16">addBook(1205)</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">lib.addBook(1205); lib.addBook(1101);</text><text x="450" y="362" font-size="16" text-anchor="middle">Library member functions forward the work to the data member ids</text></g> <g data-step="2"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 forwarding</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 interface</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 inheritance</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="80" font-size="18" font-weight="700">lib (Library)</text><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><text x="636" y="104" font-size="16">1 0</text><rect class="cell obj" x="40" y="96" width="370" height="184"/><text x="56" y="124" font-size="16">name</text><text x="56" y="148" font-size="16" font-weight="700">"Central"</text><rect class="cell heap" x="196" y="104" width="204" height="168"/><text x="206" y="126" font-size="16">ids (SearchTree)</text><line class="edge" x1="313" y1="187" x2="279" y2="219"/><circle class="cell obj" cx="330" cy="170" r="24"/><text x="330" y="176" font-size="18" text-anchor="middle">1205</text><circle class="hl" cx="262" cy="236" r="32"/><circle class="cell obj" cx="262" cy="236" r="24"/><text x="262" y="242" font-size="18" text-anchor="middle">1101</text><line class="arrow" x1="560" y1="170" x2="424" y2="170"/><polygon class="head" points="412,170 426,163 426,177"/><text x="425" y="200" font-size="16">hasBook forwards</text><text x="425" y="222" font-size="16">to ids.contains</text><text x="425" y="244" font-size="16">1101 found: 1</text><text x="425" y="266" font-size="16">9999 absent: 0</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">hasBook(1101) hasBook(9999)</text><text x="450" y="362" font-size="16" text-anchor="middle">The search answers 1 for a stored id and 0 for a missing one</text></g> <g data-step="3"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 forwarding</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">2 interface</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 inheritance</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="80" font-size="18" font-weight="700">lib (Library)</text><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><text x="636" y="104" font-size="16">1 0</text><rect class="cell obj" x="40" y="96" width="370" height="184"/><text x="56" y="124" font-size="16">name</text><text x="56" y="148" font-size="16" font-weight="700">"Central"</text><rect class="cell heap" x="196" y="104" width="204" height="168"/><text x="206" y="126" font-size="16">ids (SearchTree)</text><line class="edge" x1="313" y1="187" x2="279" y2="219"/><circle class="cell obj" cx="330" cy="170" r="24"/><text x="330" y="176" font-size="18" text-anchor="middle">1205</text><circle class="cell obj" cx="262" cy="236" r="24"/><text x="262" y="242" font-size="18" text-anchor="middle">1101</text><line class="arrow" x1="560" y1="170" x2="440" y2="170" style="stroke-dasharray:6 5"/><text x="420" y="178" font-size="28" text-anchor="middle" font-weight="700" fill="currentColor">X</text><text x="425" y="100" font-size="16">lib.insert(42)</text><text x="425" y="216" font-size="16">blocked: not in</text><text x="425" y="238" font-size="16">the public</text><text x="425" y="260" font-size="16">interface</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">lib.insert(42); // compile error</text><text x="450" y="362" font-size="16" text-anchor="middle">error: no member named 'insert' in 'Library'</text></g> <g data-step="4"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 forwarding</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 interface</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">3 inheritance</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="80" font-size="18" font-weight="700">bad (BadLibrary)</text><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><text x="636" y="104" font-size="16">1 0</text><text x="636" y="126" font-size="16">1</text><rect class="cell obj" x="40" y="96" width="370" height="184"/><text x="56" y="124" font-size="16">SearchTree part</text><text x="56" y="170" font-size="16" font-weight="700">insert()</text><text x="56" y="194" font-size="16" font-weight="700">contains()</text><text x="56" y="218" font-size="16">all public</text><circle class="hl" cx="330" cy="190" r="32"/><circle class="cell obj" cx="330" cy="190" r="24"/><text x="330" y="196" font-size="18" text-anchor="middle">42</text><line class="arrow" x1="560" y1="170" x2="424" y2="170"/><polygon class="head" points="412,170 426,163 426,177"/><text x="425" y="84" font-size="16">bad.insert(42)</text><text x="425" y="104" font-size="16">compiles: all of</text><text x="425" y="124" font-size="16">SearchTree is</text><text x="425" y="144" font-size="16">public</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">BadLibrary bad; bad.insert(42);</text><text x="450" y="362" font-size="16" text-anchor="middle">Inheritance exposes the whole SearchTree interface; contains(42) gives 1</text></g> <g data-step="5"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 forwarding</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 interface</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">3 inheritance</tspan></text><rect class="cell" x="20" y="52" width="580" height="240" style="stroke-dasharray:3 6"/><text x="36" y="80" font-size="18" font-weight="700">summary</text><rect class="cell" x="620" y="52" width="260" height="240"/><text x="636" y="80" font-size="18" font-weight="700">output</text><text x="636" y="104" font-size="16">1 0</text><text x="636" y="126" font-size="16">1</text><text x="36" y="120" font-size="16" font-weight="700">has-a: a data member (composition)</text><text x="36" y="146" font-size="16">Library has a SearchTree; it exposes only</text><text x="36" y="168" font-size="16">addBook and hasBook</text><text x="36" y="214" font-size="16" font-weight="700">is-a: public inheritance</text><text x="36" y="240" font-size="16">only if every SearchTree operation makes</text><text x="36" y="262" font-size="16">sense on the derived class</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">has-a: data member. is-a: public inheritance.</text><text x="450" y="362" font-size="16" text-anchor="middle">Choose composition when the new class merely uses the old one</text></g> </svg> </figure>

## Common errors · Inheritance | Error | Example | Result | |---|---|---| | Forget `public` | `class SearchTree : BinaryTree` | private inheritance: `'size' is a private member of 'BinaryTree'` | | Name a private base member | `count(root.get());` in `SearchTree` | compile error | | Base operation the derived class cannot honor | `grow(t)` calls `addLeftmost` | broken invariant; no error message | | Inherit for has-a | `class BadLibrary : public SearchTree` | exposes every `SearchTree` operation | | Base without a default constructor | no `Base(args)` in the initializer list | compile error |

## Poll 2: Which lines compile? <div class="course-poll-layout"> <div> ~~~cpp class Base { private: int x = 1; protected: int y = 2; public: int z = 3; }; class Derived : public Base { public: int f() { return x; } // 1 int g() { return y; } // 2 }; int main() { Derived d; int a = d.y; // 3 int b = d.z; // 4 } ~~~ **A)** all four · **B)** 2 and 4 only<br>**C)** 1, 2, and 4 · **D)** 2, 3, and 4 </div> <figure class="course-slido-qr"><img src="assets/slido-lecture19.svg" alt="QR code that opens the Lecture 19 Slido event." width="360" height="360"><figcaption>📊 sli.do · #2413622</figcaption></figure> </div>

## Questions about inheritance | Question | Answer | |---|---| | Is the base class's private data in a derived object? | Yes, it is part of the object, but the derived class cannot name it. | | Is friendship inherited? | No. A friend of `BinaryTree` is not a friend of `SearchTree`. | | A derived function with the same name as a base function? | It hides the base one; through a `BinaryTree&` the base version runs. Lecture 20: virtual functions. | | Why not just copy the class? | One copy of the code and of the invariant to maintain. | | Can a derived class be a base class? | Yes; base and derived classes form a class hierarchy. |

## Summary: inheritance - **Public inheritance** is is-a: pass a `SearchTree` as a `BinaryTree&`. - The **base class** is constructed first and destroyed last. - `protected` serves derived classes; a **friend** is not inherited. - Inherit only if base operations keep the derived **invariant**; else use **composition**. **Reading:** Stroustrup, *PPP* (2nd ed.), “Graphics Class Design”, section “Base and derived classes”; Savitch, “Inheritance”.

## Lab practice: base and derived classes 1. Derive `SearchTree` from `BinaryTree`; print `size()` after each `insert`. 1. Add `Tag` data members to both classes; predict the construction and destruction order, then run. 1. Make `root` private; read the compiler's error, then restore `protected`. 1. Replace `BadLibrary` by composition; list which operations you hid. [IC151 lab setup and batch schedule](ic151.html)