<p class="course-title-kicker">CS103 · Lecture 17</p> # Classes and Constructors <p class="course-title-tagline">A class protects its invariant, and a constructor establishes it</p> <p class="course-title-instructor">Dr. Debasish Pattanayak · <a href="https://drdebmath.github.io">drdebmath.github.io</a></p>

## Where Lecture 16 ended · A rule every step must keep A recursive function is correct when every call keeps a rule, and its **pre-condition** is what the caller must guarantee (Lecture 16). A `struct` groups **data members**, and any code may change any of them (Lecture 13). **Today's question.** How can a type keep a rule about its own data true, whatever the rest of the program does?

## Binary search · Look at the middle, discard a half <figure class="course-stepper" data-course-stepper> <svg class="course-array-address-figure course-bsorted-figure" viewBox="0 0 900 340" role="img" aria-label="A step-by-step trace of std::binary_search for 40 on two vectors, first and second, in 7 frames. Frames 1 to 3, first vector 35, 40, 52, 58, 70: the whole range is searched; the middle value is 52 and 40 is less than 52, so 52, 58 and 70 are discarded and the left half 35, 40 is kept; the next middle is 40, which is found, so the result is true. Frames 4 to 6, second vector 35, 52, 58, 70, 40: the whole range is searched; the middle value is 58 and 40 is less than 58, so 58, 70 and the 40 at the end are discarded; in the left half 35, 52 the value 40 is never examined and the result is false. Frame 7: the rule is a pre-condition that the values are sorted; binary_search cannot check it, so the caller must keep it." xmlns="http://www.w3.org/2000/svg"> <style> .course-bsorted-figure text{font-family:ui-monospace,Menlo,Consolas,monospace;fill:currentColor} .course-bsorted-figure .cell{fill:none;stroke:currentColor;stroke-width:2} .course-bsorted-figure .cell.obj{fill:rgba(142,232,216,.18)} .course-bsorted-figure .cell.found{fill:rgba(110,220,130,.45)} .course-bsorted-figure .cell.heap{fill:rgba(255,214,102,.22)} .course-bsorted-figure .cell.dead{fill:rgba(255,120,120,.22);stroke-dasharray:6 5} .course-bsorted-figure .hl{fill:rgba(110,170,255,.35);stroke:none} .course-bsorted-figure .arrow{fill:none;stroke:currentColor;stroke-width:2.5} .course-bsorted-figure .head{fill:currentColor} </style> <g data-step="0"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 first example</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 second example</tspan></text><text x="20" y="64" font-size="18">target = 40</text><rect class="hl" x="220" y="100" width="460" height="66"/><text x="20" y="139" font-size="18" font-weight="700">first</text><rect class="cell obj" x="225" y="105" width="90" height="56"/><text x="270" y="143" font-size="22" text-anchor="middle">35</text><text x="270" y="97" font-size="15" text-anchor="middle" opacity=".7">0</text><rect class="cell obj" x="315" y="105" width="90" height="56"/><text x="360" y="143" font-size="22" text-anchor="middle">40</text><text x="360" y="97" font-size="15" text-anchor="middle" opacity=".7">1</text><rect class="cell obj" x="405" y="105" width="90" height="56"/><text x="450" y="143" font-size="22" text-anchor="middle">52</text><text x="450" y="97" font-size="15" text-anchor="middle" opacity=".7">2</text><rect class="cell obj" x="495" y="105" width="90" height="56"/><text x="540" y="143" font-size="22" text-anchor="middle">58</text><text x="540" y="97" font-size="15" text-anchor="middle" opacity=".7">3</text><rect class="cell obj" x="585" y="105" width="90" height="56"/><text x="630" y="143" font-size="22" text-anchor="middle">70</text><text x="630" y="97" font-size="15" text-anchor="middle" opacity=".7">4</text><text x="20" y="288" font-size="20" font-weight="700">binary_search(first.begin(), first.end(), 40)</text><text x="20" y="318" font-size="19">The whole range is searched for 40.</text></g> <g data-step="1"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 first example</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 second example</tspan></text><text x="20" y="64" font-size="18">target = 40</text><rect class="hl" x="220" y="100" width="190" height="66"/><text x="20" y="139" font-size="18" font-weight="700">first</text><rect class="cell obj" x="225" y="105" width="90" height="56"/><text x="270" y="143" font-size="22" text-anchor="middle">35</text><text x="270" y="97" font-size="15" text-anchor="middle" opacity=".7">0</text><rect class="cell obj" x="315" y="105" width="90" height="56"/><text x="360" y="143" font-size="22" text-anchor="middle">40</text><text x="360" y="97" font-size="15" text-anchor="middle" opacity=".7">1</text><rect class="cell dead" x="405" y="105" width="90" height="56"/><text x="450" y="143" font-size="22" text-anchor="middle">52</text><text x="450" y="97" font-size="15" text-anchor="middle" opacity=".7">2</text><rect class="cell dead" x="495" y="105" width="90" height="56"/><text x="540" y="143" font-size="22" text-anchor="middle">58</text><text x="540" y="97" font-size="15" text-anchor="middle" opacity=".7">3</text><rect class="cell dead" x="585" y="105" width="90" height="56"/><text x="630" y="143" font-size="22" text-anchor="middle">70</text><text x="630" y="97" font-size="15" text-anchor="middle" opacity=".7">4</text><line class="arrow" x1="450" y1="205" x2="450" y2="176"/><polygon class="head" points="450,166 443,180 457,180"/><text x="450" y="228" font-size="18" text-anchor="middle">mid</text><text x="20" y="288" font-size="20" font-weight="700">mid = 52, and 40 < 52: keep the left half</text><text x="20" y="318" font-size="19">40 < 52, so 40 cannot be to the right of 52.</text></g> <g data-step="2"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 first example</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 second example</tspan></text><text x="20" y="64" font-size="18">target = 40</text><rect class="hl" x="220" y="100" width="190" height="66"/><text x="20" y="139" font-size="18" font-weight="700">first</text><rect class="cell obj" x="225" y="105" width="90" height="56"/><text x="270" y="143" font-size="22" text-anchor="middle">35</text><text x="270" y="97" font-size="15" text-anchor="middle" opacity=".7">0</text><rect class="cell found" x="315" y="105" width="90" height="56"/><text x="360" y="143" font-size="22" text-anchor="middle">40</text><text x="360" y="97" font-size="15" text-anchor="middle" opacity=".7">1</text><rect class="cell dead" x="405" y="105" width="90" height="56"/><text x="450" y="143" font-size="22" text-anchor="middle">52</text><text x="450" y="97" font-size="15" text-anchor="middle" opacity=".7">2</text><rect class="cell dead" x="495" y="105" width="90" height="56"/><text x="540" y="143" font-size="22" text-anchor="middle">58</text><text x="540" y="97" font-size="15" text-anchor="middle" opacity=".7">3</text><rect class="cell dead" x="585" y="105" width="90" height="56"/><text x="630" y="143" font-size="22" text-anchor="middle">70</text><text x="630" y="97" font-size="15" text-anchor="middle" opacity=".7">4</text><line class="arrow" x1="360" y1="205" x2="360" y2="176"/><polygon class="head" points="360,166 353,180 367,180"/><text x="360" y="228" font-size="18" text-anchor="middle">found</text><text x="20" y="288" font-size="20" font-weight="700">found 40 → true</text><text x="20" y="318" font-size="19">Discarding the right half was safe here.</text></g> <g data-step="3"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 first example</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">2 second example</tspan></text><text x="20" y="64" font-size="18">target = 40</text><text x="460" y="64" font-size="18" font-weight="700">40 is last</text><rect class="hl" x="220" y="100" width="460" height="66"/><text x="20" y="139" font-size="18" font-weight="700">second</text><rect class="cell obj" x="225" y="105" width="90" height="56"/><text x="270" y="143" font-size="22" text-anchor="middle">35</text><text x="270" y="97" font-size="15" text-anchor="middle" opacity=".7">0</text><rect class="cell obj" x="315" y="105" width="90" height="56"/><text x="360" y="143" font-size="22" text-anchor="middle">52</text><text x="360" y="97" font-size="15" text-anchor="middle" opacity=".7">1</text><rect class="cell obj" x="405" y="105" width="90" height="56"/><text x="450" y="143" font-size="22" text-anchor="middle">58</text><text x="450" y="97" font-size="15" text-anchor="middle" opacity=".7">2</text><rect class="cell obj" x="495" y="105" width="90" height="56"/><text x="540" y="143" font-size="22" text-anchor="middle">70</text><text x="540" y="97" font-size="15" text-anchor="middle" opacity=".7">3</text><rect class="cell obj" x="585" y="105" width="90" height="56"/><text x="630" y="143" font-size="22" text-anchor="middle">40</text><text x="630" y="97" font-size="15" text-anchor="middle" opacity=".7">4</text><text x="20" y="288" font-size="20" font-weight="700">binary_search(second.begin(), second.end(), 40)</text><text x="20" y="318" font-size="19">The same call, but the values are not in order.</text></g> <g data-step="4"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 first example</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">2 second example</tspan></text><text x="20" y="64" font-size="18">target = 40</text><rect class="hl" x="220" y="100" width="190" height="66"/><text x="20" y="139" font-size="18" font-weight="700">second</text><rect class="cell obj" x="225" y="105" width="90" height="56"/><text x="270" y="143" font-size="22" text-anchor="middle">35</text><text x="270" y="97" font-size="15" text-anchor="middle" opacity=".7">0</text><rect class="cell obj" x="315" y="105" width="90" height="56"/><text x="360" y="143" font-size="22" text-anchor="middle">52</text><text x="360" y="97" font-size="15" text-anchor="middle" opacity=".7">1</text><rect class="cell dead" x="405" y="105" width="90" height="56"/><text x="450" y="143" font-size="22" text-anchor="middle">58</text><text x="450" y="97" font-size="15" text-anchor="middle" opacity=".7">2</text><rect class="cell dead" x="495" y="105" width="90" height="56"/><text x="540" y="143" font-size="22" text-anchor="middle">70</text><text x="540" y="97" font-size="15" text-anchor="middle" opacity=".7">3</text><rect class="cell dead" x="585" y="105" width="90" height="56"/><text x="630" y="143" font-size="22" text-anchor="middle">40</text><text x="630" y="97" font-size="15" text-anchor="middle" opacity=".7">4</text><line class="arrow" x1="450" y1="205" x2="450" y2="176"/><polygon class="head" points="450,166 443,180 457,180"/><text x="450" y="228" font-size="18" text-anchor="middle">mid</text><text x="630" y="228" font-size="18" text-anchor="middle" font-weight="700">discarded!</text><text x="20" y="288" font-size="20" font-weight="700">mid = 58, and 40 < 58: keep the left half</text><text x="20" y="318" font-size="19">But the 40 at the end is thrown away with 58 and 70.</text></g> <g data-step="5"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 first example</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">2 second example</tspan></text><text x="20" y="64" font-size="18">target = 40</text><rect class="hl" x="220" y="100" width="190" height="66"/><text x="20" y="139" font-size="18" font-weight="700">second</text><rect class="cell obj" x="225" y="105" width="90" height="56"/><text x="270" y="143" font-size="22" text-anchor="middle">35</text><text x="270" y="97" font-size="15" text-anchor="middle" opacity=".7">0</text><rect class="cell obj" x="315" y="105" width="90" height="56"/><text x="360" y="143" font-size="22" text-anchor="middle">52</text><text x="360" y="97" font-size="15" text-anchor="middle" opacity=".7">1</text><rect class="cell dead" x="405" y="105" width="90" height="56"/><text x="450" y="143" font-size="22" text-anchor="middle">58</text><text x="450" y="97" font-size="15" text-anchor="middle" opacity=".7">2</text><rect class="cell dead" x="495" y="105" width="90" height="56"/><text x="540" y="143" font-size="22" text-anchor="middle">70</text><text x="540" y="97" font-size="15" text-anchor="middle" opacity=".7">3</text><rect class="cell dead" x="585" y="105" width="90" height="56"/><text x="630" y="143" font-size="22" text-anchor="middle">40</text><text x="630" y="97" font-size="15" text-anchor="middle" opacity=".7">4</text><text x="630" y="228" font-size="18" text-anchor="middle" font-weight="700">discarded!</text><text x="270" y="228" font-size="18" text-anchor="middle">35 < 40</text><text x="360" y="228" font-size="18" text-anchor="middle">52 > 40</text><text x="20" y="288" font-size="20" font-weight="700">40 is never examined → false</text><text x="20" y="318" font-size="19">Nothing lies between 35 and 52, so the search stops.</text></g> <g data-step="6"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 first example</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">2 second example</tspan></text><text x="20" y="84" font-size="18" font-weight="700">first</text><rect class="cell obj" x="225" y="60" width="60" height="40"/><text x="255" y="87" font-size="18" text-anchor="middle">35</text><text x="255" y="52" font-size="15" text-anchor="middle" opacity=".7">0</text><rect class="cell obj" x="285" y="60" width="60" height="40"/><text x="315" y="87" font-size="18" text-anchor="middle">40</text><text x="315" y="52" font-size="15" text-anchor="middle" opacity=".7">1</text><rect class="cell obj" x="345" y="60" width="60" height="40"/><text x="375" y="87" font-size="18" text-anchor="middle">52</text><text x="375" y="52" font-size="15" text-anchor="middle" opacity=".7">2</text><rect class="cell obj" x="405" y="60" width="60" height="40"/><text x="435" y="87" font-size="18" text-anchor="middle">58</text><text x="435" y="52" font-size="15" text-anchor="middle" opacity=".7">3</text><rect class="cell obj" x="465" y="60" width="60" height="40"/><text x="495" y="87" font-size="18" text-anchor="middle">70</text><text x="495" y="52" font-size="15" text-anchor="middle" opacity=".7">4</text><text x="560" y="96" font-size="18">true</text><text x="20" y="174" font-size="18" font-weight="700">second</text><rect class="cell obj" x="225" y="150" width="60" height="40"/><text x="255" y="177" font-size="18" text-anchor="middle">35</text><text x="255" y="142" font-size="15" text-anchor="middle" opacity=".7">0</text><rect class="cell obj" x="285" y="150" width="60" height="40"/><text x="315" y="177" font-size="18" text-anchor="middle">52</text><text x="315" y="142" font-size="15" text-anchor="middle" opacity=".7">1</text><rect class="cell obj" x="345" y="150" width="60" height="40"/><text x="375" y="177" font-size="18" text-anchor="middle">58</text><text x="375" y="142" font-size="15" text-anchor="middle" opacity=".7">2</text><rect class="cell obj" x="405" y="150" width="60" height="40"/><text x="435" y="177" font-size="18" text-anchor="middle">70</text><text x="435" y="142" font-size="15" text-anchor="middle" opacity=".7">3</text><rect class="cell dead" x="465" y="150" width="60" height="40"/><text x="495" y="177" font-size="18" text-anchor="middle">40</text><text x="495" y="142" font-size="15" text-anchor="middle" opacity=".7">4</text><text x="545" y="195" font-size="18">false</text><text x="20" y="250" font-size="19" font-weight="700">pre-condition: the values are sorted.</text><text x="20" y="282" font-size="19">binary_search cannot check it;</text><text x="20" y="310" font-size="19">the caller must keep it.</text></g> </svg> </figure>

## Binary search in code · It assumes the values are sorted ~~~cpp std::vector<int> first{35, 40, 52, 58, 70}; std::vector<int> second{35, 52, 58, 70, 40}; bool a = std::binary_search(first.begin(), first.end(), 40); bool b = std::binary_search(second.begin(), second.end(), 40); std::cout << std::boolalpha << a << '\n' << b << '\n'; // true, then false ~~~ `std::binary_search` looks at the middle element and discards the half that cannot hold the target. That is correct only for sorted values: sortedness is a **pre-condition**, and the function does not check it.

## Poll 1: Which call can give a wrong answer? <div class="course-poll-layout"> <div> `std::binary_search(v.begin(), v.end(), 7)` with: - **A)** `{1, 3, 5, 7, 9}` - **B)** `{7, 7, 7, 7}` - **C)** `{9, 7, 5, 3, 1}` - **D)** `{2, 4, 6, 7}` </div> <figure class="course-slido-qr"><img src="assets/slido-lecture17.svg" alt="QR code that opens the Lecture 17 Slido event." width="360" height="360"><figcaption>📊 sli.do · #3128457</figcaption></figure> </div>

## A struct cannot protect its rule · Any code may change it ~~~cpp struct Scores { std::vector<int> values; // rule: ascending order }; bool contains(const Scores& s, int x) { return std::binary_search(s.values.begin(), s.values.end(), x); } int main() { Scores s{{35, 52, 58, 70}}; std::cout << std::boolalpha << contains(s, 58) << '\n'; // true s.values.push_back(40); // breaks the rule std::cout << contains(s, 40) << '\n'; // false } ~~~

## The struct example step by step <figure class="course-stepper" data-course-stepper> <svg class="course-array-address-figure course-structbreak-figure" viewBox="0 0 900 380" role="img" aria-label="A step-by-step trace of a struct Scores whose rule is that values stay in ascending order, in 7 frames. Frame 1: object s holds 35, 52, 58, 70 and is sorted. Frames 2 and 3: contains(s, 58) runs a binary search, checks the middle value 58, finds it, and prints true. Frame 4: main calls s.values.push_back(40) straight into the cells, because a struct has no wall; the values are now 35, 52, 58, 70, 40 and the rule is broken. Frames 5 to 7: contains(s, 40) compares the middle 58, which is greater than 40, goes left, compares 52, goes left, compares 35, stops between 35 and 52, and returns false although 40 is at the end and was never examined. The output is true then false: the struct could not protect its rule." xmlns="http://www.w3.org/2000/svg"> <style> .course-structbreak-figure text{font-family:ui-monospace,Menlo,Consolas,monospace;fill:currentColor} .course-structbreak-figure .cell{fill:none;stroke:currentColor;stroke-width:2} .course-structbreak-figure .cell.obj{fill:rgba(142,232,216,.18)} .course-structbreak-figure .cell.heap{fill:rgba(255,214,102,.22)} .course-structbreak-figure .cell.dead{fill:rgba(255,120,120,.22);stroke-dasharray:6 5} .course-structbreak-figure .hl{fill:rgba(110,170,255,.35);stroke:none} .course-structbreak-figure .arrow{fill:none;stroke:currentColor;stroke-width:2.5} .course-structbreak-figure .head{fill:currentColor} </style> <g data-step="0"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 create</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 contains(s, 58)</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 push_back</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 contains(s, 40)</tspan></text><rect class="cell" x="20" y="52" width="640" height="200" style="stroke-dasharray:3 6"/><text x="36" y="80" font-size="18" font-weight="700">s : Scores</text><text x="36" y="130" font-size="16">values</text><rect class="cell obj" x="130" y="100" width="80" height="48"/><text x="170" y="132" font-size="22" text-anchor="middle">35</text><rect class="cell obj" x="210" y="100" width="80" height="48"/><text x="250" y="132" font-size="22" text-anchor="middle">52</text><rect class="cell obj" x="290" y="100" width="80" height="48"/><text x="330" y="132" font-size="22" text-anchor="middle">58</text><rect class="cell obj" x="370" y="100" width="80" height="48"/><text x="410" y="132" font-size="22" text-anchor="middle">70</text><text x="36" y="190" font-size="16">rule: ascending order, sorted ✓</text><rect class="cell obj" x="700" y="70" width="170" height="50"/><text x="785" y="102" font-size="18" text-anchor="middle">main</text><text x="20" y="280" font-size="16">struct: every member is open to any code (no wall)</text><text x="20" y="308" font-size="18">printed: </text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">Scores s{{35, 52, 58, 70}};</text><text x="450" y="362" font-size="16" text-anchor="middle">s holds its values in ascending order, as the rule requires</text></g> <g data-step="1"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 create</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">2 contains(s, 58)</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 push_back</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 contains(s, 40)</tspan></text><rect class="cell" x="20" y="52" width="640" height="200" style="stroke-dasharray:3 6"/><text x="36" y="80" font-size="18" font-weight="700">s : Scores</text><text x="36" y="130" font-size="16">values</text><rect class="hl" x="285" y="95" width="90" height="58"/><rect class="cell obj" x="130" y="100" width="80" height="48"/><text x="170" y="132" font-size="22" text-anchor="middle">35</text><rect class="cell obj" x="210" y="100" width="80" height="48"/><text x="250" y="132" font-size="22" text-anchor="middle">52</text><rect class="cell obj" x="290" y="100" width="80" height="48"/><text x="330" y="132" font-size="22" text-anchor="middle">58</text><rect class="cell obj" x="370" y="100" width="80" height="48"/><text x="410" y="132" font-size="22" text-anchor="middle">70</text><text x="36" y="190" font-size="16">rule: ascending order, sorted ✓</text><text x="36" y="226" font-size="16">binary search checks the middle value: 58</text><rect class="cell obj" x="700" y="70" width="170" height="50"/><text x="785" y="102" font-size="18" text-anchor="middle">main</text><path class="arrow" d="M700 124 H462"/><polygon class="head" points="450,124 464,117 464,131"/><text x="785" y="150" font-size="16" text-anchor="middle">contains(s, 58)</text><text x="20" y="280" font-size="16">struct: every member is open to any code (no wall)</text><text x="20" y="308" font-size="18">printed: </text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">contains(s, 58)</text><text x="450" y="362" font-size="16" text-anchor="middle">binary_search looks at the middle value first</text></g> <g data-step="2"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 create</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">2 contains(s, 58)</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 push_back</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 contains(s, 40)</tspan></text><rect class="cell" x="20" y="52" width="640" height="200" style="stroke-dasharray:3 6"/><text x="36" y="80" font-size="18" font-weight="700">s : Scores</text><text x="36" y="130" font-size="16">values</text><rect class="hl" x="285" y="95" width="90" height="58"/><rect class="cell obj" x="130" y="100" width="80" height="48"/><text x="170" y="132" font-size="22" text-anchor="middle">35</text><rect class="cell obj" x="210" y="100" width="80" height="48"/><text x="250" y="132" font-size="22" text-anchor="middle">52</text><rect class="cell heap" x="290" y="100" width="80" height="48"/><text x="330" y="132" font-size="22" text-anchor="middle">58</text><rect class="cell obj" x="370" y="100" width="80" height="48"/><text x="410" y="132" font-size="22" text-anchor="middle">70</text><text x="36" y="190" font-size="16">rule: ascending order, sorted ✓</text><text x="36" y="226" font-size="16">found 58 in the middle, so contains returns true</text><rect class="cell obj" x="700" y="70" width="170" height="50"/><text x="785" y="102" font-size="18" text-anchor="middle">main</text><path class="arrow" d="M700 124 H462"/><polygon class="head" points="450,124 464,117 464,131"/><text x="785" y="150" font-size="16" text-anchor="middle">contains(s, 58)</text><text x="20" y="280" font-size="16">struct: every member is open to any code (no wall)</text><text x="20" y="308" font-size="18">printed: true</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">std::cout << contains(s, 58);</text><text x="450" y="362" font-size="16" text-anchor="middle">Output: true, correct while the values are sorted</text></g> <g data-step="3"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 create</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 contains(s, 58)</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">3 push_back</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 contains(s, 40)</tspan></text><rect class="cell" x="20" y="52" width="640" height="200" style="stroke-dasharray:3 6"/><text x="36" y="80" font-size="18" font-weight="700">s : Scores</text><text x="36" y="130" font-size="16">values</text><rect class="hl" x="445" y="95" width="90" height="58"/><rect class="cell obj" x="130" y="100" width="80" height="48"/><text x="170" y="132" font-size="22" text-anchor="middle">35</text><rect class="cell obj" x="210" y="100" width="80" height="48"/><text x="250" y="132" font-size="22" text-anchor="middle">52</text><rect class="cell obj" x="290" y="100" width="80" height="48"/><text x="330" y="132" font-size="22" text-anchor="middle">58</text><rect class="cell obj" x="370" y="100" width="80" height="48"/><text x="410" y="132" font-size="22" text-anchor="middle">70</text><rect class="cell heap" x="450" y="100" width="80" height="48"/><text x="490" y="132" font-size="22" text-anchor="middle">40</text><text x="36" y="190" font-size="16">rule: ascending order, not sorted ✗</text><rect class="cell obj" x="700" y="70" width="170" height="50"/><text x="785" y="102" font-size="18" text-anchor="middle">main</text><path class="arrow" d="M700 124 H554"/><polygon class="head" points="542,124 556,117 556,131"/><text x="785" y="150" font-size="16" text-anchor="middle">push_back(40)</text><text x="20" y="280" font-size="16">struct: every member is open to any code (no wall)</text><text x="20" y="308" font-size="18">printed: true</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">s.values.push_back(40);</text><text x="450" y="362" font-size="16" text-anchor="middle">main reaches straight into values: 40 lands at the end, out of order</text></g> <g data-step="4"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 create</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 contains(s, 58)</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 push_back</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">4 contains(s, 40)</tspan></text><rect class="cell" x="20" y="52" width="640" height="200" style="stroke-dasharray:3 6"/><text x="36" y="80" font-size="18" font-weight="700">s : Scores</text><text x="36" y="130" font-size="16">values</text><rect class="hl" x="285" y="95" width="90" height="58"/><rect class="cell obj" x="130" y="100" width="80" height="48"/><text x="170" y="132" font-size="22" text-anchor="middle">35</text><rect class="cell obj" x="210" y="100" width="80" height="48"/><text x="250" y="132" font-size="22" text-anchor="middle">52</text><g opacity=".35"><rect class="cell obj" x="290" y="100" width="80" height="48"/><text x="330" y="132" font-size="22" text-anchor="middle">58</text></g><g opacity=".35"><rect class="cell obj" x="370" y="100" width="80" height="48"/><text x="410" y="132" font-size="22" text-anchor="middle">70</text></g><g opacity=".35"><rect class="cell obj" x="450" y="100" width="80" height="48"/><text x="490" y="132" font-size="22" text-anchor="middle">40</text></g><text x="36" y="190" font-size="16">rule: ascending order, not sorted ✗</text><text x="36" y="226" font-size="16">middle is 58; 58 > 40, so search the left half [35 52]</text><rect class="cell obj" x="700" y="70" width="170" height="50"/><text x="785" y="102" font-size="18" text-anchor="middle">main</text><path class="arrow" d="M700 124 H554"/><polygon class="head" points="542,124 556,117 556,131"/><text x="785" y="150" font-size="16" text-anchor="middle">contains(s, 40)</text><text x="20" y="280" font-size="16">struct: every member is open to any code (no wall)</text><text x="20" y="308" font-size="18">printed: true</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">contains(s, 40)</text><text x="450" y="362" font-size="16" text-anchor="middle">The binary search compares 40 with the middle value, 58</text></g> <g data-step="5"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 create</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 contains(s, 58)</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 push_back</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">4 contains(s, 40)</tspan></text><rect class="cell" x="20" y="52" width="640" height="200" style="stroke-dasharray:3 6"/><text x="36" y="80" font-size="18" font-weight="700">s : Scores</text><text x="36" y="130" font-size="16">values</text><rect class="hl" x="205" y="95" width="90" height="58"/><rect class="cell obj" x="130" y="100" width="80" height="48"/><text x="170" y="132" font-size="22" text-anchor="middle">35</text><g opacity=".35"><rect class="cell obj" x="210" y="100" width="80" height="48"/><text x="250" y="132" font-size="22" text-anchor="middle">52</text></g><g opacity=".35"><rect class="cell obj" x="290" y="100" width="80" height="48"/><text x="330" y="132" font-size="22" text-anchor="middle">58</text></g><g opacity=".35"><rect class="cell obj" x="370" y="100" width="80" height="48"/><text x="410" y="132" font-size="22" text-anchor="middle">70</text></g><g opacity=".35"><rect class="cell obj" x="450" y="100" width="80" height="48"/><text x="490" y="132" font-size="22" text-anchor="middle">40</text></g><text x="36" y="190" font-size="16">rule: ascending order, not sorted ✗</text><text x="36" y="226" font-size="16">middle of [35 52] is 52; 52 > 40, so search left [35]</text><rect class="cell obj" x="700" y="70" width="170" height="50"/><text x="785" y="102" font-size="18" text-anchor="middle">main</text><path class="arrow" d="M700 124 H554"/><polygon class="head" points="542,124 556,117 556,131"/><text x="785" y="150" font-size="16" text-anchor="middle">contains(s, 40)</text><text x="20" y="280" font-size="16">struct: every member is open to any code (no wall)</text><text x="20" y="308" font-size="18">printed: true</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">contains(s, 40)</text><text x="450" y="362" font-size="16" text-anchor="middle">Next it compares 40 with 52 and goes left again</text></g> <g data-step="6"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 create</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 contains(s, 58)</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 push_back</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">4 contains(s, 40)</tspan></text><rect class="cell" x="20" y="52" width="640" height="200" style="stroke-dasharray:3 6"/><text x="36" y="80" font-size="18" font-weight="700">s : Scores</text><text x="36" y="130" font-size="16">values</text><rect class="hl" x="125" y="95" width="90" height="58"/><rect class="cell obj" x="130" y="100" width="80" height="48"/><text x="170" y="132" font-size="22" text-anchor="middle">35</text><rect class="cell obj" x="210" y="100" width="80" height="48"/><text x="250" y="132" font-size="22" text-anchor="middle">52</text><rect class="cell obj" x="290" y="100" width="80" height="48"/><text x="330" y="132" font-size="22" text-anchor="middle">58</text><rect class="cell obj" x="370" y="100" width="80" height="48"/><text x="410" y="132" font-size="22" text-anchor="middle">70</text><rect class="cell dead" x="450" y="100" width="80" height="48"/><text x="490" y="132" font-size="22" text-anchor="middle">40</text><text x="36" y="190" font-size="16">rule: ascending order, not sorted ✗</text><text x="36" y="226" font-size="16">35 < 40: stop between 35 and 52; 52 ≠ 40, so false</text><text x="490" y="172" font-size="16" text-anchor="middle">never examined</text><rect class="cell obj" x="700" y="70" width="170" height="50"/><text x="785" y="102" font-size="18" text-anchor="middle">main</text><path class="arrow" d="M700 124 H554"/><polygon class="head" points="542,124 556,117 556,131"/><text x="785" y="150" font-size="16" text-anchor="middle">contains(s, 40)</text><text x="20" y="280" font-size="16">struct: every member is open to any code (no wall)</text><text x="20" y="308" font-size="18">printed: true false</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">std::cout << contains(s, 40);</text><text x="450" y="362" font-size="16" text-anchor="middle">Output: false — the struct could not protect its rule</text></g> </svg> </figure>

## A class keeps its rule · Private data, public operations ~~~cpp class SortedScores { public: SortedScores(const std::vector<int>& v) : values(v) { std::sort(values.begin(), values.end()); } void add(int x) { values.insert(std::lower_bound(values.begin(), values.end(), x), x); } bool contains(int x) const { return std::binary_search(values.begin(), values.end(), x); } void print() const { for (int v : values) std::cout << v << ' '; std::cout << '\n'; } private: std::vector<int> values; // invariant: sorted, established by the constructor }; // s({70, 35, 58, 52}); s.print(); s.add(40); s.print(); → 35 52 58 70, then 35 40 52 58 70 ~~~

## The class example step by step <figure class="course-stepper" data-course-stepper> <svg class="course-array-address-figure course-classkeep-figure" viewBox="0 0 900 380" role="img" aria-label="A step-by-step trace of class SortedScores, whose private data member values must stay in ascending order, in 7 frames. The object s has a thick wall with four public doors: constructor, add, contains, and print. main sits outside and reaches values only through the doors. Frame 1: the constructor is called with 70, 35, 58, 52 and the member initializer list values(v) copies them. Frame 2: the constructor body sorts them to 35, 52, 58, 70 and the invariant is established. Frame 3: print goes through its door and outputs 35 52 58 70. Frame 4: s.add(40) enters through the add door and lower_bound finds the first value not less than 40, which is 52 at index 1. Frame 5: insert shifts 52, 58, 70 right, giving 35, 40, 52, 58, 70 and the invariant is kept. Frame 6: s.contains(40) goes through the contains door, a const member function, and returns true. Frame 7: main cannot reach values directly, so only member functions touch values and every one can keep the invariant." xmlns="http://www.w3.org/2000/svg"> <style> .course-classkeep-figure text{font-family:ui-monospace,Menlo,Consolas,monospace;fill:currentColor} .course-classkeep-figure .cell{fill:none;stroke:currentColor;stroke-width:2} .course-classkeep-figure .cell.obj{fill:rgba(142,232,216,.18)} .course-classkeep-figure .cell.heap{fill:rgba(255,214,102,.22)} .course-classkeep-figure .cell.dead{fill:rgba(255,120,120,.22);stroke-dasharray:6 5} .course-classkeep-figure .hl{fill:rgba(110,170,255,.35);stroke:none} .course-classkeep-figure .arrow{fill:none;stroke:currentColor;stroke-width:2.5} .course-classkeep-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 print</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 add</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 contains</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">5 summary</tspan></text><rect class="cell" x="250" y="64" width="630" height="220" style="stroke-width:8"/><text x="284" y="88" font-size="18" font-weight="700">s : SortedScores</text><rect class="cell" x="420" y="100" width="450" height="170" style="stroke-dasharray:3 6"/><text x="436" y="124" font-size="16">private: values</text><rect class="cell obj" x="436" y="150" width="70" height="46"/><text x="471" y="182" font-size="22" text-anchor="middle">70</text><rect class="cell obj" x="506" y="150" width="70" height="46"/><text x="541" y="182" font-size="22" text-anchor="middle">35</text><rect class="cell obj" x="576" y="150" width="70" height="46"/><text x="611" y="182" font-size="22" text-anchor="middle">58</text><rect class="cell obj" x="646" y="150" width="70" height="46"/><text x="681" y="182" font-size="22" text-anchor="middle">52</text><rect class="cell heap" x="236" y="106" width="28" height="32"/><text x="284" y="128" font-size="16">constructor</text><rect class="cell obj" x="236" y="146" width="28" height="32"/><text x="284" y="168" font-size="16">add</text><rect class="cell obj" x="236" y="186" width="28" height="32"/><text x="284" y="208" font-size="16">contains</text><rect class="cell obj" x="236" y="226" width="28" height="32"/><text x="284" y="248" font-size="16">print</text><text x="436" y="232" font-size="16">invariant: not yet true</text><text x="436" y="256" font-size="16">member initializer list: values(v)</text><rect class="cell obj" x="10" y="146" width="84" height="48"/><text x="52" y="177" font-size="18" text-anchor="middle">main</text><path class="arrow" d="M94 170 H160 V122 H222"/><polygon class="head" points="236,122 222,115 222,129"/><text x="10" y="222" font-size="15">s({70,35,58,52})</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">SortedScores s({70, 35, 58, 52});</text><text x="450" y="362" font-size="16" text-anchor="middle">The initializer list values(v) copies the argument into the data member</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 print</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 add</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 contains</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">5 summary</tspan></text><rect class="cell" x="250" y="64" width="630" height="220" style="stroke-width:8"/><text x="284" y="88" font-size="18" font-weight="700">s : SortedScores</text><rect class="cell" x="420" y="100" width="450" height="170" style="stroke-dasharray:3 6"/><text x="436" y="124" font-size="16">private: values</text><rect class="cell obj" x="436" y="150" width="70" height="46"/><text x="471" y="182" font-size="22" text-anchor="middle">35</text><rect class="cell obj" x="506" y="150" width="70" height="46"/><text x="541" y="182" font-size="22" text-anchor="middle">52</text><rect class="cell obj" x="576" y="150" width="70" height="46"/><text x="611" y="182" font-size="22" text-anchor="middle">58</text><rect class="cell obj" x="646" y="150" width="70" height="46"/><text x="681" y="182" font-size="22" text-anchor="middle">70</text><rect class="cell heap" x="236" y="106" width="28" height="32"/><text x="284" y="128" font-size="16">constructor</text><rect class="cell obj" x="236" y="146" width="28" height="32"/><text x="284" y="168" font-size="16">add</text><rect class="cell obj" x="236" y="186" width="28" height="32"/><text x="284" y="208" font-size="16">contains</text><rect class="cell obj" x="236" y="226" width="28" height="32"/><text x="284" y="248" font-size="16">print</text><text x="436" y="232" font-size="16">invariant established ✓</text><text x="436" y="256" font-size="16">constructor body: std::sort(...)</text><rect class="cell obj" x="10" y="146" width="84" height="48"/><text x="52" y="177" font-size="18" text-anchor="middle">main</text><path class="arrow" d="M94 170 H160 V122 H222"/><polygon class="head" points="236,122 222,115 222,129"/><text x="10" y="222" font-size="15">s({70,35,58,52})</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">std::sort(values.begin(), values.end());</text><text x="450" y="362" font-size="16" text-anchor="middle">The constructor body sorts, so values is ascending before main uses s</text></g> <g data-step="2"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 construct</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">2 print</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 add</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 contains</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">5 summary</tspan></text><rect class="cell" x="250" y="64" width="630" height="220" style="stroke-width:8"/><text x="284" y="88" font-size="18" font-weight="700">s : SortedScores</text><rect class="cell" x="420" y="100" width="450" height="170" style="stroke-dasharray:3 6"/><text x="436" y="124" font-size="16">private: values</text><rect class="cell obj" x="436" y="150" width="70" height="46"/><text x="471" y="182" font-size="22" text-anchor="middle">35</text><rect class="cell obj" x="506" y="150" width="70" height="46"/><text x="541" y="182" font-size="22" text-anchor="middle">52</text><rect class="cell obj" x="576" y="150" width="70" height="46"/><text x="611" y="182" font-size="22" text-anchor="middle">58</text><rect class="cell obj" x="646" y="150" width="70" height="46"/><text x="681" y="182" font-size="22" text-anchor="middle">70</text><rect class="cell obj" x="236" y="106" width="28" height="32"/><text x="284" y="128" font-size="16">constructor</text><rect class="cell obj" x="236" y="146" width="28" height="32"/><text x="284" y="168" font-size="16">add</text><rect class="cell obj" x="236" y="186" width="28" height="32"/><text x="284" y="208" font-size="16">contains</text><rect class="cell heap" x="236" y="226" width="28" height="32"/><text x="284" y="248" font-size="16">print</text><text x="436" y="232" font-size="16">invariant: ascending ✓</text><text x="436" y="256" font-size="16">print walks values in order</text><rect class="cell obj" x="10" y="146" width="84" height="48"/><text x="52" y="177" font-size="18" text-anchor="middle">main</text><path class="arrow" d="M94 170 H160 V242 H222"/><polygon class="head" points="236,242 222,235 222,249"/><text x="10" y="222" font-size="15">s.print()</text><text x="20" y="306" font-size="18">printed: 35 52 58 70</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">s.print();</text><text x="450" y="362" font-size="16" text-anchor="middle">print goes through its door and only reads values</text></g> <g data-step="3"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 construct</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 print</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">3 add</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 contains</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">5 summary</tspan></text><rect class="cell" x="250" y="64" width="630" height="220" style="stroke-width:8"/><text x="284" y="88" font-size="18" font-weight="700">s : SortedScores</text><rect class="cell" x="420" y="100" width="450" height="170" style="stroke-dasharray:3 6"/><text x="436" y="124" font-size="16">private: values</text><rect class="hl" x="501" y="145" width="80" height="56"/><rect class="cell obj" x="436" y="150" width="70" height="46"/><text x="471" y="182" font-size="22" text-anchor="middle">35</text><rect class="cell obj" x="506" y="150" width="70" height="46"/><text x="541" y="182" font-size="22" text-anchor="middle">52</text><rect class="cell obj" x="576" y="150" width="70" height="46"/><text x="611" y="182" font-size="22" text-anchor="middle">58</text><rect class="cell obj" x="646" y="150" width="70" height="46"/><text x="681" y="182" font-size="22" text-anchor="middle">70</text><rect class="cell dead" x="503" y="142" width="6" height="62" style="stroke-width:1"/><rect class="cell obj" x="236" y="106" width="28" height="32"/><text x="284" y="128" font-size="16">constructor</text><rect class="cell heap" x="236" y="146" width="28" height="32"/><text x="284" y="168" font-size="16">add</text><rect class="cell obj" x="236" y="186" width="28" height="32"/><text x="284" y="208" font-size="16">contains</text><rect class="cell obj" x="236" y="226" width="28" height="32"/><text x="284" y="248" font-size="16">print</text><text x="436" y="232" font-size="16">invariant: ascending ✓</text><text x="436" y="256" font-size="16">lower_bound: first not less than 40 is 52</text><rect class="cell obj" x="10" y="146" width="84" height="48"/><text x="52" y="177" font-size="18" text-anchor="middle">main</text><path class="arrow" d="M94 170 H160 V162 H222"/><polygon class="head" points="236,162 222,155 222,169"/><text x="10" y="222" font-size="15">s.add(40)</text><text x="20" y="306" font-size="18">printed: 35 52 58 70</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">s.add(40);</text><text x="450" y="362" font-size="16" text-anchor="middle">add is called through its door; lower_bound finds position 1, before 52</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 opacity=".5">2 print</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">3 add</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 contains</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">5 summary</tspan></text><rect class="cell" x="250" y="64" width="630" height="220" style="stroke-width:8"/><text x="284" y="88" font-size="18" font-weight="700">s : SortedScores</text><rect class="cell" x="420" y="100" width="450" height="170" style="stroke-dasharray:3 6"/><text x="436" y="124" font-size="16">private: values</text><rect class="hl" x="501" y="145" width="80" height="56"/><rect class="cell obj" x="436" y="150" width="70" height="46"/><text x="471" y="182" font-size="22" text-anchor="middle">35</text><rect class="cell heap" x="506" y="150" width="70" height="46"/><text x="541" y="182" font-size="22" text-anchor="middle">40</text><rect class="cell obj" x="576" y="150" width="70" height="46"/><text x="611" y="182" font-size="22" text-anchor="middle">52</text><rect class="cell obj" x="646" y="150" width="70" height="46"/><text x="681" y="182" font-size="22" text-anchor="middle">58</text><rect class="cell obj" x="716" y="150" width="70" height="46"/><text x="751" y="182" font-size="22" text-anchor="middle">70</text><rect class="cell obj" x="236" y="106" width="28" height="32"/><text x="284" y="128" font-size="16">constructor</text><rect class="cell heap" x="236" y="146" width="28" height="32"/><text x="284" y="168" font-size="16">add</text><rect class="cell obj" x="236" y="186" width="28" height="32"/><text x="284" y="208" font-size="16">contains</text><rect class="cell obj" x="236" y="226" width="28" height="32"/><text x="284" y="248" font-size="16">print</text><text x="436" y="232" font-size="16">invariant kept ✓</text><text x="436" y="256" font-size="16">insert shifted 52 58 70 one place right</text><rect class="cell obj" x="10" y="146" width="84" height="48"/><text x="52" y="177" font-size="18" text-anchor="middle">main</text><path class="arrow" d="M94 170 H160 V162 H222"/><polygon class="head" points="236,162 222,155 222,169"/><text x="10" y="222" font-size="15">s.add(40)</text><text x="20" y="306" font-size="18">printed: 35 52 58 70</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">values.insert(position, 40);</text><text x="450" y="362" font-size="16" text-anchor="middle">insert makes room and puts 40 in place, so values stays ascending</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 print</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 add</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">4 contains</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">5 summary</tspan></text><rect class="cell" x="250" y="64" width="630" height="220" style="stroke-width:8"/><text x="284" y="88" font-size="18" font-weight="700">s : SortedScores</text><rect class="cell" x="420" y="100" width="450" height="170" style="stroke-dasharray:3 6"/><text x="436" y="124" font-size="16">private: values</text><rect class="hl" x="501" y="145" width="80" height="56"/><rect class="cell obj" x="436" y="150" width="70" height="46"/><text x="471" y="182" font-size="22" text-anchor="middle">35</text><rect class="cell obj" x="506" y="150" width="70" height="46"/><text x="541" y="182" font-size="22" text-anchor="middle">40</text><rect class="cell obj" x="576" y="150" width="70" height="46"/><text x="611" y="182" font-size="22" text-anchor="middle">52</text><rect class="cell obj" x="646" y="150" width="70" height="46"/><text x="681" y="182" font-size="22" text-anchor="middle">58</text><rect class="cell obj" x="716" y="150" width="70" height="46"/><text x="751" y="182" font-size="22" text-anchor="middle">70</text><rect class="cell obj" x="236" y="106" width="28" height="32"/><text x="284" y="128" font-size="16">constructor</text><rect class="cell obj" x="236" y="146" width="28" height="32"/><text x="284" y="168" font-size="16">add</text><rect class="cell heap" x="236" y="186" width="28" height="32"/><text x="284" y="208" font-size="16">contains</text><rect class="cell obj" x="236" y="226" width="28" height="32"/><text x="284" y="248" font-size="16">print</text><text x="436" y="232" font-size="16">invariant: ascending ✓</text><text x="436" y="256" font-size="16">const member function: reads, never changes</text><rect class="cell obj" x="10" y="146" width="84" height="48"/><text x="52" y="177" font-size="18" text-anchor="middle">main</text><path class="arrow" d="M94 170 H160 V202 H222"/><polygon class="head" points="236,202 222,195 222,209"/><text x="10" y="222" font-size="15">s.contains(40)</text><text x="20" y="306" font-size="18">printed: 35 52 58 70 / 35 40 52 58 70 / true</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">std::cout << s.contains(40);</text><text x="450" y="362" font-size="16" text-anchor="middle">Output: true — contains uses binary_search on sorted values</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 print</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 add</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 contains</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">5 summary</tspan></text><rect class="cell" x="250" y="64" width="630" height="220" style="stroke-width:8"/><text x="284" y="88" font-size="18" font-weight="700">s : SortedScores</text><rect class="cell" x="420" y="100" width="450" height="170" style="stroke-dasharray:3 6"/><text x="436" y="124" font-size="16">private: values</text><rect class="cell obj" x="436" y="150" width="70" height="46"/><text x="471" y="182" font-size="22" text-anchor="middle">35</text><rect class="cell obj" x="506" y="150" width="70" height="46"/><text x="541" y="182" font-size="22" text-anchor="middle">40</text><rect class="cell obj" x="576" y="150" width="70" height="46"/><text x="611" y="182" font-size="22" text-anchor="middle">52</text><rect class="cell obj" x="646" y="150" width="70" height="46"/><text x="681" y="182" font-size="22" text-anchor="middle">58</text><rect class="cell obj" x="716" y="150" width="70" height="46"/><text x="751" y="182" font-size="22" text-anchor="middle">70</text><rect class="cell heap" x="236" y="106" width="28" height="32"/><text x="284" y="128" font-size="16">constructor</text><rect class="cell heap" x="236" y="146" width="28" height="32"/><text x="284" y="168" font-size="16">add</text><rect class="cell heap" x="236" y="186" width="28" height="32"/><text x="284" y="208" font-size="16">contains</text><rect class="cell heap" x="236" y="226" width="28" height="32"/><text x="284" y="248" font-size="16">print</text><text x="436" y="232" font-size="16">invariant: ascending ✓</text><rect class="cell obj" x="10" y="146" width="84" height="48"/><text x="52" y="177" font-size="18" text-anchor="middle">main</text><path class="arrow" d="M94 170 H206" style="stroke-dasharray:6 5"/><text x="216" y="176" font-size="22" text-anchor="middle">✗</text><text x="10" y="222" font-size="15">no direct access</text><text x="20" y="306" font-size="18">printed: 35 52 58 70 / 35 40 52 58 70 / true</text><text x="450" y="336" font-size="18" text-anchor="middle" font-weight="700">private: std::vector<int> values;</text><text x="450" y="362" font-size="16" text-anchor="middle">Only member functions touch values, so every one can keep the invariant</text></g> </svg> </figure>

## Class definition: the general form | Part | Meaning | | --- | --- | | `class Name { ... };` | A user-defined type; a semicolon ends it. | | `public:` | The **interface**: any code may use these members. | | `private:` | The **representation**: only member functions may use it. | | `Name(params) : m(v) { }` | A **constructor** with a **member initializer list**. | | `Type f() const;` | A member function that does not change the object. | | `Type Name::f() { }` | A member function defined outside the class. |

## Access control · The compiler rejects outside access ~~~cpp int main() { SortedScores s({70, 35, 58, 52}); s.values.push_back(40); // line 11 } ~~~ ~~~text private-error.cpp:11:7: error: 'values' is a private member of 'SortedScores' private-error.cpp:7:22: note: declared private here ~~~

## Access control step by step <figure class="course-stepper" data-course-stepper> <svg class="course-array-address-figure course-access-figure" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 360" role="img" aria-label="Step-by-step figure in 5 frames. An object s of class SortedScores is drawn as a box with a thick wall; inside, a private region holds values with cells 35, 52, 58, 70 and the note invariant: ascending order; public doors on the wall are add, print, and size. Frame 1: after construction from 70, 35, 58, 52 the vector is sorted. Frame 2: main tries s.values.push_back(40) and an arrow points at the private cells. Frame 3: the arrow stops at the wall with a red cross and the compiler prints error: 'values' is a private member of 'SortedScores', note declared private here; no program is produced. Frame 4: the fix s.add(40) goes through the public add door and the member function inserts 40 in order, giving 35, 40, 52, 58, 70. Frame 5: summary: private means only member functions may name values, public is the interface everyone may call; in a struct the default is public, in a class it is private."> <style> .course-access-figure text{font-family:ui-monospace,Menlo,Consolas,monospace;fill:currentColor} .course-access-figure .cell{fill:none;stroke:currentColor;stroke-width:2} .course-access-figure .cell.obj{fill:rgba(142,232,216,.18)} .course-access-figure .cell.heap{fill:rgba(255,214,102,.22)} .course-access-figure .cell.dead{fill:rgba(255,120,120,.22);stroke-dasharray:6 5} .course-access-figure .hl{fill:rgba(110,170,255,.35);stroke:none} .course-access-figure .arrow{fill:none;stroke:currentColor;stroke-width:2.5} .course-access-figure .head{fill:currentColor} .course-access-figure .wall{fill:rgba(142,232,216,.08);stroke:currentColor;stroke-width:6} .course-access-figure .door{fill:rgba(60,190,110,.5);stroke:currentColor;stroke-width:2} .course-access-figure .door.bad{fill:rgba(255,120,120,.4)} .course-access-figure .bad{stroke:#ff6b6b;stroke-width:4;fill:none} .course-access-figure .no{fill:#ff6b6b;stroke:none} .course-access-figure .no text,.course-access-figure text.no{fill:#ff6b6b} .course-access-figure .ok{fill:#3dbb6e} </style> <g class="course-access-frame" data-step="0"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 object</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 compile error</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 the fix</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 the rule</tspan></text><text x="12" y="56" font-size="15" font-weight="700">main:</text><text x="12" y="84" font-size="15">SortedScores s({70, 35, 58, 52});</text><rect class="wall" x="350" y="40" width="535" height="210"/><text x="372" y="64" font-size="16" font-weight="700">s : SortedScores</text><text x="366" y="84" font-size="15" opacity=".7">public</text><rect class="cell heap" x="530" y="72" width="345" height="168" stroke-dasharray="8 5"/><text x="770" y="92" font-size="15" opacity=".7">private</text><rect class="cell obj" x="545" y="145" width="56" height="40"/><text x="573" y="171" font-size="16" text-anchor="middle">35</text><rect class="cell obj" x="601" y="145" width="56" height="40"/><text x="629" y="171" font-size="16" text-anchor="middle">52</text><rect class="cell obj" x="657" y="145" width="56" height="40"/><text x="685" y="171" font-size="16" text-anchor="middle">58</text><rect class="cell obj" x="713" y="145" width="56" height="40"/><text x="741" y="171" font-size="16" text-anchor="middle">70</text><text x="545" y="203" font-size="15">values</text><text x="545" y="228" font-size="15">invariant: ascending order</text><rect class="door" x="343" y="93" width="14" height="24"/><text x="366" y="110" font-size="15">add(x)</text><rect class="door" x="343" y="133" width="14" height="24"/><text x="366" y="150" font-size="15">print()</text><rect class="door" x="343" y="173" width="14" height="24"/><text x="366" y="190" font-size="15">size()</text><text x="20" y="324" font-size="16" font-weight="700">SortedScores s({70, 35, 58, 52});</text><text x="20" y="346" font-size="15">The constructor sorts the vector; values is private, and the invariant is ascending order.</text></g> <g class="course-access-frame" data-step="1"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 object</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">2 compile error</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 the fix</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 the rule</tspan></text><text x="12" y="56" font-size="15" font-weight="700">main:</text><text x="12" y="84" font-size="15">SortedScores s({70, 35, 58, 52});</text><rect class="hl" x="6" y="151" width="219" height="26"/><text x="12" y="169" font-size="15">s.values.push_back(40);</text><rect class="wall" x="350" y="40" width="535" height="210"/><text x="372" y="64" font-size="16" font-weight="700">s : SortedScores</text><text x="366" y="84" font-size="15" opacity=".7">public</text><rect class="cell heap" x="530" y="72" width="345" height="168" stroke-dasharray="8 5"/><text x="770" y="92" font-size="15" opacity=".7">private</text><rect class="cell obj" x="545" y="145" width="56" height="40"/><text x="573" y="171" font-size="16" text-anchor="middle">35</text><rect class="cell obj" x="601" y="145" width="56" height="40"/><text x="629" y="171" font-size="16" text-anchor="middle">52</text><rect class="cell obj" x="657" y="145" width="56" height="40"/><text x="685" y="171" font-size="16" text-anchor="middle">58</text><rect class="cell obj" x="713" y="145" width="56" height="40"/><text x="741" y="171" font-size="16" text-anchor="middle">70</text><text x="545" y="203" font-size="15">values</text><text x="545" y="228" font-size="15">invariant: ascending order</text><rect class="door" x="343" y="93" width="14" height="24"/><text x="366" y="110" font-size="15">add(x)</text><rect class="door" x="343" y="133" width="14" height="24"/><text x="366" y="150" font-size="15">print()</text><rect class="door" x="343" y="173" width="14" height="24"/><text x="366" y="190" font-size="15">size()</text><path class="arrow" d="M228 165 L515 165"/><polygon class="head" points="530,165 516,158 516,172"/><text x="20" y="324" font-size="16" font-weight="700">s.values.push_back(40);</text><text x="20" y="346" font-size="15">main names the private data member values directly and tries to reach the cells.</text></g> <g class="course-access-frame" data-step="2"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 object</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">2 compile error</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 the fix</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 the rule</tspan></text><text x="12" y="56" font-size="15" font-weight="700">main:</text><text x="12" y="84" font-size="15">SortedScores s({70, 35, 58, 52});</text><rect class="hl" x="6" y="151" width="219" height="26"/><text x="12" y="169" font-size="15">s.values.push_back(40);</text><rect class="wall" x="350" y="40" width="535" height="210"/><text x="372" y="64" font-size="16" font-weight="700">s : SortedScores</text><text x="366" y="84" font-size="15" opacity=".7">public</text><rect class="cell heap" x="530" y="72" width="345" height="168" stroke-dasharray="8 5"/><text x="770" y="92" font-size="15" opacity=".7">private</text><rect class="cell obj" x="545" y="145" width="56" height="40"/><text x="573" y="171" font-size="16" text-anchor="middle">35</text><rect class="cell obj" x="601" y="145" width="56" height="40"/><text x="629" y="171" font-size="16" text-anchor="middle">52</text><rect class="cell obj" x="657" y="145" width="56" height="40"/><text x="685" y="171" font-size="16" text-anchor="middle">58</text><rect class="cell obj" x="713" y="145" width="56" height="40"/><text x="741" y="171" font-size="16" text-anchor="middle">70</text><text x="545" y="203" font-size="15">values</text><text x="545" y="228" font-size="15">invariant: ascending order</text><rect class="door" x="343" y="93" width="14" height="24"/><text x="366" y="110" font-size="15">add(x)</text><rect class="door" x="343" y="133" width="14" height="24"/><text x="366" y="150" font-size="15">print()</text><rect class="door" x="343" y="173" width="14" height="24"/><text x="366" y="190" font-size="15">size()</text><path class="arrow" d="M228 165 L296 165"/><rect class="no" x="343" y="141" width="14" height="48" opacity=".55"/><text x="306" y="175" font-size="34" font-weight="700" class="no">✗</text><text x="20" y="268" font-size="15" style="fill:#ff6b6b">private-error.cpp:11:7: error: 'values' is a private member of 'SortedScores'</text><text x="20" y="286" font-size="15" opacity=".8">private-error.cpp:7:22: note: declared private here</text><text x="20" y="324" font-size="16" font-weight="700">s.values.push_back(40);</text><text x="20" y="346" font-size="15">Access control is checked by the compiler: compile time, no program is produced.</text></g> <g class="course-access-frame" data-step="3"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 object</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 compile error</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">3 the fix</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 the rule</tspan></text><text x="12" y="56" font-size="15" font-weight="700">main:</text><text x="12" y="84" font-size="15">SortedScores s({70, 35, 58, 52});</text><rect class="hl" x="6" y="151" width="102" height="26"/><text x="12" y="169" font-size="15">s.add(40);</text><rect class="wall" x="350" y="40" width="535" height="210"/><text x="372" y="64" font-size="16" font-weight="700">s : SortedScores</text><text x="366" y="84" font-size="15" opacity=".7">public</text><rect class="cell heap" x="530" y="72" width="345" height="168" stroke-dasharray="8 5"/><text x="770" y="92" font-size="15" opacity=".7">private</text><rect class="cell obj" x="545" y="145" width="56" height="40"/><text x="573" y="171" font-size="16" text-anchor="middle">35</text><rect class="cell obj" x="601" y="145" width="56" height="40"/><text x="629" y="171" font-size="16" text-anchor="middle">40</text><rect class="cell obj" x="657" y="145" width="56" height="40"/><text x="685" y="171" font-size="16" text-anchor="middle">52</text><rect class="cell obj" x="713" y="145" width="56" height="40"/><text x="741" y="171" font-size="16" text-anchor="middle">58</text><rect class="cell obj" x="769" y="145" width="56" height="40"/><text x="797" y="171" font-size="16" text-anchor="middle">70</text><text x="545" y="203" font-size="15">values</text><text x="545" y="228" font-size="15">invariant: ascending order</text><rect class="door" x="343" y="93" width="14" height="24"/><text x="366" y="110" font-size="15">add(x)</text><rect class="door" x="343" y="133" width="14" height="24"/><text x="366" y="150" font-size="15">print()</text><rect class="door" x="343" y="173" width="14" height="24"/><text x="366" y="190" font-size="15">size()</text><rect class="hl" x="601" y="145" width="56" height="40"/><text x="629" y="171" font-size="16" font-weight="700" text-anchor="middle">40</text><path class="arrow" d="M110 165 L250 105 L330 105"/><polygon class="head" points="343,105 329,98 329,112"/><path class="arrow" d="M428 105 L629 105 L629 131"/><polygon class="head" points="629,143 622,129 636,129"/><text x="20" y="324" font-size="16" font-weight="700">s.add(40);</text><text x="20" y="346" font-size="15">The call goes through the public add door; add inserts 40 in order: 35 40 52 58 70.</text></g> <g class="course-access-frame" data-step="4"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 object</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 compile error</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 the fix</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">4 the rule</tspan></text><text x="12" y="56" font-size="15" font-weight="700">main:</text><text x="12" y="84" font-size="15">SortedScores s({70, 35, 58, 52});</text><rect class="wall" x="350" y="40" width="535" height="210"/><text x="372" y="64" font-size="16" font-weight="700">s : SortedScores</text><text x="366" y="84" font-size="15" opacity=".7">public</text><rect class="cell heap" x="530" y="72" width="345" height="168" stroke-dasharray="8 5"/><text x="770" y="92" font-size="15" opacity=".7">private</text><rect class="cell obj" x="545" y="145" width="56" height="40"/><text x="573" y="171" font-size="16" text-anchor="middle">35</text><rect class="cell obj" x="601" y="145" width="56" height="40"/><text x="629" y="171" font-size="16" text-anchor="middle">52</text><rect class="cell obj" x="657" y="145" width="56" height="40"/><text x="685" y="171" font-size="16" text-anchor="middle">58</text><rect class="cell obj" x="713" y="145" width="56" height="40"/><text x="741" y="171" font-size="16" text-anchor="middle">70</text><text x="545" y="203" font-size="15">values</text><text x="545" y="228" font-size="15">invariant: ascending order</text><rect class="door" x="343" y="93" width="14" height="24"/><text x="366" y="110" font-size="15">add(x)</text><rect class="door" x="343" y="133" width="14" height="24"/><text x="366" y="150" font-size="15">print()</text><rect class="door" x="343" y="173" width="14" height="24"/><text x="366" y="190" font-size="15">size()</text><text x="20" y="268" font-size="15">private: only member functions may name values.</text><text x="20" y="286" font-size="15">public: the interface everyone may call.</text><text x="20" y="324" font-size="16" font-weight="700">class: default private; struct: default public</text><text x="20" y="346" font-size="15">Choose the access so that outside code cannot break the invariant.</text></g> </svg> </figure>

## Constructors · Every object starts valid ~~~cpp class SortedScores { public: SortedScores() { std::cout << "default constructor\n"; } SortedScores(const std::vector<int>& v) : values(v) { std::sort(values.begin(), values.end()); std::cout << "vector constructor\n"; } SortedScores(int count, int score) : values(count, score) { std::cout << "count constructor\n"; } int size() const { return static_cast<int>(values.size()); } private: std::vector<int> values; // invariant: sorted }; // SortedScores a; SortedScores b({70, 35, 58}); SortedScores c(3, 50); → default, vector, count ~~~

## Constructors step by step <figure class="course-stepper" data-course-stepper> <svg class="course-array-address-figure course-ctor-figure" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 360" role="img" aria-label="A step-by-step trace of overloaded constructors of the class SortedScores in 6 frames. The left side lists three constructors: the default constructor, one taking a const vector of int, and one taking an int count and an int score. The right side shows objects a, b, and c with their values. Frame 1: SortedScores a; has no arguments, so the default constructor runs and a has an empty values vector, which is sorted; it prints default constructor. Frame 2: SortedScores b with the braced list 70, 35, 58 selects the vector constructor, and the member initializer list copies 70, 35, 58 into b. Frame 3: the constructor body sorts the values to 35, 58, 70 and prints vector constructor. Frame 4: SortedScores c(3, 50) selects the count constructor, and values(3, 50) gives 50, 50, 50; it prints count constructor. Frame 5: the sizes print as 0 3 3. Frame 6: the rule is that every constructor must leave the invariant true and the member initializer list runs before the body; SortedScores a(); would declare a function, not an object."> <style> .course-ctor-figure text{font-family:ui-monospace,Menlo,Consolas,monospace;fill:currentColor} .course-ctor-figure .cell{fill:none;stroke:currentColor;stroke-width:2} .course-ctor-figure .cell.obj{fill:rgba(142,232,216,.18)} .course-ctor-figure .cell.heap{fill:rgba(255,214,102,.22)} .course-ctor-figure .cell.dead{fill:rgba(255,120,120,.22);stroke-dasharray:6 5} .course-ctor-figure .hl{fill:rgba(110,170,255,.35);stroke:none} .course-ctor-figure .arrow{fill:none;stroke:currentColor;stroke-width:2.5} .course-ctor-figure .head{fill:currentColor} </style> <g class="course-ctor-frame" data-step="0"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 default</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 vector</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 count</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 print</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">5 rule</tspan></text><rect class="hl" x="14" y="44" width="352" height="56"/><rect class="cell obj" x="20" y="50" width="340" height="44"/><text x="30" y="78" font-size="15">SortedScores()</text><rect class="cell" x="20" y="106" width="340" height="44"/><text x="30" y="134" font-size="15">SortedScores(const vector<int>&)</text><rect class="cell" x="20" y="162" width="340" height="44"/><text x="30" y="190" font-size="15">SortedScores(int count, int score)</text><line class="arrow" x1="366" y1="72" x2="406" y2="72"/><polygon class="head" points="416,72 404,65 404,79"/><rect class="cell" x="420" y="50" width="460" height="60"/><text x="432" y="68" font-size="15" font-weight="700">a : SortedScores</text><text x="432" y="96" font-size="15">values</text><text x="540" y="96" font-size="15">(empty vector)</text><text x="700" y="68" font-size="15" opacity=".7">empty is sorted</text><rect class="cell" x="20" y="212" width="340" height="90"/><text x="32" y="234" font-size="15">default constructor</text><text x="20" y="334" font-size="16" font-weight="700">SortedScores a;</text><text x="20" y="354" font-size="15">No arguments, so the compiler picks the default constructor; an empty vector is sorted.</text></g> <g class="course-ctor-frame" data-step="1"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 default</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">2 vector</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 count</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 print</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">5 rule</tspan></text><rect class="cell" x="20" y="50" width="340" height="44"/><text x="30" y="78" font-size="15">SortedScores()</text><rect class="hl" x="14" y="100" width="352" height="56"/><rect class="cell obj" x="20" y="106" width="340" height="44"/><text x="30" y="134" font-size="15">SortedScores(const vector<int>&)</text><rect class="cell" x="20" y="162" width="340" height="44"/><text x="30" y="190" font-size="15">SortedScores(int count, int score)</text><line class="arrow" x1="366" y1="128" x2="406" y2="128"/><polygon class="head" points="416,128 404,121 404,135"/><rect class="cell" x="420" y="50" width="460" height="60"/><text x="432" y="68" font-size="15" font-weight="700">a : SortedScores</text><text x="432" y="96" font-size="15">values</text><text x="540" y="96" font-size="15">(empty vector)</text><rect class="cell" x="420" y="120" width="460" height="60"/><text x="432" y="138" font-size="15" font-weight="700">b : SortedScores</text><text x="432" y="166" font-size="15">values</text><rect class="cell heap" x="540" y="146" width="60" height="28"/><text x="570" y="166" font-size="15" text-anchor="middle">70</text><rect class="cell heap" x="604" y="146" width="60" height="28"/><text x="634" y="166" font-size="15" text-anchor="middle">35</text><rect class="cell heap" x="668" y="146" width="60" height="28"/><text x="698" y="166" font-size="15" text-anchor="middle">58</text><rect class="cell" x="20" y="212" width="340" height="90"/><text x="32" y="234" font-size="15">default constructor</text><text x="20" y="334" font-size="16" font-weight="700">SortedScores b({70, 35, 58});</text><text x="20" y="354" font-size="15">One vector argument: the initializer list copies it into values before the body runs.</text></g> <g class="course-ctor-frame" data-step="2"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 default</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">2 vector</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 count</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 print</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">5 rule</tspan></text><rect class="cell" x="20" y="50" width="340" height="44"/><text x="30" y="78" font-size="15">SortedScores()</text><rect class="hl" x="14" y="100" width="352" height="56"/><rect class="cell obj" x="20" y="106" width="340" height="44"/><text x="30" y="134" font-size="15">SortedScores(const vector<int>&)</text><rect class="cell" x="20" y="162" width="340" height="44"/><text x="30" y="190" font-size="15">SortedScores(int count, int score)</text><rect class="cell" x="420" y="50" width="460" height="60"/><text x="432" y="68" font-size="15" font-weight="700">a : SortedScores</text><text x="432" y="96" font-size="15">values</text><text x="540" y="96" font-size="15">(empty vector)</text><rect class="cell" x="420" y="120" width="460" height="60"/><text x="432" y="138" font-size="15" font-weight="700">b : SortedScores</text><text x="432" y="166" font-size="15">values</text><rect class="cell obj" x="540" y="146" width="60" height="28"/><text x="570" y="166" font-size="15" text-anchor="middle">35</text><rect class="cell obj" x="604" y="146" width="60" height="28"/><text x="634" y="166" font-size="15" text-anchor="middle">58</text><rect class="cell obj" x="668" y="146" width="60" height="28"/><text x="698" y="166" font-size="15" text-anchor="middle">70</text><text x="432" y="262" font-size="15">body: sort(values.begin(), values.end())</text><rect class="cell" x="20" y="212" width="340" height="90"/><text x="32" y="234" font-size="15">default constructor</text><text x="32" y="254" font-size="15">vector constructor</text><text x="20" y="334" font-size="16" font-weight="700">std::sort(values.begin(), values.end());</text><text x="20" y="354" font-size="15">The body sorts the copy, so the invariant (values are sorted) is true when it ends.</text></g> <g class="course-ctor-frame" data-step="3"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 default</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 vector</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">3 count</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 print</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">5 rule</tspan></text><rect class="cell" x="20" y="50" width="340" height="44"/><text x="30" y="78" font-size="15">SortedScores()</text><rect class="cell" x="20" y="106" width="340" height="44"/><text x="30" y="134" font-size="15">SortedScores(const vector<int>&)</text><rect class="hl" x="14" y="156" width="352" height="56"/><rect class="cell obj" x="20" y="162" width="340" height="44"/><text x="30" y="190" font-size="15">SortedScores(int count, int score)</text><line class="arrow" x1="366" y1="184" x2="406" y2="184"/><polygon class="head" points="416,184 404,177 404,191"/><rect class="cell" x="420" y="50" width="460" height="60"/><text x="432" y="68" font-size="15" font-weight="700">a : SortedScores</text><text x="432" y="96" font-size="15">values</text><text x="540" y="96" font-size="15">(empty vector)</text><rect class="cell" x="420" y="120" width="460" height="60"/><text x="432" y="138" font-size="15" font-weight="700">b : SortedScores</text><text x="432" y="166" font-size="15">values</text><rect class="cell obj" x="540" y="146" width="60" height="28"/><text x="570" y="166" font-size="15" text-anchor="middle">35</text><rect class="cell obj" x="604" y="146" width="60" height="28"/><text x="634" y="166" font-size="15" text-anchor="middle">58</text><rect class="cell obj" x="668" y="146" width="60" height="28"/><text x="698" y="166" font-size="15" text-anchor="middle">70</text><rect class="cell" x="420" y="190" width="460" height="60"/><text x="432" y="208" font-size="15" font-weight="700">c : SortedScores</text><text x="432" y="236" font-size="15">values</text><rect class="cell obj" x="540" y="216" width="60" height="28"/><text x="570" y="236" font-size="15" text-anchor="middle">50</text><rect class="cell obj" x="604" y="216" width="60" height="28"/><text x="634" y="236" font-size="15" text-anchor="middle">50</text><rect class="cell obj" x="668" y="216" width="60" height="28"/><text x="698" y="236" font-size="15" text-anchor="middle">50</text><rect class="cell" x="20" y="212" width="340" height="90"/><text x="32" y="234" font-size="15">default constructor</text><text x="32" y="254" font-size="15">vector constructor</text><text x="32" y="274" font-size="15">count constructor</text><text x="20" y="334" font-size="16" font-weight="700">SortedScores c(3, 50);</text><text x="20" y="354" font-size="15">Two ints: values(3, 50) makes three copies of 50, which is already sorted.</text></g> <g class="course-ctor-frame" data-step="4"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 default</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 vector</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 count</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">4 print</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">5 rule</tspan></text><rect class="cell" x="20" y="50" width="340" height="44"/><text x="30" y="78" font-size="15">SortedScores()</text><rect class="cell" x="20" y="106" width="340" height="44"/><text x="30" y="134" font-size="15">SortedScores(const vector<int>&)</text><rect class="cell" x="20" y="162" width="340" height="44"/><text x="30" y="190" font-size="15">SortedScores(int count, int score)</text><rect class="cell" x="420" y="50" width="460" height="60"/><text x="432" y="68" font-size="15" font-weight="700">a : SortedScores</text><text x="432" y="96" font-size="15">values</text><text x="540" y="96" font-size="15">(empty vector)</text><rect class="cell" x="420" y="120" width="460" height="60"/><text x="432" y="138" font-size="15" font-weight="700">b : SortedScores</text><text x="432" y="166" font-size="15">values</text><rect class="cell obj" x="540" y="146" width="60" height="28"/><text x="570" y="166" font-size="15" text-anchor="middle">35</text><rect class="cell obj" x="604" y="146" width="60" height="28"/><text x="634" y="166" font-size="15" text-anchor="middle">58</text><rect class="cell obj" x="668" y="146" width="60" height="28"/><text x="698" y="166" font-size="15" text-anchor="middle">70</text><rect class="cell" x="420" y="190" width="460" height="60"/><text x="432" y="208" font-size="15" font-weight="700">c : SortedScores</text><text x="432" y="236" font-size="15">values</text><rect class="cell obj" x="540" y="216" width="60" height="28"/><text x="570" y="236" font-size="15" text-anchor="middle">50</text><rect class="cell obj" x="604" y="216" width="60" height="28"/><text x="634" y="236" font-size="15" text-anchor="middle">50</text><rect class="cell obj" x="668" y="216" width="60" height="28"/><text x="698" y="236" font-size="15" text-anchor="middle">50</text><rect class="cell" x="20" y="212" width="340" height="90"/><text x="32" y="234" font-size="15">default constructor</text><text x="32" y="254" font-size="15">vector constructor</text><text x="32" y="274" font-size="15">count constructor</text><text x="32" y="294" font-size="15">0 3 3</text><text x="432" y="296" font-size="15">sizes: a.size() b.size() c.size()</text><text x="20" y="334" font-size="16" font-weight="700">std::cout << a.size() << ' ' << b.size() << ' ' << c.size();</text><text x="20" y="354" font-size="15">The sizes print as 0 3 3, one for each object.</text></g> <g class="course-ctor-frame" data-step="5"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 default</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 vector</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 count</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 print</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">5 rule</tspan></text><rect class="cell" x="20" y="50" width="340" height="44"/><text x="30" y="78" font-size="15">SortedScores()</text><rect class="cell" x="20" y="106" width="340" height="44"/><text x="30" y="134" font-size="15">SortedScores(const vector<int>&)</text><rect class="cell" x="20" y="162" width="340" height="44"/><text x="30" y="190" font-size="15">SortedScores(int count, int score)</text><rect class="cell" x="420" y="50" width="460" height="60"/><text x="432" y="68" font-size="15" font-weight="700">a : SortedScores</text><text x="432" y="96" font-size="15">values</text><text x="540" y="96" font-size="15">(empty vector)</text><rect class="cell" x="420" y="120" width="460" height="60"/><text x="432" y="138" font-size="15" font-weight="700">b : SortedScores</text><text x="432" y="166" font-size="15">values</text><rect class="cell obj" x="540" y="146" width="60" height="28"/><text x="570" y="166" font-size="15" text-anchor="middle">35</text><rect class="cell obj" x="604" y="146" width="60" height="28"/><text x="634" y="166" font-size="15" text-anchor="middle">58</text><rect class="cell obj" x="668" y="146" width="60" height="28"/><text x="698" y="166" font-size="15" text-anchor="middle">70</text><rect class="cell" x="420" y="190" width="460" height="60"/><text x="432" y="208" font-size="15" font-weight="700">c : SortedScores</text><text x="432" y="236" font-size="15">values</text><rect class="cell obj" x="540" y="216" width="60" height="28"/><text x="570" y="236" font-size="15" text-anchor="middle">50</text><rect class="cell obj" x="604" y="216" width="60" height="28"/><text x="634" y="236" font-size="15" text-anchor="middle">50</text><rect class="cell obj" x="668" y="216" width="60" height="28"/><text x="698" y="236" font-size="15" text-anchor="middle">50</text><rect class="cell" x="20" y="212" width="340" height="90"/><text x="32" y="234" font-size="15">default constructor</text><text x="32" y="254" font-size="15">vector constructor</text><text x="32" y="274" font-size="15">count constructor</text><text x="32" y="294" font-size="15">0 3 3</text><rect class="cell dead" x="420" y="260" width="460" height="44"/><text x="432" y="280" font-size="15" font-weight="700">SortedScores a();</text><text x="432" y="298" font-size="15">declares a function, not an object</text><text x="20" y="334" font-size="16" font-weight="700">Rule: every constructor leaves the invariant true.</text><text x="20" y="354" font-size="15">The member initializer list runs before the body. Write SortedScores a; with no parentheses.</text></g> </svg> </figure>

## const member functions · Reading without changing ~~~cpp void report(const SortedScores& s) { std::cout << s.contains(58) << '\n'; // allowed: contains is const s.add(99); // line 14: add may change s } ~~~ ~~~text const-error.cpp:14:5: error: 'this' argument to member function 'add' has type 'const SortedScores', but function is not marked const ~~~ Through a `const` reference only `const` member functions may be called. Mark every member function that does not change the object `const`.

## const member functions step by step <figure class="course-stepper" data-course-stepper> <svg class="course-array-address-figure course-constfn-figure" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 360" role="img" aria-label="Step-by-step figure in 5 frames. An object s of class SortedScores is drawn as a box with a thick wall; inside, a private region holds values with cells 35, 52, 58, 70 and the note invariant: ascending order. Public doors on the wall are contains(x) const, print() const, size() const, and add(x), which is not const. Frame 1: report receives s by const reference (Lecture 8), shown with a const, read-only badge on the object. Frame 2: the call s.contains(58) goes through the const contains door, reads the cells, finds 58, and returns true. Frame 3: the call s.add(99) is blocked at the non-const add door with a red cross, and the compiler prints error: 'this' argument to member function 'add' has type 'const SortedScores', but function is not marked const. Frame 4: a const object or const reference can call only const member functions; contains is allowed, add is an error. Frame 5: the rule: mark every member function that does not change the object const, namely contains, print, and size, and leave add non-const."> <style> .course-constfn-figure text{font-family:ui-monospace,Menlo,Consolas,monospace;fill:currentColor} .course-constfn-figure .cell{fill:none;stroke:currentColor;stroke-width:2} .course-constfn-figure .cell.obj{fill:rgba(142,232,216,.18)} .course-constfn-figure .cell.heap{fill:rgba(255,214,102,.22)} .course-constfn-figure .cell.dead{fill:rgba(255,120,120,.22);stroke-dasharray:6 5} .course-constfn-figure .hl{fill:rgba(110,170,255,.35);stroke:none} .course-constfn-figure .arrow{fill:none;stroke:currentColor;stroke-width:2.5} .course-constfn-figure .head{fill:currentColor} .course-constfn-figure .wall{fill:rgba(142,232,216,.08);stroke:currentColor;stroke-width:6} .course-constfn-figure .door{fill:rgba(60,190,110,.5);stroke:currentColor;stroke-width:2} .course-constfn-figure .door.bad{fill:rgba(255,120,120,.4)} .course-constfn-figure .bad{stroke:#ff6b6b;stroke-width:4;fill:none} .course-constfn-figure .no{fill:#ff6b6b;stroke:none} .course-constfn-figure .no text,.course-constfn-figure text.no{fill:#ff6b6b} .course-constfn-figure .ok{fill:#3dbb6e} </style> <g class="course-constfn-frame" data-step="0"><text x="20" y="28" font-size="18"><tspan font-weight="700">1 const reference</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 const call</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 non-const call</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 the rule</tspan></text><text x="12" y="56" font-size="15" font-weight="700">void report(const SortedScores& s)</text><text x="12" y="110" font-size="15">s.contains(58);</text><text x="12" y="230" font-size="15">s.add(99);</text><rect class="wall" x="350" y="40" width="535" height="210"/><text x="372" y="64" font-size="16" font-weight="700">s : SortedScores</text><text x="366" y="84" font-size="15" opacity=".7">public</text><rect class="cell heap" x="530" y="72" width="345" height="168" stroke-dasharray="8 5"/><text x="770" y="92" font-size="15" opacity=".7">private</text><rect class="cell obj" x="545" y="145" width="56" height="40"/><text x="573" y="171" font-size="16" text-anchor="middle">35</text><rect class="cell obj" x="601" y="145" width="56" height="40"/><text x="629" y="171" font-size="16" text-anchor="middle">52</text><rect class="cell obj" x="657" y="145" width="56" height="40"/><text x="685" y="171" font-size="16" text-anchor="middle">58</text><rect class="cell obj" x="713" y="145" width="56" height="40"/><text x="741" y="171" font-size="16" text-anchor="middle">70</text><text x="545" y="203" font-size="15">values</text><text x="545" y="228" font-size="15">invariant: ascending order</text><rect class="door" x="343" y="93" width="14" height="24"/><text x="366" y="110" font-size="15">contains(x)<tspan class="ok" font-weight="700"> const</tspan></text><rect class="door" x="343" y="133" width="14" height="24"/><text x="366" y="150" font-size="15">print()<tspan class="ok" font-weight="700"> const</tspan></text><rect class="door" x="343" y="173" width="14" height="24"/><text x="366" y="190" font-size="15">size()<tspan class="ok" font-weight="700"> const</tspan></text><rect class="door" x="343" y="213" width="14" height="24"/><text x="366" y="230" font-size="15">add(x)</text><rect class="cell dead" x="690" y="45" width="180" height="22" stroke-dasharray="none"/><text x="780" y="62" font-size="15" font-weight="700" text-anchor="middle">const s : read-only</text><text x="20" y="324" font-size="16" font-weight="700">void report(const SortedScores& s)</text><text x="20" y="346" font-size="15">report receives s by const reference (Lecture 8): s is read-only inside report.</text></g> <g class="course-constfn-frame" data-step="1"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 const reference</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">2 const call</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 non-const call</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 the rule</tspan></text><text x="12" y="56" font-size="15" font-weight="700">void report(const SortedScores& s)</text><rect class="hl" x="6" y="92" width="147" height="26"/><text x="12" y="110" font-size="15">s.contains(58);</text><text x="12" y="230" font-size="15">s.add(99);</text><rect class="wall" x="350" y="40" width="535" height="210"/><text x="372" y="64" font-size="16" font-weight="700">s : SortedScores</text><text x="366" y="84" font-size="15" opacity=".7">public</text><rect class="cell heap" x="530" y="72" width="345" height="168" stroke-dasharray="8 5"/><text x="770" y="92" font-size="15" opacity=".7">private</text><rect class="cell obj" x="545" y="145" width="56" height="40"/><text x="573" y="171" font-size="16" text-anchor="middle">35</text><rect class="cell obj" x="601" y="145" width="56" height="40"/><text x="629" y="171" font-size="16" text-anchor="middle">52</text><rect class="cell obj" x="657" y="145" width="56" height="40"/><text x="685" y="171" font-size="16" text-anchor="middle">58</text><rect class="cell obj" x="713" y="145" width="56" height="40"/><text x="741" y="171" font-size="16" text-anchor="middle">70</text><text x="545" y="203" font-size="15">values</text><text x="545" y="228" font-size="15">invariant: ascending order</text><rect class="door" x="343" y="93" width="14" height="24"/><text x="366" y="110" font-size="15">contains(x)<tspan class="ok" font-weight="700"> const</tspan></text><rect class="door" x="343" y="133" width="14" height="24"/><text x="366" y="150" font-size="15">print()<tspan class="ok" font-weight="700"> const</tspan></text><rect class="door" x="343" y="173" width="14" height="24"/><text x="366" y="190" font-size="15">size()<tspan class="ok" font-weight="700"> const</tspan></text><rect class="door" x="343" y="213" width="14" height="24"/><text x="366" y="230" font-size="15">add(x)</text><rect class="cell dead" x="690" y="45" width="180" height="22" stroke-dasharray="none"/><text x="780" y="62" font-size="15" font-weight="700" text-anchor="middle">const s : read-only</text><path class="arrow" d="M160 105 L329 105"/><polygon class="head" points="343,105 329,98 329,112"/><path class="arrow" d="M524 105 L689 105 L689 131"/><polygon class="head" points="689,143 682,129 696,129"/><rect class="hl" x="657" y="145" width="56" height="40"/><text x="685" y="171" font-size="16" font-weight="700" text-anchor="middle">58</text><text x="705" y="128" font-size="16" font-weight="700" class="ok">true</text><text x="20" y="324" font-size="16" font-weight="700">s.contains(58);</text><text x="20" y="346" font-size="15">contains is marked const: it promises not to change the object, so the call is allowed.</text></g> <g class="course-constfn-frame" data-step="2"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 const reference</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 const call</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">3 non-const call</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 the rule</tspan></text><text x="12" y="56" font-size="15" font-weight="700">void report(const SortedScores& s)</text><text x="12" y="110" font-size="15">s.contains(58);</text><rect class="hl" x="6" y="212" width="102" height="26"/><text x="12" y="230" font-size="15">s.add(99);</text><rect class="wall" x="350" y="40" width="535" height="210"/><text x="372" y="64" font-size="16" font-weight="700">s : SortedScores</text><text x="366" y="84" font-size="15" opacity=".7">public</text><rect class="cell heap" x="530" y="72" width="345" height="168" stroke-dasharray="8 5"/><text x="770" y="92" font-size="15" opacity=".7">private</text><rect class="cell obj" x="545" y="145" width="56" height="40"/><text x="573" y="171" font-size="16" text-anchor="middle">35</text><rect class="cell obj" x="601" y="145" width="56" height="40"/><text x="629" y="171" font-size="16" text-anchor="middle">52</text><rect class="cell obj" x="657" y="145" width="56" height="40"/><text x="685" y="171" font-size="16" text-anchor="middle">58</text><rect class="cell obj" x="713" y="145" width="56" height="40"/><text x="741" y="171" font-size="16" text-anchor="middle">70</text><text x="545" y="203" font-size="15">values</text><text x="545" y="228" font-size="15">invariant: ascending order</text><rect class="door" x="343" y="93" width="14" height="24"/><text x="366" y="110" font-size="15">contains(x)<tspan class="ok" font-weight="700"> const</tspan></text><rect class="door" x="343" y="133" width="14" height="24"/><text x="366" y="150" font-size="15">print()<tspan class="ok" font-weight="700"> const</tspan></text><rect class="door" x="343" y="173" width="14" height="24"/><text x="366" y="190" font-size="15">size()<tspan class="ok" font-weight="700"> const</tspan></text><rect class="door bad" x="343" y="213" width="14" height="24"/><text x="366" y="230" font-size="15">add(x)</text><rect class="cell dead" x="690" y="45" width="180" height="22" stroke-dasharray="none"/><text x="780" y="62" font-size="15" font-weight="700" text-anchor="middle">const s : read-only</text><path class="arrow" d="M112 225 L296 225"/><text x="306" y="235" font-size="34" font-weight="700" class="no">✗</text><text x="20" y="268" font-size="15" style="fill:#ff6b6b">const-error.cpp:14:5: error: 'this' argument to member function 'add'</text><text x="20" y="286" font-size="15" style="fill:#ff6b6b">has type 'const SortedScores', but function is not marked const</text><text x="20" y="324" font-size="16" font-weight="700">s.add(99);</text><text x="20" y="346" font-size="15">add is not const: it may change the object, so the compiler refuses the call.</text></g> <g class="course-constfn-frame" data-step="3"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 const reference</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 const call</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">3 non-const call</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">4 the rule</tspan></text><text x="12" y="56" font-size="15" font-weight="700">void report(const SortedScores& s)</text><rect class="hl" x="6" y="92" width="147" height="26"/><text x="12" y="110" font-size="15">s.contains(58);</text><rect class="hl" x="6" y="212" width="102" height="26"/><text x="12" y="230" font-size="15">s.add(99);</text><rect class="wall" x="350" y="40" width="535" height="210"/><text x="372" y="64" font-size="16" font-weight="700">s : SortedScores</text><text x="366" y="84" font-size="15" opacity=".7">public</text><rect class="cell heap" x="530" y="72" width="345" height="168" stroke-dasharray="8 5"/><text x="770" y="92" font-size="15" opacity=".7">private</text><rect class="cell obj" x="545" y="145" width="56" height="40"/><text x="573" y="171" font-size="16" text-anchor="middle">35</text><rect class="cell obj" x="601" y="145" width="56" height="40"/><text x="629" y="171" font-size="16" text-anchor="middle">52</text><rect class="cell obj" x="657" y="145" width="56" height="40"/><text x="685" y="171" font-size="16" text-anchor="middle">58</text><rect class="cell obj" x="713" y="145" width="56" height="40"/><text x="741" y="171" font-size="16" text-anchor="middle">70</text><text x="545" y="203" font-size="15">values</text><text x="545" y="228" font-size="15">invariant: ascending order</text><rect class="door" x="343" y="93" width="14" height="24"/><text x="366" y="110" font-size="15">contains(x)<tspan class="ok" font-weight="700"> const</tspan></text><rect class="door" x="343" y="133" width="14" height="24"/><text x="366" y="150" font-size="15">print()<tspan class="ok" font-weight="700"> const</tspan></text><rect class="door" x="343" y="173" width="14" height="24"/><text x="366" y="190" font-size="15">size()<tspan class="ok" font-weight="700"> const</tspan></text><rect class="door bad" x="343" y="213" width="14" height="24"/><text x="366" y="230" font-size="15">add(x)</text><rect class="cell dead" x="690" y="45" width="180" height="22" stroke-dasharray="none"/><text x="780" y="62" font-size="15" font-weight="700" text-anchor="middle">const s : read-only</text><text x="20" y="268" font-size="15">A const object (or const reference) can call only const member functions.</text><text x="20" y="286" font-size="15">contains: allowed (const). add: error (not const).</text><text x="20" y="324" font-size="16" font-weight="700">const object -> const member functions only</text><text x="20" y="346" font-size="15">The member function, not the caller, declares whether it may change the object.</text></g> <g class="course-constfn-frame" data-step="4"><text x="20" y="28" font-size="18"><tspan opacity=".5">1 const reference</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">2 const call</tspan><tspan opacity=".5"> · </tspan><tspan opacity=".5">3 non-const call</tspan><tspan opacity=".5"> · </tspan><tspan font-weight="700">4 the rule</tspan></text><text x="12" y="56" font-size="15" font-weight="700">void report(const SortedScores& s)</text><rect class="wall" x="350" y="40" width="535" height="210"/><text x="372" y="64" font-size="16" font-weight="700">s : SortedScores</text><text x="366" y="84" font-size="15" opacity=".7">public</text><rect class="cell heap" x="530" y="72" width="345" height="168" stroke-dasharray="8 5"/><text x="770" y="92" font-size="15" opacity=".7">private</text><rect class="cell obj" x="545" y="145" width="56" height="40"/><text x="573" y="171" font-size="16" text-anchor="middle">35</text><rect class="cell obj" x="601" y="145" width="56" height="40"/><text x="629" y="171" font-size="16" text-anchor="middle">52</text><rect class="cell obj" x="657" y="145" width="56" height="40"/><text x="685" y="171" font-size="16" text-anchor="middle">58</text><rect class="cell obj" x="713" y="145" width="56" height="40"/><text x="741" y="171" font-size="16" text-anchor="middle">70</text><text x="545" y="203" font-size="15">values</text><text x="545" y="228" font-size="15">invariant: ascending order</text><rect class="door" x="343" y="93" width="14" height="24"/><text x="366" y="110" font-size="15">contains(x)<tspan class="ok" font-weight="700"> const</tspan></text><rect class="door" x="343" y="133" width="14" height="24"/><text x="366" y="150" font-size="15">print()<tspan class="ok" font-weight="700"> const</tspan></text><rect class="door" x="343" y="173" width="14" height="24"/><text x="366" y="190" font-size="15">size()<tspan class="ok" font-weight="700"> const</tspan></text><rect class="door" x="343" y="213" width="14" height="24"/><text x="366" y="230" font-size="15">add(x)</text><text x="20" y="268" font-size="15">Mark every member function that does not change the object const:</text><text x="20" y="286" font-size="15">contains, print, size. Leave add non-const.</text><text x="20" y="324" font-size="16" font-weight="700">bool contains(int x) const;</text><text x="20" y="346" font-size="15">A const after the parameter list is part of the interface, and callers with const references need it.</text></g> </svg> </figure>

## Poll 2: What does main print? <div class="course-poll-layout"> <div> ~~~cpp class Box { public: Box() : n(0) { std::cout << "D"; } Box(int k) : n(k) { std::cout << "I"; } private: int n; }; int main() { Box a; Box b(3); Box c = 4; Box d[2]; } ~~~ - **A)** `DIIDD` · **B)** `DII` · **C)** `DIDDD` · **D)** `DIID` </div> <figure class="course-slido-qr"><img src="assets/slido-lecture17.svg" alt="QR code that opens the Lecture 17 Slido event." width="360" height="360"><figcaption>📊 sli.do · #3128457</figcaption></figure> </div>

## Summary: classes and constructors - A **class** bundles data members with member functions; its **class invariant** is a rule they all keep. - `private` members can be named only by member functions; the compiler checks it. - A **constructor** has no return type and establishes the invariant. - Mark readers `const`. Common errors: no `;` after the class, `T a();`, a missing `Name::`. **Reading:** Stroustrup, *PPP* (2nd ed.), “Technicalities: Classes, etc.”; Savitch, “Defining Classes”.

## Lab practice: classes and constructors 1. Add `int median() const` to `SortedScores`. 1. Write `class Fraction`: positive denominator, lowest terms. 1. Write `class Account`: the balance is never negative. 1. Store `Time` as hours and minutes; keep the interface. [IC151 lab setup and batch schedule](ic151.html)