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<a href="#func-members">Functions</a> </div>
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<div class="title">cut_rod.cpp File Reference</div> </div>
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<div class="contents">
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<p>Implementation of cutting a rod problem.
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <array></code><br />
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<code>#include <cassert></code><br />
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<code>#include <climits></code><br />
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<code>#include <iostream></code><br />
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Namespaces</h2></td></tr>
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<tr class="memitem:dd/d24/namespacedynamic__programming"><td class="memItemLeft" align="right" valign="top">  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d24/namespacedynamic__programming.html">dynamic_programming</a></td></tr>
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<tr class="memdesc:dd/d24/namespacedynamic__programming"><td class="mdescLeft"> </td><td class="mdescRight">Dynamic Programming algorithms. <br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:d8/d36/namespacecut__rod"><td class="memItemLeft" align="right" valign="top">  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d36/namespacecut__rod.html">cut_rod</a></td></tr>
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<tr class="memdesc:d8/d36/namespacecut__rod"><td class="mdescLeft"> </td><td class="mdescRight">Implementation of cutting a rod problem. <br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:ae550b90e6057a7f976c9d643f706c4f5"><td class="memTemplParams" colspan="2">template<size_t T> </td></tr>
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<tr class="memitem:ae550b90e6057a7f976c9d643f706c4f5"><td class="memTemplItemLeft" align="right" valign="top">int </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d6/d10/cut__rod_8cpp.html#ae550b90e6057a7f976c9d643f706c4f5">dynamic_programming::cut_rod::maxProfitByCuttingRod</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, T > &price, const int n)</td></tr>
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<tr class="memdesc:ae550b90e6057a7f976c9d643f706c4f5"><td class="mdescLeft"> </td><td class="mdescRight">Cuts the rod in different pieces and stores the maximum profit for each piece of the rod. <a href="../../d6/d10/cut__rod_8cpp.html#ae550b90e6057a7f976c9d643f706c4f5">More...</a><br /></td></tr>
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<tr class="separator:ae550b90e6057a7f976c9d643f706c4f5"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d10/cut__rod_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
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<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft"> </td><td class="mdescRight">Function to test above algorithm. <a href="../../d6/d10/cut__rod_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
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<tr class="separator:aa8dca7b867074164d5f45b0f3851269d"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d10/cut__rod_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft"> </td><td class="mdescRight">Main function. <a href="../../d6/d10/cut__rod_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></td></tr>
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<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p>Implementation of cutting a rod problem. </p>
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<p>Given a rod of length n inches and an array of prices that contains prices of all pieces of size<=n. Determine the maximum profit obtainable by cutting up the rod and selling the pieces.</p>
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<h3><a class="anchor" id="autotoc_md43"></a>
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Algorithm</h3>
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<p>The idea is to break the given rod into every smaller piece as possible and then check profit for each piece, by calculating maximum profit for smaller pieces we will build the solution for larger pieces in bottom-up manner.</p>
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<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Anmol3299">Anmol</a> </dd>
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<dd>
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<a href="https://github.com/Pardeep009">Pardeep</a> </dd></dl>
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</div><h2 class="groupheader">Function Documentation</h2>
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<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">◆ </a></span>main()</h2>
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<div class="memitem">
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<div class="memproto">
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<td class="memname">int main </td>
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<td>(</td>
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<td class="paramtype">void </td>
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<td class="paramname"></td><td>)</td>
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<td></td>
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</div><div class="memdoc">
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<p>Main function. </p>
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<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
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<div class="fragment"><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  {</div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="comment">// Testing</span></div>
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<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <a class="code" href="../../d6/d10/cut__rod_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>();</div>
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span> }</div>
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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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<div class="dyncontent">
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../d6/d10/cut__rod_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="274" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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</div>
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</div>
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</div>
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<a id="ae550b90e6057a7f976c9d643f706c4f5"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ae550b90e6057a7f976c9d643f706c4f5">◆ </a></span>maxProfitByCuttingRod()</h2>
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<div class="memtemplate">
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template<size_t T> </div>
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<table class="memname">
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<tr>
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<td class="memname">int dynamic_programming::cut_rod::maxProfitByCuttingRod </td>
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<td>(</td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< int, T > & </td>
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<td class="paramname"><em>price</em>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">const int </td>
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<td class="paramname"><em>n</em> </td>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</div><div class="memdoc">
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<p>Cuts the rod in different pieces and stores the maximum profit for each piece of the rod. </p>
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<dl class="tparams"><dt>Template Parameters</dt><dd>
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<table class="tparams">
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<tr><td class="paramname">T</td><td>size of the price array </td></tr>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">n</td><td>size of the rod in inches </td></tr>
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<tr><td class="paramname">price</td><td>an array of prices that contains prices of all pieces of size<=n </td></tr>
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>maximum profit obtainable for</dd></dl>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">n</td><td>inch rod. </td></tr>
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</dd>
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<div class="fragment"><div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  {</div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keywordtype">int</span> *profit =</div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="keyword">new</span> <span class="keywordtype">int</span>[n + 1]; <span class="comment">// profit[i] will hold maximum profit for i inch rod</span></div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  </div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  profit[0] = 0; <span class="comment">// if length of rod is zero, then no profit</span></div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  </div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="comment">// outer loop will select size of rod, starting from 1 inch to n inch rod.</span></div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="comment">// inner loop will evaluate the maximum profit we can get for i inch rod by</span></div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="comment">// making every possible cut on it and will store it in profit[i].</span></div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 1; i <= n; i++) {</div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keywordtype">int</span> q = INT_MIN;</div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 1; j <= i; j++) {</div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  q = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(q, price[j - 1] + profit[i - j]);</div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  }</div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  profit[i] = q;</div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  }</div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = profit[n];</div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="keyword">delete</span>[] profit;</div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keywordflow">return</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>; <span class="comment">// returning maximum profit</span></div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span> }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">◆ </a></span>test()</h2>
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<td class="memname">static void test </td>
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<td class="paramname"></td><td>)</td>
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<span class="mlabels"><span class="mlabel">static</span></span> </td>
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<p>Function to test above algorithm. </p>
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<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
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<div class="fragment"><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  {</div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="comment">// Test 1</span></div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> n1 = 8; <span class="comment">// size of rod</span></div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<int, n1></a> price1 = {1, 5, 8, 9, 10, 17, 17, 20}; <span class="comment">// price array</span></div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> max_profit1 =</div>
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<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <a class="code" href="../../d6/d10/cut__rod_8cpp.html#ae550b90e6057a7f976c9d643f706c4f5">dynamic_programming::cut_rod::maxProfitByCuttingRod</a>(price1, n1);</div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> expected_max_profit1 = 22;</div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  assert(max_profit1 == expected_max_profit1);</div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Maximum profit with "</span> << n1 << <span class="stringliteral">" inch road is "</span> << max_profit1</div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  << <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  </div>
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<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="comment">// Test 2</span></div>
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<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> n2 = 30; <span class="comment">// size of rod</span></div>
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<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<int, n2></a> price2 = {</div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  1, 5, 8, 9, 10, 17, 17, 20, 24, 30, <span class="comment">// price array</span></div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  31, 32, 33, 34, 35, 36, 37, 38, 39, 40,</div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  41, 42, 43, 44, 45, 46, 47, 48, 49, 50};</div>
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<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> max_profit2 =</div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <a class="code" href="../../d6/d10/cut__rod_8cpp.html#ae550b90e6057a7f976c9d643f706c4f5">dynamic_programming::cut_rod::maxProfitByCuttingRod</a>(price2, n2);</div>
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<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> expected_max_profit2 = 90;</div>
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<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  assert(max_profit2 == expected_max_profit2);</div>
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<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Maximum profit with "</span> << n2 << <span class="stringliteral">" inch road is "</span> << max_profit2</div>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  << <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a name="l00094"></a><span class="lineno"> 94</span> }</div>
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<div class="ttc" id="amatrix__exponentiation_8cpp_html_ad8389ed58fd0ec66df248014775ad1fa"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a></div><div class="ttdeci">ll ans(ll n)</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:91</div></div>
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<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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<div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a></div><div class="ttdoc">STL class.</div></div>
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<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
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<div class="ttc" id="amax_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a></div><div class="ttdeci">T max(T... args)</div></div>
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<div class="ttc" id="acut__rod_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d6/d10/cut__rod_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Function to test above algorithm.</div><div class="ttdef"><b>Definition:</b> cut_rod.cpp:71</div></div>
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<div class="ttc" id="acut__rod_8cpp_html_ae550b90e6057a7f976c9d643f706c4f5"><div class="ttname"><a href="../../d6/d10/cut__rod_8cpp.html#ae550b90e6057a7f976c9d643f706c4f5">dynamic_programming::cut_rod::maxProfitByCuttingRod</a></div><div class="ttdeci">int maxProfitByCuttingRod(const std::array< int, T > &price, const int n)</div><div class="ttdoc">Cuts the rod in different pieces and stores the maximum profit for each piece of the rod.</div><div class="ttdef"><b>Definition:</b> cut_rod.cpp:44</div></div>
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