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<div class="headertitle"><div class="title">matrix_chain_multiplication.cpp</div></div>
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<div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="preprocessor">#include &lt;climits&gt;</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="keyword">using namespace </span>std;</div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span> </div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="preprocessor">#define MAX 10</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span> </div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">// dp table to store the solution for already computed sub problems</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="keywordtype">int</span> <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[MAX][MAX];</div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span> </div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment">// Function to find the most efficient way to multiply the given sequence of</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment">// matrices</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="keywordtype">int</span> MatrixChainMultiplication(<span class="keywordtype">int</span> dim[], <span class="keywordtype">int</span> i, <span class="keywordtype">int</span> j) {</div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> <span class="comment">// base case: one matrix</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span> <span class="keywordflow">if</span> (j &lt;= i + 1)</div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> </div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span> <span class="comment">// stores minimum number of scalar multiplications (i.e., cost)</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span> <span class="comment">// needed to compute the matrix M[i+1]...M[j] = M[i..j]</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> <span class="keywordtype">int</span> min = INT_MAX;</div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span> </div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> <span class="comment">// if dp[i][j] is not calculated (calculate it!!)</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> </div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> <span class="keywordflow">if</span> (<a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i][j] == 0) {</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> <span class="comment">// take the minimum over each possible position at which the</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> <span class="comment">// sequence of matrices can be split</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> </div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = i + 1; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> &lt;= j - 1; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> <span class="comment">// recur for M[i+1]..M[k] to get a i x k matrix</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> <span class="keywordtype">int</span> cost = MatrixChainMultiplication(dim, i, k);</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> </div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> <span class="comment">// recur for M[k+1]..M[j] to get a k x j matrix</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> cost += MatrixChainMultiplication(dim, k, j);</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> </div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="comment">// cost to multiply two (i x k) and (k x j) matrix</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> cost += dim[i] * dim[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>] * dim[j];</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> </div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="keywordflow">if</span> (cost &lt; min)</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> min = cost; <span class="comment">// store the minimum cost</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> }</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i][j] = min;</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> }</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> </div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="comment">// return min cost to multiply M[j+1]..M[j]</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="keywordflow">return</span> <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[i][j];</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span>}</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> </div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="comment">// main function</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="keywordtype">int</span> <a class="code hl_function" href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="comment">// Matrix i has Dimensions dim[i-1] &amp; dim[i] for i=1..n</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// input is 10 x 30 matrix, 30 x 5 matrix, 5 x 60 matrix</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keywordtype">int</span> dim[] = {10, 30, 5, 60};</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keywordtype">int</span> n = <span class="keyword">sizeof</span>(dim) / <span class="keyword">sizeof</span>(dim[0]);</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> </div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="comment">// Function Calling: MatrixChainMultiplications(dimensions_array, starting,</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// ending);</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> </div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> cout &lt;&lt; <span class="stringliteral">&quot;Minimum cost is &quot;</span> &lt;&lt; MatrixChainMultiplication(dim, 0, n - 1)</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> </div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span>}</div>
<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d18/composite__simpson__rule_8cpp_source.html#l00117">composite_simpson_rule.cpp:117</a></div></div>
<div class="ttc" id="agenerate__parentheses_8cpp_html_gae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="../../dd/d1e/generate__parentheses_8cpp_source.html#l00110">generate_parentheses.cpp:110</a></div></div>
<div class="ttc" id="anamespacedp_html"><div class="ttname"><a href="../../df/d88/namespacedp.html">dp</a></div><div class="ttdoc">for std::vector</div><div class="ttdef"><b>Definition</b> <a href="../../de/d8c/partition__problem_8cpp_source.html#l00039">partition_problem.cpp:39</a></div></div>
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