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<div class="headertitle"><div class="title">coin_change_topdown.cpp File Reference</div></div>
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<div class="contents">
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<p><a href="https://leetcode.com/problems/coin-change/" target="_blank">Minimum coins</a> change problem is a problem used to find the minimum number of coins required to completely reach a target amount.
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<a href="#details">More...</a></p>
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<div class="textblock"><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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<code>#include <vector></code><br />
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</div><div class="textblock"><div class="dynheader">
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Include dependency graph for coin_change_topdown.cpp:</div>
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<div class="dyncontent">
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<p><a href="../../d9/d31/coin__change__topdown_8cpp_source.html">Go to the source code of this file.</a></p>
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 id="header-namespaces" class="groupheader"><a id="namespaces" name="namespaces"></a>
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Namespaces</h2></td></tr>
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<tr class="memitem:dynamic_5Fprogramming" id="r_dynamic_5Fprogramming"><td class="memItemLeft" align="right" valign="top">namespace  </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="memitem:mincoins_5Ftopdown" id="r_mincoins_5Ftopdown"><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/db8/namespacemincoins__topdown.html">mincoins_topdown</a></td></tr>
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<tr class="memdesc:d5/db8/namespacemincoins__topdown"><td class="mdescLeft"> </td><td class="mdescRight">Functions for <a href="https://leetcode.com/problems/coin-change/" target="_blank">minimum coin exchange</a> problem. <br /></td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 id="header-func-members" class="groupheader"><a id="func-members" name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:ac816a4ae8a29c156b90377041000929a" id="r_ac816a4ae8a29c156b90377041000929a"><td class="memTemplParams" colspan="2">template<typename T> </td></tr>
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<tr class="memitem:ac816a4ae8a29c156b90377041000929a template"><td class="memItemLeft" align="right" valign="top">int64_t </td><td class="memItemRight" valign="bottom"><a class="el" href="#ac816a4ae8a29c156b90377041000929a">dynamic_programming::mincoins_topdown::mincoins</a> (const T &n, const std::vector< T > &coins, const int16_t &t, std::vector< T > dp)</td></tr>
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<tr class="memdesc:ac816a4ae8a29c156b90377041000929a"><td class="mdescLeft"> </td><td class="mdescRight">This implementation is for finding minimum number of coins . <br /></td></tr>
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<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d" id="r_aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void </td><td class="memItemRight" valign="bottom"><a class="el" href="#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
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<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft"> </td><td class="mdescRight">Test implementations. <br /></td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft"> </td><td class="mdescRight">Main function. <br /></td></tr>
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</table>
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<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
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<div class="textblock"><p><a href="https://leetcode.com/problems/coin-change/" target="_blank">Minimum coins</a> change problem is a problem used to find the minimum number of coins required to completely reach a target amount. </p>
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<p>This problem can be solved using 2 methods:</p><ol type="1">
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<li>Top down approach</li>
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<li>Bottom up appraoch Top down approach involves a vector with all elements initialised to 0. It is based on optimal substructure and overlapping subproblems. Overall time complexity of coin change problem is O(n*t) For example: example 1:- Coins: {1,7,10} Target:15 Therfore minimum number of coins required = 3 of denomination 1,7 and 7. <dl class="section author"><dt>Author</dt><dd><a href="https://github.com/webdesignbydivyansh" target="_blank">Divyansh Kushwaha</a> </dd></dl>
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</li>
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</ol>
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<p class="definition">Definition in file <a class="el" href="../../d9/d31/coin__change__topdown_8cpp_source.html">coin_change_topdown.cpp</a>.</p>
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</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
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<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="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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<td class="memname">int main </td>
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<td>(</td>
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<td class="paramtype">void</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<td></td>
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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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<p class="definition">Definition at line <a class="el" href="../../d9/d31/coin__change__topdown_8cpp_source.html#l00091">91</a> of file <a class="el" href="../../d9/d31/coin__change__topdown_8cpp_source.html">coin_change_topdown.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 91</span> {</div>
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<div class="line"><span class="lineno"> 92</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// execute the test</span></div>
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<div class="line"><span class="lineno"> 93</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 94</span>}</div>
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<div class="ttc" id="acoin__change__topdown_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Test implementations.</div><div class="ttdef"><b>Definition</b> <a href="../../d9/d31/coin__change__topdown_8cpp_source.html#l00074">coin_change_topdown.cpp:74</a></div></div>
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</div><!-- fragment -->
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</div>
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<a id="ac816a4ae8a29c156b90377041000929a" name="ac816a4ae8a29c156b90377041000929a"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ac816a4ae8a29c156b90377041000929a">◆ </a></span>mincoins()</h2>
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<div class="memtemplate">
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template<typename T> </div>
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<td class="memname">int64_t dynamic_programming::mincoins_topdown::mincoins </td>
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<td>(</td>
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<td class="paramtype">const T &</td> <td class="paramname"><span class="paramname"><em>n</em></span>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">const std::vector< T > &</td> <td class="paramname"><span class="paramname"><em>coins</em></span>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">const int16_t &</td> <td class="paramname"><span class="paramname"><em>t</em></span>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">std::vector< T ></td> <td class="paramname"><span class="paramname"><em>dp</em></span> )</td>
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</div><div class="memdoc">
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<p>This implementation is for finding minimum number of coins . </p>
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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">T</td><td>template-type to use any kind of value </td></tr>
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<tr><td class="paramname">n</td><td>amount to be reached </td></tr>
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<tr><td class="paramname">coins</td><td>vector of coins </td></tr>
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<tr><td class="paramname">t</td><td>deontes the number of coins </td></tr>
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<tr><td class="paramname">dp</td><td>initilised to 0 </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>minimum number of coins </dd></dl>
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<p class="definition">Definition at line <a class="el" href="../../d9/d31/coin__change__topdown_8cpp_source.html#l00047">47</a> of file <a class="el" href="../../d9/d31/coin__change__topdown_8cpp_source.html">coin_change_topdown.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 48</span> {</div>
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<div class="line"><span class="lineno"> 49</span> <span class="keywordflow">if</span> (n == 0) {</div>
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<div class="line"><span class="lineno"> 50</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 51</span> }</div>
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<div class="line"><span class="lineno"> 52</span> <span class="keywordflow">if</span> (<a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[n] != 0) {</div>
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<div class="line"><span class="lineno"> 53</span> <span class="keywordflow">return</span> <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>[n];</div>
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<div class="line"><span class="lineno"> 54</span> }</div>
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<div class="line"><span class="lineno"> 55</span> <span class="keywordtype">int</span> ans = INT_MAX; <span class="comment">// variable to store min coins</span></div>
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<div class="line"><span class="lineno"> 56</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < t; i++) {</div>
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<div class="line"><span class="lineno"> 57</span> <span class="keywordflow">if</span> (n - coins[i] >= 0) { <span class="comment">// if after subtracting the current</span></div>
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<div class="line"><span class="lineno"> 58</span> <span class="comment">// denomination is it greater than 0 or not</span></div>
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<div class="line"><span class="lineno"> 59</span> <span class="keywordtype">int</span> sub = mincoins(n - coins[i], coins, t, <a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>);</div>
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<div class="line"><span class="lineno"> 60</span> ans = std::min(ans, sub + 1);</div>
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<div class="line"><span class="lineno"> 61</span> }</div>
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<div class="line"><span class="lineno"> 62</span> }</div>
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<div class="line"><span class="lineno"> 63</span> dp[n] = ans;</div>
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<div class="line"><span class="lineno"> 64</span> <span class="keywordflow">return</span> dp[n]; <span class="comment">// returns minimum number of coins</span></div>
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<div class="line"><span class="lineno"> 65</span>}</div>
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<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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</div><!-- fragment -->
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<a id="aa8dca7b867074164d5f45b0f3851269d" name="aa8dca7b867074164d5f45b0f3851269d"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">◆ </a></span>test()</h2>
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<td class="memname">void test </td>
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<td>(</td>
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<span class="mlabels"><span class="mlabel static">static</span></span> </td>
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<p>Test implementations. </p>
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<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
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<p class="definition">Definition at line <a class="el" href="../../d9/d31/coin__change__topdown_8cpp_source.html#l00074">74</a> of file <a class="el" href="../../d9/d31/coin__change__topdown_8cpp_source.html">coin_change_topdown.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 74</span> {</div>
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<div class="line"><span class="lineno"> 75</span> <span class="comment">// example 1: number of coins=3 and minimum coins required=3(7,7,1)</span></div>
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<div class="line"><span class="lineno"> 76</span> <span class="keyword">const</span> int64_t n1 = 15;</div>
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<div class="line"><span class="lineno"> 77</span> <span class="keyword">const</span> int8_t t1 = 3, a1 = 0;</div>
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<div class="line"><span class="lineno"> 78</span> std::cout << <span class="stringliteral">"\nTest 1..."</span>;</div>
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<div class="line"><span class="lineno"> 79</span> std::vector<int64_t> arr1{1, 7, 10};</div>
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<div class="line"><span class="lineno"> 80</span> std::vector<int64_t> dp1(n1 + 1);</div>
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<div class="line"><span class="lineno"> 81</span> <a class="code hl_function" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(dp1.begin(), dp1.end(), a1);</div>
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<div class="line"><span class="lineno"> 82</span> assert(<a class="code hl_function" href="#ac816a4ae8a29c156b90377041000929a">dynamic_programming::mincoins_topdown::mincoins</a>(n1, arr1, t1, dp1) ==</div>
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<div class="line"><span class="lineno"> 83</span> 3);</div>
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<div class="line"><span class="lineno"> 84</span> std::cout << <span class="stringliteral">"Passed\n"</span>;</div>
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<div class="line"><span class="lineno"> 85</span>}</div>
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<div class="ttc" id="acoin__change__topdown_8cpp_html_ac816a4ae8a29c156b90377041000929a"><div class="ttname"><a href="#ac816a4ae8a29c156b90377041000929a">dynamic_programming::mincoins_topdown::mincoins</a></div><div class="ttdeci">int64_t mincoins(const T &n, const std::vector< T > &coins, const int16_t &t, std::vector< T > dp)</div><div class="ttdoc">This implementation is for finding minimum number of coins .</div><div class="ttdef"><b>Definition</b> <a href="../../d9/d31/coin__change__topdown_8cpp_source.html#l00047">coin_change_topdown.cpp:47</a></div></div>
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<div class="ttc" id="adecimal__to__roman__numeral_8cpp_html_a88203bd297e8405160c132faa1187780"><div class="ttname"><a href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a></div><div class="ttdeci">std::string fill(char c, int n)</div><div class="ttdef"><b>Definition</b> <a href="../../de/d85/decimal__to__roman__numeral_8cpp_source.html#l00015">decimal_to_roman_numeral.cpp:15</a></div></div>
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