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<div class="summary">
<a href="#namespaces">Namespaces</a> &#124;
<a href="#func-members">Functions</a> </div>
<div class="headertitle">
<div class="title">coin_change_topdown.cpp File Reference</div> </div>
<div class="headertitle"><div class="title">coin_change_topdown.cpp File Reference</div></div>
</div><!--header-->
<div class="contents">
<p><a href="https://leetcode.com/problems/coin-change/">Minimum coins</a> change problem is a problem used to find the minimum number of coins required to completely reach a target amount.
<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.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;climits&gt;</code><br />
@@ -111,16 +110,16 @@ Include dependency graph for coin_change_topdown.cpp:</div>
</div>
</div>
</div><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="namespaces"></a>
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="namespaces" name="namespaces"></a>
Namespaces</h2></td></tr>
<tr class="memitem:dd/d24/namespacedynamic__programming"><td class="memItemLeft" align="right" valign="top"> &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d24/namespacedynamic__programming.html">dynamic_programming</a></td></tr>
<tr class="memitem:dd/d24/namespacedynamic__programming"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d24/namespacedynamic__programming.html">dynamic_programming</a></td></tr>
<tr class="memdesc:dd/d24/namespacedynamic__programming"><td class="mdescLeft">&#160;</td><td class="mdescRight">Dynamic Programming algorithms. <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:d5/db8/namespacemincoins__topdown"><td class="memItemLeft" align="right" valign="top"> &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/db8/namespacemincoins__topdown.html">mincoins_topdown</a></td></tr>
<tr class="memdesc:d5/db8/namespacemincoins__topdown"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for <a href="https://leetcode.com/problems/coin-change/">minimum coin exchange</a> problem. <br /></td></tr>
<tr class="memitem:d5/db8/namespacemincoins__topdown"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/db8/namespacemincoins__topdown.html">mincoins_topdown</a></td></tr>
<tr class="memdesc:d5/db8/namespacemincoins__topdown"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for <a href="https://leetcode.com/problems/coin-change/" target="_blank">minimum coin exchange</a> problem. <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
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Functions</h2></td></tr>
<tr class="memitem:ac816a4ae8a29c156b90377041000929a"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:ac816a4ae8a29c156b90377041000929a"><td class="memTemplItemLeft" align="right" valign="top">int64_t&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d9/d31/coin__change__topdown_8cpp.html#ac816a4ae8a29c156b90377041000929a">dynamic_programming::mincoins_topdown::mincoins</a> (const T &amp;n, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; &amp;coins, const int16_t &amp;t, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; dp)</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p><a href="https://leetcode.com/problems/coin-change/">Minimum coins</a> change problem is a problem used to find the minimum number of coins required to completely reach a target amount. </p>
<p>This problem can be solved using 2 methods:</p><ol type="1">
<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>
<p >This problem can be solved using 2 methods:</p><ol type="1">
<li>Top down approach</li>
<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">Divyansh Kushwaha</a> </dd></dl>
<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>
</li>
</ol>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; {</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; <a class="code" href="../../d9/d31/coin__change__topdown_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// execute the test</span></div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> {</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <a class="code hl_function" href="../../d9/d31/coin__change__topdown_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// execute the test</span></div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span>}</div>
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</div>
<a id="ac816a4ae8a29c156b90377041000929a"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ac816a4ae8a29c156b90377041000929a">&#9670;&nbsp;</a></span>mincoins()</h2>
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</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>minimum number of coins </dd></dl>
<div class="fragment"><div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; {</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; <span class="keywordflow">if</span> (n == 0) {</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; }</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; <span class="keywordflow">if</span> (dp[n] != 0) {</div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; }</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; <span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = INT_MAX; <span class="comment">// variable to store min coins</span></div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; t; i++) {</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; <span class="keywordflow">if</span> (n - coins[i] &gt;= 0) { <span class="comment">// if after subtracting the current</span></div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <span class="comment">// denomination is it greater than 0 or not</span></div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; <span class="keywordtype">int</span> sub = <a class="code" href="../../d9/d31/coin__change__topdown_8cpp.html#ac816a4ae8a29c156b90377041000929a">mincoins</a>(n - coins[i], coins, t, dp);</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>, sub + 1);</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; }</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; }</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; dp[n] = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <span class="keywordflow">return</span> dp[n]; <span class="comment">// returns minimum number of coins</span></div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> {</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keywordflow">if</span> (n == 0) {</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> }</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keywordflow">if</span> (dp[n] != 0) {</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keywordflow">return</span> dp[n];</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> }</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keywordtype">int</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = INT_MAX; <span class="comment">// variable to store min coins</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; t; i++) {</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="keywordflow">if</span> (n - coins[i] &gt;= 0) { <span class="comment">// if after subtracting the current</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="comment">// denomination is it greater than 0 or not</span></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="keywordtype">int</span> sub = <a class="code hl_function" href="../../d9/d31/coin__change__topdown_8cpp.html#ac816a4ae8a29c156b90377041000929a">mincoins</a>(n - coins[i], coins, t, dp);</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(<a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>, sub + 1);</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> }</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> }</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> dp[n] = <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
<div class="line"><a id="l00064" name="l00064"></a><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="ttc" id="acoin__change__topdown_8cpp_html_ac816a4ae8a29c156b90377041000929a"><div class="ttname"><a href="../../d9/d31/coin__change__topdown_8cpp.html#ac816a4ae8a29c156b90377041000929a">dynamic_programming::mincoins_topdown::mincoins</a></div><div class="ttdeci">int64_t mincoins(const T &amp;n, const std::vector&lt; T &gt; &amp;coins, const int16_t &amp;t, std::vector&lt; T &gt; dp)</div><div class="ttdoc">This implementation is for finding minimum number of coins .</div><div class="ttdef"><b>Definition:</b> coin_change_topdown.cpp:47</div></div>
<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>
<div class="ttc" id="amin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a></div><div class="ttdeci">T min(T... args)</div></div>
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<p>Test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; {</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <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"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> dp1(n1 + 1);</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; <a class="code" href="../../de/d85/decimal__to__roman__numeral_8cpp.html#a88203bd297e8405160c132faa1187780">fill</a>(dp1.begin(), dp1.end(), a1);</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; assert(dynamic_programming::mincoins_topdown::mincoins(n1, arr1, t1, dp1) ==</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; 3);</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed\n&quot;</span>;</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160;}</div>
<div class="fragment"><div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> {</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="comment">// example 1: number of coins=3 and minimum coins required=3(7,7,1)</span></div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keyword">const</span> int64_t n1 = 15;</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keyword">const</span> int8_t t1 = 3, a1 = 0;</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nTest 1...&quot;</span>;</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr1{1, 7, 10};</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> dp1(n1 + 1);</div>
<div class="line"><a id="l00081" name="l00081"></a><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>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> assert(dynamic_programming::mincoins_topdown::mincoins(n1, arr1, t1, dp1) ==</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> 3);</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Passed\n&quot;</span>;</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span>}</div>
<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>
<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> decimal_to_roman_numeral.cpp:15</div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; int64_t &gt;</a></div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
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