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<h1 id="151">15.1 &nbsp; 탐욕 알고리즘<a class="headerlink" href="#151" title="고유 링크">&para;</a></h1>
<p><u>탐욕 알고리즘(greedy algorithm)</u>은 최적화 문제를 푸는 대표적인 알고리즘이다. 매 결정 단계에서 현재 가장 좋아 보이는 선택, 즉 국소적으로 최적인 결정을 탐욕적으로 내려 전역 최적해를 얻으려는 것이 기본 아이디어다. 간결하고 효율적이어서 많은 실제 문제에 널리 쓰인다.</p>
<p>탐욕 알고리즘과 동적 계획법은 모두 최적화 문제에 자주 사용한다. 최적 부분 구조에 의존한다는 공통점 등이 있지만 작동 원리는 다르다.</p>
<ul>
<li>동적 계획법은 이전 단계의 모든 결정을 바탕으로 현재 결정을 고려하고, 과거 부분 문제의 해로 현재 부분 문제의 해를 구성한다.</li>
<li>탐욕 알고리즘은 과거 결정을 고려하지 않고 계속 앞으로 나아가며 탐욕적으로 선택한다. 문제의 범위를 점차 줄여 해결될 때까지 진행한다.</li>
</ul>
<p>먼저 '동전 교환' 예제로 탐욕 알고리즘의 원리를 알아보자. '무한 배낭 문제' 절에서 소개한 문제라 익숙할 것이다.</p>
<div class="admonition question">
<p class="admonition-title">문제</p>
<p>동전 <span class="arithmatex">\(n\)</span> 종류가 주어지며 <span class="arithmatex">\(i\)</span> 번째 동전의 액면가는 <span class="arithmatex">\(coins[i - 1]\)</span>이고 목표 금액은 <span class="arithmatex">\(amt\)</span>다. 각 종류의 동전을 반복해서 선택할 수 있을 때 목표 금액을 만드는 최소 동전 수를 구하라. 만들 수 없다면 <span class="arithmatex">\(-1\)</span>을 반환하라.</p>
</div>
<p>이 문제에서 사용하는 탐욕 전략은 아래 그림(15-1)과 같다. 주어진 목표 금액에 대해 <strong>그 금액을 넘지 않으면서 가장 가까운 액면가의 동전을 탐욕적으로 고르고</strong>, 목표 금액을 만들 때까지 반복한다.</p>
<p><img alt="동전 교환의 탐욕 전략" class="animation-figure" src="../greedy_algorithm.assets/coin_change_greedy_strategy.png" /></p>
<p align="center"> 그림 15-1 &nbsp; 동전 교환의 탐욕 전략 </p>
<p>구현 코드는 다음과 같다.</p>
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<div class="highlight"><span class="filename">coin_change_greedy.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_greedy</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">amt</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="sd">"""동전 교환: 탐욕"""</span>
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="c1"># coins 리스트가 정렬되어 있다고 가정한다</span>
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="n">i</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">coins</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="c1"># 남은 금액이 없을 때까지 탐욕적 선택을 반복한다</span>
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="k">while</span> <span class="n">amt</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="c1"># 남은 금액보다 작으면서 가장 가까운 금액의 동전을 찾는다</span>
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="k">while</span> <span class="n">i</span> <span class="o">&gt;</span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">amt</span><span class="p">:</span>
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="n">i</span> <span class="o">-=</span> <span class="mi">1</span>
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a> <span class="c1"># coins[i]를 선택한다</span>
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a> <span class="n">amt</span> <span class="o">-=</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a> <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a> <span class="c1"># 가능한 방법을 찾지 못하면 -1을 반환한다</span>
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a> <span class="k">return</span> <span class="n">count</span> <span class="k">if</span> <span class="n">amt</span> <span class="o">==</span> <span class="mi">0</span> <span class="k">else</span> <span class="o">-</span><span class="mi">1</span>
</code></pre></div>
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<div class="highlight"><span class="filename">coin_change_greedy.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 동전 교환: 탐욕 */</span>
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeGreedy</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w"> </span><span class="c1">// coins 리스트가 정렬되어 있다고 가정한다</span>
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w"> </span><span class="c1">// 남은 금액이 없을 때까지 탐욕적 선택을 반복한다</span>
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w"> </span><span class="c1">// 남은 금액보다 작으면서 가장 가까운 금액의 동전을 찾는다</span>
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">;</span>
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w"> </span><span class="c1">// coins[i]를 선택한다</span>
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w"> </span><span class="c1">// 가능한 방법을 찾지 못하면 -1을 반환한다</span>
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">coin_change_greedy.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 동전 교환: 탐욕 */</span>
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeGreedy</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w"> </span><span class="c1">// coins 리스트가 정렬되어 있다고 가정한다</span>
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w"> </span><span class="c1">// 남은 금액이 없을 때까지 탐욕적 선택을 반복한다</span>
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w"> </span><span class="c1">// 남은 금액보다 작으면서 가장 가까운 금액의 동전을 찾는다</span>
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">;</span>
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w"> </span><span class="c1">// coins[i]를 선택한다</span>
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w"> </span><span class="c1">// 가능한 방법을 찾지 못하면 -1을 반환한다</span>
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">coin_change_greedy.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 동전 교환: 탐욕 */</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">CoinChangeGreedy</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="c1">// coins 리스트가 정렬되어 있다고 가정한다</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="c1">// 남은 금액이 없을 때까지 탐욕적 선택을 반복한다</span>
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="c1">// 남은 금액보다 작으면서 가장 가까운 금액의 동전을 찾는다</span>
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">;</span>
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w"> </span><span class="c1">// coins[i]를 선택한다</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w"> </span><span class="c1">// 가능한 방법을 찾지 못하면 -1을 반환한다</span>
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">coin_change_greedy.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 동전 교환: 탐욕 */</span>
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">coinChangeGreedy</span><span class="p">(</span><span class="nx">coins</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w"> </span><span class="c1">// coins 리스트가 정렬되어 있다고 가정한다</span>
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">coins</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="c1">// 남은 금액이 없을 때까지 탐욕적 선택을 반복한다</span>
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="c1">// 남은 금액보다 작으면서 가장 가까운 금액의 동전을 찾는다</span>
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w"> </span><span class="nx">i</span><span class="o">--</span>
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w"> </span><span class="c1">// coins[i]를 선택한다</span>
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span>
<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w"> </span><span class="c1">// 가능한 방법을 찾지 못하면 -1을 반환한다</span>
<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">coin_change_greedy.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 동전 교환: 탐욕 */</span>
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">coinChangeGreedy</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">],</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w"> </span><span class="c1">// coins 리스트가 정렬되어 있다고 가정한다</span>
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="bp">count</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">amt</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">amt</span>
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w"> </span><span class="c1">// 남은 금액이 없을 때까지 탐욕적 선택을 반복한다</span>
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w"> </span><span class="c1">// 남은 금액보다 작으면서 가장 가까운 금액의 동전을 찾는다</span>
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w"> </span><span class="c1">// coins[i]를 선택한다</span>
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w"> </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w"> </span><span class="c1">// 가능한 방법을 찾지 못하면 -1을 반환한다</span>
<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">?</span><span class="w"> </span><span class="bp">count</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">coin_change_greedy.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 동전 교환: 탐욕 */</span>
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">coinChangeGreedy</span><span class="p">(</span><span class="nx">coins</span><span class="p">,</span><span class="w"> </span><span class="nx">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w"> </span><span class="c1">// coins 배열이 정렬되어 있다고 가정한다</span>
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coins</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w"> </span><span class="c1">// 남은 금액이 없을 때까지 탐욕적 선택을 반복한다</span>
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w"> </span><span class="c1">// 남은 금액보다 작으면서 가장 가까운 금액의 동전을 찾는다</span>
<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">;</span>
<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w"> </span><span class="c1">// coins[i]를 선택한다</span>
<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w"> </span><span class="c1">// 가능한 방법을 찾지 못하면 -1을 반환한다</span>
<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">coin_change_greedy.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 동전 교환: 탐욕 */</span>
<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">coinChangeGreedy</span><span class="p">(</span><span class="nx">coins</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">amt</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w"> </span><span class="c1">// coins 배열이 정렬되어 있다고 가정한다</span>
<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coins</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w"> </span><span class="c1">// 남은 금액이 없을 때까지 탐욕적 선택을 반복한다</span>
<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w"> </span><span class="c1">// 남은 금액보다 작으면서 가장 가까운 금액의 동전을 찾는다</span>
<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">;</span>
<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w"> </span><span class="c1">// coins[i]를 선택한다</span>
<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="nx">coins</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w"> </span><span class="c1">// 가능한 방법을 찾지 못하면 -1을 반환한다</span>
<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">amt</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">coin_change_greedy.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 동전 교환: 탐욕 */</span>
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">coinChangeGreedy</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w"> </span><span class="c1">// coins 리스트가 정렬되어 있다고 가정한다</span>
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w"> </span><span class="c1">// 남은 금액이 없을 때까지 탐욕적 선택을 반복한다</span>
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w"> </span><span class="c1">// 남은 금액보다 작으면서 가장 가까운 금액의 동전을 찾는다</span>
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">;</span>
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w"> </span><span class="c1">// coins[i]를 선택한다</span>
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w"> </span><span class="c1">// 가능한 방법을 찾지 못하면 -1을 반환한다</span>
<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">;</span>
<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">coin_change_greedy.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 동전 교환: 탐욕 */</span>
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">coin_change_greedy</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w"> </span><span class="c1">// coins 리스트가 정렬되어 있다고 가정한다</span>
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w"> </span><span class="c1">// 남은 금액이 없을 때까지 탐욕적 선택을 반복한다</span>
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w"> </span><span class="c1">// 남은 금액보다 작으면서 가장 가까운 금액의 동전을 찾는다</span>
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w"> </span><span class="c1">// coins[i]를 선택한다</span>
<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w"> </span><span class="c1">// 가능한 방법을 찾지 못하면 -1을 반환한다</span>
<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w"> </span><span class="n">count</span>
<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">coin_change_greedy.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 동전 교환: 탐욕 */</span>
<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeGreedy</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w"> </span><span class="c1">// coins 리스트가 정렬되어 있다고 가정한다</span>
<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w"> </span><span class="c1">// 남은 금액이 없을 때까지 탐욕적 선택을 반복한다</span>
<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w"> </span><span class="c1">// 남은 금액보다 작으면서 가장 가까운 금액의 동전을 찾는다</span>
<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">;</span>
<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w"> </span><span class="c1">// coins[i]를 선택한다</span>
<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w"> </span><span class="c1">// 가능한 방법을 찾지 못하면 -1을 반환한다</span>
<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">coin_change_greedy.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 동전 교환: 탐욕 */</span>
<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">coinChangeGreedy</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w"> </span><span class="c1">// coins 리스트가 정렬되어 있다고 가정한다</span>
<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">am</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span>
<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span>
<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span>
<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w"> </span><span class="c1">// 남은 금액이 없을 때까지 탐욕적 선택을 반복한다</span>
<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">am</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w"> </span><span class="c1">// 남은 금액보다 작으면서 가장 가까운 금액의 동전을 찾는다</span>
<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">am</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w"> </span><span class="n">i</span><span class="o">--</span>
<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w"> </span><span class="c1">// coins[i]를 선택한다</span>
<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w"> </span><span class="n">am</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span>
<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w"> </span><span class="c1">// 가능한 방법을 찾지 못하면 -1을 반환한다</span>
<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">am</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="o">-</span><span class="m">1</span>
<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">coin_change_greedy.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 동전 교환: 탐욕 ###</span>
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_greedy</span><span class="p">(</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span>
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="c1"># coins 리스트가 정렬되어 있다고 가정한다</span>
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="o">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="c1"># 남은 금액이 없을 때까지 탐욕적 선택을 반복한다</span>
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="c1"># 남은 금액보다 작으면서 가장 가까운 금액의 동전을 찾는다</span>
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">amt</span>
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w"> </span><span class="c1"># coins[i]를 선택한다</span>
<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w"> </span><span class="c1"># 가능한 방법을 찾지 못하면 -1을 반환한다</span>
<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="k">end</span>
</code></pre></div>
</div>
</div>
</div>
<details class="pythontutor">
<summary>코드 시각화</summary>
<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" title="코드 시각화" src="https://pythontutor.com/iframe-embed.html#code=def%20coin_change_greedy%28coins%3A%20list%5Bint%5D,%20amt%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%EB%8F%99%EC%A0%84%20%EA%B5%90%ED%99%98%3A%20%ED%83%90%EC%9A%95%22%22%22%0A%20%20%20%20%23%20coins%20%EB%A6%AC%EC%8A%A4%ED%8A%B8%EA%B0%80%20%EC%A0%95%EB%A0%AC%EB%90%98%EC%96%B4%20%EC%9E%88%EB%8B%A4%EA%B3%A0%20%EA%B0%80%EC%A0%95%ED%95%9C%EB%8B%A4%0A%20%20%20%20i%20%3D%20len%28coins%29%20-%201%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%EB%82%A8%EC%9D%80%20%EA%B8%88%EC%95%A1%EC%9D%B4%20%EC%97%86%EC%9D%84%20%EB%95%8C%EA%B9%8C%EC%A7%80%20%ED%83%90%EC%9A%95%EC%A0%81%20%EC%84%A0%ED%83%9D%EC%9D%84%20%EB%B0%98%EB%B3%B5%ED%95%9C%EB%8B%A4%0A%20%20%20%20while%20amt%20%3E%200%3A%0A%20%20%20%20%20%20%20%20%23%20%EB%82%A8%EC%9D%80%20%EA%B8%88%EC%95%A1%EB%B3%B4%EB%8B%A4%20%EC%9E%91%EC%9C%BC%EB%A9%B4%EC%84%9C%20%EA%B0%80%EC%9E%A5%20%EA%B0%80%EA%B9%8C%EC%9A%B4%20%EA%B8%88%EC%95%A1%EC%9D%98%20%EB%8F%99%EC%A0%84%EC%9D%84%20%EC%B0%BE%EB%8A%94%EB%8B%A4%0A%20%20%20%20%20%20%20%20while%20i%20%3E%200%20and%20coins%5Bi%5D%20%3E%20amt%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20-%3D%201%0A%20%20%20%20%20%20%20%20%23%20coins%5Bi%5D%EB%A5%BC%20%EC%84%A0%ED%83%9D%ED%95%9C%EB%8B%A4%0A%20%20%20%20%20%20%20%20amt%20-%3D%20coins%5Bi%5D%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20%23%20%EA%B0%80%EB%8A%A5%ED%95%9C%20%EB%B0%A9%EB%B2%95%EC%9D%84%20%EC%B0%BE%EC%A7%80%20%EB%AA%BB%ED%95%98%EB%A9%B4%20-1%EC%9D%84%20%EB%B0%98%ED%99%98%ED%95%9C%EB%8B%A4%0A%20%20%20%20return%20count%20if%20amt%20%3D%3D%200%20else%20-1%0A%0A%0A%22%22%22%EC%8B%A4%ED%96%89%20%EC%BD%94%EB%93%9C%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%ED%83%90%EC%9A%95%3A%20%EC%A0%84%EC%97%AD%20%EC%B5%9C%EC%A0%81%ED%95%B4%EB%A5%BC%20%EC%B0%BE%EB%8A%94%20%EA%B2%83%EC%9D%B4%20%EB%B3%B4%EC%9E%A5%EB%90%9C%EB%8B%A4%0A%20%20%20%20coins%20%3D%20%5B1,%205,%2010,%2020,%2050,%20100%5D%0A%20%20%20%20amt%20%3D%20186%0A%20%20%20%20res%20%3D%20coin_change_greedy%28coins,%20amt%29%0A%20%20%20%20print%28f%22%5Cncoins%20%3D%20%7Bcoins%7D,%20amt%20%3D%20%7Bamt%7D%22%29%0A%20%20%20%20print%28f%22%EB%AA%A9%ED%91%9C%20%EA%B8%88%EC%95%A1%20%7Bamt%7D%EC%97%90%20%ED%95%84%EC%9A%94%ED%95%9C%20%EC%B5%9C%EC%86%8C%20%EB%8F%99%EC%A0%84%20%EA%B0%9C%EC%88%98%EB%8A%94%20%7Bres%7D%EA%B0%9C%EC%9D%B4%EB%8B%A4%22%29%0A%0A%20%20%20%20%23%20%ED%83%90%EC%9A%95%3A%20%EC%A0%84%EC%97%AD%20%EC%B5%9C%EC%A0%81%ED%95%B4%EB%A5%BC%20%EC%B0%BE%EB%8A%94%20%EA%B2%83%EC%9D%B4%20%EB%B3%B4%EC%9E%A5%EB%90%98%EC%A7%80%20%EC%95%8A%EB%8A%94%EB%8B%A4%0A%20%20%20%20coins%20%3D%20%5B1,%2020,%2050%5D%0A%20%20%20%20amt%20%3D%2060%0A%20%20%20%20res%20%3D%20coin_change_greedy%28coins,%20amt%29%0A%20%20%20%20print%28f%22%5Cncoins%20%3D%20%7Bcoins%7D,%20amt%20%3D%20%7Bamt%7D%22%29%0A%20%20%20%20print%28f%22%EB%AA%A9%ED%91%9C%20%EA%B8%88%EC%95%A1%20%7Bamt%7D%EC%97%90%20%ED%95%84%EC%9A%94%ED%95%9C%20%EC%B5%9C%EC%86%8C%20%EB%8F%99%EC%A0%84%20%EA%B0%9C%EC%88%98%EB%8A%94%20%7Bres%7D%EA%B0%9C%EC%9D%B4%EB%8B%A4%22%29%0A%20%20%20%20print%28f%22%EC%8B%A4%EC%A0%9C%EB%A1%9C%20%ED%95%84%EC%9A%94%ED%95%9C%20%EC%B5%9C%EC%86%8C%20%EA%B0%9C%EC%88%98%EB%8A%94%203%EA%B0%9C%EC%9D%B4%EB%A9%B0,%2020%20%2B%2020%20%2B%2020%EC%9D%B4%EB%8B%A4%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20coin_change_greedy%28coins%3A%20list%5Bint%5D,%20amt%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%EB%8F%99%EC%A0%84%20%EA%B5%90%ED%99%98%3A%20%ED%83%90%EC%9A%95%22%22%22%0A%20%20%20%20%23%20coins%20%EB%A6%AC%EC%8A%A4%ED%8A%B8%EA%B0%80%20%EC%A0%95%EB%A0%AC%EB%90%98%EC%96%B4%20%EC%9E%88%EB%8B%A4%EA%B3%A0%20%EA%B0%80%EC%A0%95%ED%95%9C%EB%8B%A4%0A%20%20%20%20i%20%3D%20len%28coins%29%20-%201%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20%23%20%EB%82%A8%EC%9D%80%20%EA%B8%88%EC%95%A1%EC%9D%B4%20%EC%97%86%EC%9D%84%20%EB%95%8C%EA%B9%8C%EC%A7%80%20%ED%83%90%EC%9A%95%EC%A0%81%20%EC%84%A0%ED%83%9D%EC%9D%84%20%EB%B0%98%EB%B3%B5%ED%95%9C%EB%8B%A4%0A%20%20%20%20while%20amt%20%3E%200%3A%0A%20%20%20%20%20%20%20%20%23%20%EB%82%A8%EC%9D%80%20%EA%B8%88%EC%95%A1%EB%B3%B4%EB%8B%A4%20%EC%9E%91%EC%9C%BC%EB%A9%B4%EC%84%9C%20%EA%B0%80%EC%9E%A5%20%EA%B0%80%EA%B9%8C%EC%9A%B4%20%EA%B8%88%EC%95%A1%EC%9D%98%20%EB%8F%99%EC%A0%84%EC%9D%84%20%EC%B0%BE%EB%8A%94%EB%8B%A4%0A%20%20%20%20%20%20%20%20while%20i%20%3E%200%20and%20coins%5Bi%5D%20%3E%20amt%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20-%3D%201%0A%20%20%20%20%20%20%20%20%23%20coins%5Bi%5D%EB%A5%BC%20%EC%84%A0%ED%83%9D%ED%95%9C%EB%8B%A4%0A%20%20%20%20%20%20%20%20amt%20-%3D%20coins%5Bi%5D%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20%23%20%EA%B0%80%EB%8A%A5%ED%95%9C%20%EB%B0%A9%EB%B2%95%EC%9D%84%20%EC%B0%BE%EC%A7%80%20%EB%AA%BB%ED%95%98%EB%A9%B4%20-1%EC%9D%84%20%EB%B0%98%ED%99%98%ED%95%9C%EB%8B%A4%0A%20%20%20%20return%20count%20if%20amt%20%3D%3D%200%20else%20-1%0A%0A%0A%22%22%22%EC%8B%A4%ED%96%89%20%EC%BD%94%EB%93%9C%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%ED%83%90%EC%9A%95%3A%20%EC%A0%84%EC%97%AD%20%EC%B5%9C%EC%A0%81%ED%95%B4%EB%A5%BC%20%EC%B0%BE%EB%8A%94%20%EA%B2%83%EC%9D%B4%20%EB%B3%B4%EC%9E%A5%EB%90%9C%EB%8B%A4%0A%20%20%20%20coins%20%3D%20%5B1,%205,%2010,%2020,%2050,%20100%5D%0A%20%20%20%20amt%20%3D%20186%0A%20%20%20%20res%20%3D%20coin_change_greedy%28coins,%20amt%29%0A%20%20%20%20print%28f%22%5Cncoins%20%3D%20%7Bcoins%7D,%20amt%20%3D%20%7Bamt%7D%22%29%0A%20%20%20%20print%28f%22%EB%AA%A9%ED%91%9C%20%EA%B8%88%EC%95%A1%20%7Bamt%7D%EC%97%90%20%ED%95%84%EC%9A%94%ED%95%9C%20%EC%B5%9C%EC%86%8C%20%EB%8F%99%EC%A0%84%20%EA%B0%9C%EC%88%98%EB%8A%94%20%7Bres%7D%EA%B0%9C%EC%9D%B4%EB%8B%A4%22%29%0A%0A%20%20%20%20%23%20%ED%83%90%EC%9A%95%3A%20%EC%A0%84%EC%97%AD%20%EC%B5%9C%EC%A0%81%ED%95%B4%EB%A5%BC%20%EC%B0%BE%EB%8A%94%20%EA%B2%83%EC%9D%B4%20%EB%B3%B4%EC%9E%A5%EB%90%98%EC%A7%80%20%EC%95%8A%EB%8A%94%EB%8B%A4%0A%20%20%20%20coins%20%3D%20%5B1,%2020,%2050%5D%0A%20%20%20%20amt%20%3D%2060%0A%20%20%20%20res%20%3D%20coin_change_greedy%28coins,%20amt%29%0A%20%20%20%20print%28f%22%5Cncoins%20%3D%20%7Bcoins%7D,%20amt%20%3D%20%7Bamt%7D%22%29%0A%20%20%20%20print%28f%22%EB%AA%A9%ED%91%9C%20%EA%B8%88%EC%95%A1%20%7Bamt%7D%EC%97%90%20%ED%95%84%EC%9A%94%ED%95%9C%20%EC%B5%9C%EC%86%8C%20%EB%8F%99%EC%A0%84%20%EA%B0%9C%EC%88%98%EB%8A%94%20%7Bres%7D%EA%B0%9C%EC%9D%B4%EB%8B%A4%22%29%0A%20%20%20%20print%28f%22%EC%8B%A4%EC%A0%9C%EB%A1%9C%20%ED%95%84%EC%9A%94%ED%95%9C%20%EC%B5%9C%EC%86%8C%20%EA%B0%9C%EC%88%98%EB%8A%94%203%EA%B0%9C%EC%9D%B4%EB%A9%B0,%2020%20%2B%2020%20%2B%2020%EC%9D%B4%EB%8B%A4%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=5&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">전체 화면 &gt;</a></div></p>
</details>
<p>'정말 간결하다!'라는 감탄이 나올 만하다. 탐욕 알고리즘은 약 열 줄의 코드만으로 동전 교환 문제를 해결했다.</p>
<h2 id="1511">15.1.1 &nbsp; 탐욕 알고리즘의 장점과 한계<a class="headerlink" href="#1511" title="고유 링크">&para;</a></h2>
<p><strong>탐욕 알고리즘은 연산이 직접적이고 구현이 간단할 뿐 아니라 보통 효율도 매우 높다</strong>. 위 코드에서 최소 액면가를 <span class="arithmatex">\(\min(coins)\)</span>라고 하면 탐욕적 선택은 최대 <span class="arithmatex">\(amt / \min(coins)\)</span> 번 반복하므로 시간 복잡도는 <span class="arithmatex">\(O(amt / \min(coins))\)</span>이다. 동적 계획법의 <span class="arithmatex">\(O(n \times amt)\)</span>보다 한 차수 낮다.</p>
<p>하지만 <strong>일부 동전 액면가 조합에서는 최적해를 찾지 못한다</strong>. 아래 그림(15-2)은 두 예를 보여 준다.</p>
<ul>
<li><strong>성립 예 <span class="arithmatex">\(coins = [1, 5, 10, 20, 50, 100]\)</span></strong>: 이 동전 조합에서는 어떤 <span class="arithmatex">\(amt\)</span>에 대해서도 탐욕 알고리즘이 최적해를 찾는다.</li>
<li><strong>반례 <span class="arithmatex">\(coins = [1, 20, 50]\)</span></strong>: <span class="arithmatex">\(amt = 60\)</span>이면 탐욕 알고리즘은 <span class="arithmatex">\(50 + 1 \times 10\)</span>으로 동전 <span class="arithmatex">\(11\)</span> 개를 고른다. 하지만 동적 계획법은 <span class="arithmatex">\(20 + 20 + 20\)</span>이라는 최적해를 찾아 <span class="arithmatex">\(3\)</span> 개만 사용한다.</li>
<li><strong>반례 <span class="arithmatex">\(coins = [1, 49, 50]\)</span></strong>: <span class="arithmatex">\(amt = 98\)</span>이면 탐욕 알고리즘은 <span class="arithmatex">\(50 + 1 \times 48\)</span>로 동전 <span class="arithmatex">\(49\)</span> 개를 고른다. 하지만 동적 계획법은 <span class="arithmatex">\(49 + 49\)</span>라는 최적해를 찾아 <span class="arithmatex">\(2\)</span> 개만 사용한다.</li>
</ul>
<p><img alt="탐욕 알고리즘이 최적해를 찾지 못하는 예" class="animation-figure" src="../greedy_algorithm.assets/coin_change_greedy_vs_dp.png" /></p>
<p align="center"> 그림 15-2 &nbsp; 탐욕 알고리즘이 최적해를 찾지 못하는 예 </p>
<p>즉, 동전 교환에서 탐욕 알고리즘은 전역 최적해를 보장하지 못하고 매우 나쁜 해를 찾을 수도 있다. 이 문제는 동적 계획법으로 푸는 편이 더 적합하다.</p>
<p>일반적으로 탐욕 알고리즘을 적용하는 상황은 다음 두 가지다.</p>
<ol>
<li><strong>최적해를 보장할 수 있다</strong>: 보통 백트래킹이나 동적 계획법보다 효율적이므로 이런 경우에는 탐욕 알고리즘이 가장 좋은 선택인 경우가 많다.</li>
<li><strong>최적해에 가까운 해를 찾을 수 있다</strong>: 이 경우에도 탐욕 알고리즘을 쓸 수 있다. 복잡한 문제에서는 전역 최적해를 찾기 매우 어려우므로, 효율적으로 차선의 해를 찾는 것만으로도 유용하다.</li>
</ol>
<h2 id="1512">15.1.2 &nbsp; 탐욕 알고리즘의 특성<a class="headerlink" href="#1512" title="고유 링크">&para;</a></h2>
<p>그렇다면 어떤 문제가 탐욕 알고리즘에 적합할까? 다시 말해 어떤 경우에 최적해를 보장할 수 있을까?</p>
<p>탐욕 알고리즘은 동적 계획법보다 적용 조건이 엄격하며, 주로 다음 두 성질에 주목한다.</p>
<ul>
<li><strong>탐욕적 선택 속성</strong>: 국소 최적 선택이 항상 전역 최적해로 이어져야만 탐욕 알고리즘이 최적해를 보장할 수 있다.</li>
<li><strong>최적 부분 구조</strong>: 원래 문제의 최적해가 부분 문제의 최적해를 포함한다.</li>
</ul>
<p>최적 부분 구조는 '동적 계획법' 장에서 설명했으므로 반복하지 않는다. 일부 문제는 최적 부분 구조가 뚜렷하지 않아도 탐욕 알고리즘으로 해결할 수 있다는 점을 알아 두자.</p>
<p>여기서는 탐욕적 선택 속성을 판단하는 방법을 주로 살펴본다. 설명은 간단해 보이지만 <strong>많은 문제에서 이 속성을 증명하기는 쉽지 않다</strong>.</p>
<p>예를 들어 동전 교환에서는 반례로 탐욕적 선택 속성을 부정하기는 쉽지만 증명하기는 어렵다. <strong>어떤 조건을 만족하는 동전 조합을 탐욕 알고리즘으로 풀 수 있는가</strong>라는 질문에는 직관이나 사례를 바탕으로 애매한 답을 내놓기 쉽고, 엄밀한 수학적 증명을 제시하기는 어렵다.</p>
<div class="admonition quote">
<p class="admonition-title">참고 문헌</p>
<p>어떤 동전 조합에 대해 탐욕 알고리즘이 모든 금액의 최적해를 찾을 수 있는지 판단하는 <span class="arithmatex">\(O(n^3)\)</span> 알고리즘을 제시한 논문이 있다.</p>
<p>Pearson, D. A polynomial-time algorithm for the change-making problem[J]. Operations Research Letters, 2005, 33(3): 231-234.</p>
</div>
<h2 id="1513">15.1.3 &nbsp; 탐욕 알고리즘의 문제 해결 단계<a class="headerlink" href="#1513" title="고유 링크">&para;</a></h2>
<p>탐욕 문제의 풀이 과정은 대체로 다음 세 단계다.</p>
<ol>
<li><strong>문제 분석</strong>: 상태 정의, 최적화 목표, 제약 조건 등 문제의 특성을 정리하고 이해한다. 백트래킹과 동적 계획법에서도 필요한 단계다.</li>
<li><strong>탐욕 전략 결정</strong>: 매 단계에서 어떻게 탐욕적으로 선택할지 정한다. 각 단계에서 문제 크기를 줄여 최종적으로 전체 문제를 해결할 수 있어야 한다.</li>
<li><strong>정확성 증명</strong>: 보통 탐욕적 선택 속성과 최적 부분 구조를 증명해야 한다. 귀납법이나 귀류법 같은 수학적 증명이 필요할 수 있다.</li>
</ol>
<p>탐욕 전략을 정하는 것이 핵심 단계지만, 다음 이유로 쉽지 않을 수 있다.</p>
<ul>
<li><strong>문제마다 탐욕 전략이 크게 다르다</strong>. 많은 문제는 전략이 비교적 명확하여 대략적인 생각과 시도만으로 찾을 수 있다. 반면 복잡한 문제에서는 전략이 잘 드러나지 않아 문제 풀이 경험과 알고리즘 역량이 크게 요구된다.</li>
<li><strong>일부 탐욕 전략은 그럴듯해 보이지만 함정이 있다</strong>. 자신 있게 전략을 설계하고 코드를 작성해 제출해도 일부 테스트를 통과하지 못할 수 있다. 전략이 '부분적으로만 옳기' 때문이다. 앞에서 본 동전 교환이 대표적인 사례다.</li>
</ul>
<p>정확성을 보장하려면 탐욕 전략을 엄밀히 증명해야 하며, <strong>보통 귀류법이나 수학적 귀납법을 사용한다</strong>.</p>
<p>하지만 정확성 증명 자체도 쉽지 않을 수 있다. 실마리가 없으면 보통 테스트 사례로 코드를 디버깅하면서 탐욕 전략을 조금씩 수정하고 검증한다.</p>
<h2 id="1514">15.1.4 &nbsp; 대표적인 탐욕 알고리즘 문제<a class="headerlink" href="#1514" title="고유 링크">&para;</a></h2>
<p>탐욕 알고리즘은 탐욕적 선택 속성과 최적 부분 구조를 만족하는 최적화 문제에 자주 사용한다. 대표적인 예는 다음과 같다.</p>
<ul>
<li><strong>동전 거스름돈 문제</strong>: 일부 동전 조합에서는 탐욕 알고리즘이 항상 최적해를 얻는다.</li>
<li><strong>구간 스케줄링 문제</strong>: 각 작업이 일정 시간 구간에 걸쳐 진행될 때 가능한 한 많은 작업을 완료하는 것이 목표다. 매번 가장 일찍 끝나는 작업을 고르면 최적해를 얻을 수 있다.</li>
<li><strong>분할 가능한 배낭 문제</strong>: 물건들과 적재 용량이 주어졌을 때 총무게가 용량을 넘지 않으면서 총가치가 최대가 되도록 물건을 고른다. 매번 무게 대비 가치의 비율(가치 / 무게)이 가장 높은 물건을 고르면 일부 경우에 최적해를 얻을 수 있다.</li>
<li><strong>주식 매매 문제</strong>: 주가의 과거 기록이 주어졌을 때 여러 번 매매하여 최대 이익을 구한다. 단, 이미 주식을 보유하고 있으면 팔기 전에는 다시 살 수 없다.</li>
<li><strong>허프먼 코딩</strong>: 무손실 데이터 압축에 쓰이는 탐욕 알고리즘이다. 매번 빈도가 가장 낮은 두 노드를 합쳐 허프먼 트리를 만들면, 최종 트리의 가중 경로 길이(부호 길이)가 최소가 된다.</li>
<li><strong>Dijkstra 알고리즘</strong>: 모든 간선 가중치가 음이 아닌 그래프에서 주어진 시작 정점부터 나머지 정점까지의 최단 경로를 구하는 탐욕 알고리즘이다.</li>
</ul>
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