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<h1 id="126">12.6 &nbsp; 연습 문제<a class="headerlink" href="#126" title="고유 링크">&para;</a></h1>
<h2 id="1261">12.6.1 &nbsp; 개념 확인<a class="headerlink" href="#1261" title="고유 링크">&para;</a></h2>
<h3 id="1">1. &nbsp; 어떤 작업에 분할 정복이 적합한가<a class="headerlink" href="#1" title="고유 링크">&para;</a></h3>
<p>한 학생이 ‘먼저 둘로 나누고, 각각 해결한 뒤, 결과를 합치는’ 방식으로 다음 작업을 수행하려 한다.
각 작업이 ‘분할 정복에 적합함’, ‘분할 정복이 가능하지만 전체 작업량은 줄어들지 않음’, ‘두 부분을 독립적으로 해결할 수 없음’ 중 어디에 해당하는지 판단하고 이유를 설명하라.</p>
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<li>정렬되지 않은 배열을 정렬한다.</li>
<li>배열의 최댓값을 구한다.</li>
<li>일련의 스택 연산 <code>push(x)</code>, <code>pop()</code>을 순서대로 실행하고 각 <code>pop()</code>에서 얻은 원소를 출력한다.</li>
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<summary>참고 답안</summary>
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<li>적합함: 반으로 나눈 뒤 두 부분을 독립적으로 정렬하고, <span class="arithmatex">\(O(n)\)</span> 시간에 병합한다. 이것이 바로 병합 정렬이다.</li>
<li>분할 정복이 가능하지만 전체 작업량은 줄어들지 않음: 왼쪽과 오른쪽을 합치면 여전히 <span class="arithmatex">\(n\)</span>개 원소를 모두 확인해야 하므로,
직접 순회하는 것과 마찬가지로 <span class="arithmatex">\(O(n)\)</span> 시간이 든다.</li>
<li>두 부분을 독립적으로 해결할 수 없음: 후반부를 시작할 때의 스택 내용은 전반부의 실행 결과에 따라 달라진다.
따라서 서로의 결과를 모르는 상태에서 두 부분을 독립적으로 완료할 수 없다.</li>
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<h3 id="2">2. &nbsp; 빠른 거듭제곱은 계산을 어떻게 줄이는가<a class="headerlink" href="#2" title="고유 링크">&para;</a></h3>
<p>다음 재귀 함수는 분할 정복으로 <span class="arithmatex">\(x^n\)</span>을 계산한다.</p>
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<div class="highlight"><span class="filename">fast_power.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">fast_pow</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">n</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">"""빠른 거듭제곱"""</span>
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="k">return</span> <span class="mi">1</span>
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="n">half</span> <span class="o">=</span> <span class="n">fast_pow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">n</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span>
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="k">if</span> <span class="n">n</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="k">return</span> <span class="n">half</span> <span class="o">*</span> <span class="n">half</span>
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="k">return</span> <span class="n">half</span> <span class="o">*</span> <span class="n">half</span> <span class="o">*</span> <span class="n">x</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">fast_power.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 빠른 거듭제곱 */</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">fastPow</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</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="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</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-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w"> </span><span class="k">return</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="p">}</span>
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fastPow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">==</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="k">return</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">half</span><span class="p">;</span>
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><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="k">return</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">x</span><span class="p">;</span>
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">fast_power.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 빠른 거듭제곱 */</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">fastPow</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</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="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</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-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w"> </span><span class="k">return</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="p">}</span>
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fastPow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">==</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="k">return</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">half</span><span class="p">;</span>
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><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="k">return</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">x</span><span class="p">;</span>
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">fast_power.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 빠른 거듭제곱 */</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">FastPow</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</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="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</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-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="k">return</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="p">}</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">FastPow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">==</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="k">return</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">half</span><span class="p">;</span>
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><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="k">return</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">x</span><span class="p">;</span>
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">fast_power.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 빠른 거듭제곱 */</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">fastPow</span><span class="p">(</span><span class="nx">x</span><span class="p">,</span><span class="w"> </span><span class="nx">n</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="k">if</span><span class="w"> </span><span class="nx">n</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-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w"> </span><span class="k">return</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="p">}</span>
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="nx">half</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">fastPow</span><span class="p">(</span><span class="nx">x</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span>
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="o">%</span><span class="mi">2</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-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">half</span>
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><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="k">return</span><span class="w"> </span><span class="nx">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">x</span>
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">fast_power.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 빠른 거듭제곱 */</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">fastPow</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">,</span><span class="w"> </span><span class="n">n</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="k">if</span><span class="w"> </span><span class="n">n</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>
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w"> </span><span class="k">return</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="p">}</span>
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nv">half</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">fastPow</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">2</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>
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">half</span>
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">x</span>
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">fast_power.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 빠른 거듭제곱 */</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">fastPow</span><span class="p">(</span><span class="nx">x</span><span class="p">,</span><span class="w"> </span><span class="nx">n</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="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</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-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w"> </span><span class="k">return</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="p">}</span>
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">half</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">fastPow</span><span class="p">(</span><span class="nx">x</span><span class="p">,</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">));</span>
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">===</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="k">return</span><span class="w"> </span><span class="nx">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">half</span><span class="p">;</span>
<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><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="k">return</span><span class="w"> </span><span class="nx">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">x</span><span class="p">;</span>
<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">fast_power.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 빠른 거듭제곱 */</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">fastPow</span><span class="p">(</span><span class="nx">x</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">n</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="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</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-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w"> </span><span class="k">return</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="p">}</span>
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">half</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">fastPow</span><span class="p">(</span><span class="nx">x</span><span class="p">,</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">));</span>
<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">===</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="k">return</span><span class="w"> </span><span class="nx">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">half</span><span class="p">;</span>
<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><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="k">return</span><span class="w"> </span><span class="nx">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">x</span><span class="p">;</span>
<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">fast_power.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 빠른 거듭제곱 */</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">fastPow</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</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="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</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="p">{</span>
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w"> </span><span class="k">return</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="p">}</span>
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fastPow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="p">);</span>
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="m">2</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="p">{</span>
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">half</span><span class="p">;</span>
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><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="k">return</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">x</span><span class="p">;</span>
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">fast_power.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 빠른 거듭제곱 */</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">fast_pow</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">n</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="k">if</span><span class="w"> </span><span class="n">n</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-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w"> </span><span class="k">return</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="p">}</span>
<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fast_pow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">2</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-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">half</span><span class="p">;</span>
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><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">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">x</span>
<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">fast_power.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 빠른 거듭제곱 */</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">fastPow</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</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="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</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-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w"> </span><span class="k">return</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="p">}</span>
<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fastPow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">==</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="k">return</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">half</span><span class="p">;</span>
<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><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="k">return</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">x</span><span class="p">;</span>
<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">fast_power.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 빠른 거듭제곱 */</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">fastPow</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">n</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="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</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="p">{</span>
<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">1</span>
<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">half</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fastPow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="p">)</span>
<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="m">2</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="p">{</span>
<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">half</span>
<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">x</span>
<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">fast_power.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 빠른 거듭제곱 ###</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">fast_pow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">n</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="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fast_pow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="o">.</span><span class="n">even?</span>
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a>
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">half</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">x</span>
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="k">end</span>
</code></pre></div>
</div>
</div>
</div>
<p><code>x = 3</code>, <code>n = 5</code>로 설정하고 이 함수를 실행한다.</p>
<!-- numbered-subquestions -->
<ol>
<li>재귀 호출에서 매개변수 <code>n</code>은 차례대로 어떤 값이 되는가?</li>
<li>가장 깊은 호출부터 반환할 때 각 호출은 차례대로 어떤 값을 반환하는가?</li>
<li>곱셈 양쪽에서 같은 부분 문제를 한 번씩 호출하지 않고, 먼저 재귀 호출의 결과를 <code>half</code>에 저장하는 이유는 무엇인가?</li>
</ol>
<details class="success">
<summary>참고 답안</summary>
<ol>
<li>
<p>매개변수는 <code>5 → 2 → 1 → 0</code> 순으로 바뀐다. 종료 조건에 도달할 때까지 매번 지수를 절반으로 줄인다.</p>
</li>
<li>
<p><code>n = 0</code>이면 1을 반환한다. <code>n = 1</code>이면 <span class="arithmatex">\(1×1×3=3\)</span>을 반환한다.
<code>n = 2</code>이면 <span class="arithmatex">\(3×3=9\)</span>를, <code>n = 5</code>이면 <span class="arithmatex">\(9×9×3=243\)</span>을 반환한다.</p>
</li>
<li>
<p>곱셈 양쪽에서 같은 부분 문제를 한 번씩 호출하면 두 재귀 호출은 완전히 같은 계산을 수행한다.
먼저 결과를 <code>half</code>에 저장하면 각 단계에서 재귀 호출을 한 번만 하면 되고, 재귀 깊이는 대략 <span class="arithmatex">\(\log n\)</span>이다.
두 번 호출하면 같은 계산이 대량으로 반복된다.</p>
</li>
</ol>
</details>
<h3 id="3">3. &nbsp; 순회 결과에서 왼쪽 서브트리와 오른쪽 서브트리 나누기<a class="headerlink" href="#3" title="고유 링크">&para;</a></h3>
<p>중복된 노드가 없는 이진 트리의 전위 순회와 중위 순회 결과는 다음과 같다.</p>
<ul>
<li>전위 순회: <code>[A, B, D, E, C]</code></li>
<li>중위 순회: <code>[D, B, E, A, C]</code></li>
</ul>
<p>루트 노드 수준에서만 나누고, 더 깊이 재귀적으로 나누거나 트리 전체를 그릴 필요는 없다.</p>
<!-- numbered-subquestions -->
<ol>
<li>루트 노드는 무엇인가?</li>
<li>중위 순회에서 왼쪽 서브트리와 오른쪽 서브트리에 해당하는 구간은 각각 어디인가?</li>
<li>전위 순회에서 왼쪽 서브트리와 오른쪽 서브트리에 해당하는 구간은 각각 어디인가? 루트 노드의 직접적인 자식은 누구인가?</li>
</ol>
<details class="success">
<summary>참고 답안</summary>
<ol>
<li>
<p>전위 순회의 첫 번째 노드가 루트 노드이므로 루트는 <code>A</code>다.</p>
</li>
<li>
<p><code>A</code>를 기준으로 중위 순회가 두 부분으로 나뉜다. 왼쪽 서브트리는 <code>[D, B, E]</code>, 오른쪽 서브트리는 <code>[C]</code>다.</p>
</li>
<li>
<p>왼쪽 서브트리에 노드가 3개 있으므로 전위 순회에서 루트 노드 <code>A</code> 다음의 원소 3개가 왼쪽 서브트리에 속한다.
즉 <code>[B, D, E]</code>가 왼쪽 서브트리이고, 나머지 <code>[C]</code>가 오른쪽 서브트리다.
따라서 루트 노드의 왼쪽 자식은 <code>B</code>, 오른쪽 자식은 <code>C</code>다.</p>
</li>
</ol>
</details>
<h2 id="1262">12.6.2 &nbsp; 프로그래밍 연습<a class="headerlink" href="#1262" title="고유 링크">&para;</a></h2>
<h3 id="1_1">1. &nbsp; 빠른 거듭제곱<a class="headerlink" href="#1_1" title="고유 링크">&para;</a></h3>
<p>실수 <code>x</code>와 정수 <code>n</code>이 주어진다. 언어에서 제공하는 거듭제곱 함수를 호출하지 않고 <span class="arithmatex">\(x^n\)</span>을 계산하라.
재귀적인 분할 정복을 사용하여 매번 지수를 절반으로 줄이고, 이미 계산한 부분 문제의 결과를 재사용해야 한다.
이 문제에서는 <code>x = 0</code>인 경우를 포함하여 <span class="arithmatex">\(x^0=1\)</span>로 정한다. <code>n &lt; 0</code>일 때는 <code>x != 0</code>임이 보장되며, 답을 <span class="arithmatex">\((1/x)^{-n}\)</span>으로 바꾸어 구할 수 있다.</p>
<details class="tip">
<summary>풀이 힌트</summary>
<ol>
<li>n이 0이면 답은 1이다.</li>
<li>x의 n // 2제곱을 계산하여 half에 저장한다. 같은 재귀 호출을 두 번 하지 마라.</li>
<li>n &lt; 0이면 먼저 x를 1 / x로 바꾸고 n을 -n으로 바꾼다. C++이나 Java에서는 n을 먼저 64비트 정수로 변환하면 가장 작은 32비트 정수의 부호를 반대로 바꿀 때 발생하는 오버플로를 피할 수 있다.</li>
</ol>
</details>
<p><a class="rounded-button exercise-button" href="https://leetcode.com/problems/powx-n/" rel="noopener noreferrer" target="_blank">LeetCode</a></p>
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