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<h1 id="1112">11.12 &nbsp; 연습 문제<a class="headerlink" href="#1112" title="고유 링크">&para;</a></h1>
<h2 id="11121">11.12.1 &nbsp; 개념 확인<a class="headerlink" href="#11121" title="고유 링크">&para;</a></h2>
<h3 id="1">1. &nbsp; 선택 정렬과 버블 정렬의 처음 몇 회전<a class="headerlink" href="#1" title="고유 링크">&para;</a></h3>
<p>배열 <code>[4, 2, 5, 1, 3]</code>이 주어진다. 다음은 모두 오름차순으로 정렬한다.</p>
<!-- numbered-subquestions -->
<ol>
<li>선택 정렬의 첫 두 회전을 따라가며 각 회전이 끝난 뒤의 배열을 적고, 어느 위치가 확정되었는지 설명하라.</li>
<li>버블 정렬의 첫 회전을 따라가며 배열 상태와 교환 횟수를 적고, 어느 위치가 확정되었는지 설명하라.</li>
</ol>
<details class="success">
<summary>참고 답안</summary>
<ol>
<li>
<p>첫 두 회전은 다음과 같다.</p>
<table>
<thead>
<tr>
<th>회전</th>
<th>배열 상태</th>
<th>설명</th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td><code>[1, 2, 5, 4, 3]</code></td>
<td>가장 작은 원소 1을 첫 번째 원소와 교환</td>
</tr>
<tr>
<td>2</td>
<td><code>[1, 2, 5, 4, 3]</code></td>
<td>값 2가 이미 인덱스 1에 있으므로 교환할 필요 없음</td>
</tr>
</tbody>
</table>
<p>이때 앞의 두 위치는 확정되었으므로, 이후에는 <code>[5, 4, 3]</code>에서 계속 최솟값을 선택하면 된다.</p>
</li>
<li>
<p>이웃한 원소를 차례대로 비교한다. 4와 2는 교환하고, 4와 5는 교환하지 않으며, 5와 1을 교환한 뒤 5와 3을 교환한다.
결과는 <code>[2, 4, 1, 3, 5]</code>이고 총 3번 교환한다. 가장 큰 원소 5가 배열 끝으로 이동했으므로 마지막 위치가 확정되었다.</p>
</li>
</ol>
</details>
<h3 id="2">2. &nbsp; 값이 같은 원소의 순서가 달라지는가<a class="headerlink" href="#2" title="고유 링크">&para;</a></h3>
<p>배열 <span class="arithmatex">\([2_a, 2_b, 1]\)</span>에서 <span class="arithmatex">\(2_a\)</span>와 <span class="arithmatex">\(2_b\)</span>는 값이 같지만, 아래 첨자로 원래 순서를 표시했다.</p>
<!-- numbered-subquestions -->
<ol>
<li>선택 정렬의 첫 회전이 끝난 뒤의 배열을 적어 보자. <span class="arithmatex">\(2_a\)</span>와 <span class="arithmatex">\(2_b\)</span>의 상대적인 순서가 바뀌었는가?</li>
<li>버블 정렬의 첫 회전이 끝난 뒤의 배열을 적어 보자. <span class="arithmatex">\(2_a\)</span>와 <span class="arithmatex">\(2_b\)</span>의 상대적인 순서가 바뀌었는가?</li>
<li>앞의 두 결과를 바탕으로, 값이 같은 원소의 원래 순서를 유지하는 측면에서 두 정렬이 어떻게 다른지 설명하라.</li>
</ol>
<details class="success">
<summary>참고 답안</summary>
<ol>
<li>
<p>선택 정렬의 첫 회전에서는 가장 작은 원소 1을 골라 첫 원소 <span class="arithmatex">\(2_a\)</span>와 교환한다. 결과는
<span class="arithmatex">\([1, 2_b, 2_a]\)</span>다. <span class="arithmatex">\(2_a\)</span>가 <span class="arithmatex">\(2_b\)</span> 뒤로 옮겨졌으므로 두 원소의 상대적인 순서가 바뀌었다.</p>
</li>
<li>
<p>버블 정렬은 먼저 <span class="arithmatex">\(2_a\)</span>와 <span class="arithmatex">\(2_b\)</span>를 비교한다. 두 값이 같으므로 교환하지 않는다. 이어서 <span class="arithmatex">\(2_b\)</span>와 1을 비교하여 교환한다.
첫 회전이 끝나면 <span class="arithmatex">\([2_a, 1, 2_b]\)</span>가 된다. <span class="arithmatex">\(2_a\)</span>가 여전히 <span class="arithmatex">\(2_b\)</span> 앞에 있으므로 상대적인 순서는 바뀌지 않았다.</p>
</li>
<li>
<p>이 예에서 선택 정렬은 값이 같은 원소의 원래 순서를 바꾼다. 버블 정렬은 왼쪽 원소가 오른쪽 원소보다 클 때만
이웃한 원소를 교환한다. 값이 같은 원소끼리는 교환하지 않으므로 원래의 앞뒤 순서를 유지할 수 있다.</p>
</li>
</ol>
</details>
<h3 id="3">3. &nbsp; 계수 정렬과 기수 정렬 비교하기<a class="headerlink" href="#3" title="고유 링크">&para;</a></h3>
<p>학교에서 자릿수가 8자리로 고정된 학번을 대량으로 정렬하려 한다. 다음에 답하라.</p>
<!-- numbered-subquestions -->
<ol>
<li>가장 낮은 자리부터 처리하는 기수 정렬은 총 몇 회전이 필요한가?</li>
<li>학번을 그대로 정수로 취급하여 계수 정렬을 하면, 사용하지 않는 계수 배열의 자리를 많이 마련하게 되는 이유는 무엇인가?</li>
<li>앞의 두 결과를 바탕으로, 8자리로 고정된 학번을 대량으로 처리하려면 계수 정렬과 기수 정렬 중 어느 것을 선택하겠는가? 이유도 설명하라.</li>
</ol>
<details class="success">
<summary>참고 답안</summary>
<ol>
<li>
<p>학번은 8자리이므로 가장 낮은 자리부터 가장 높은 자리까지 총 8회전이 필요하다. 매 회전에서는 0~9에 따라 그룹을 나누기만 하면 된다.</p>
</li>
<li>
<p>학번 전체의 출현 횟수를 직접 세려면 가능한 모든 8자리 값에 대해 자리를 마련해야 한다. 하지만 실제 학생이 사용하는 학번은 그중 일부에 불과하므로,
계수 배열의 대부분은 계속 0으로 남는다.</p>
</li>
<li>
<p>기수 정렬을 선택해야 한다. ‘자릿수가 고정되어 있고, 각 자리에 올 수 있는 값은 10가지뿐’이라는 특징을 이용하면 안정적인 그룹 나누기를 8회 반복하는 것으로 충분하다.
계수 정렬에서 8자리 학번 전체를 정수 인덱스로 사용하면 실제로는 나타나지 않을 수많은 값에 대해서도 계수 배열의 자리를 마련해야 한다.</p>
</li>
</ol>
</details>
<h2 id="11122">11.12.2 &nbsp; 프로그래밍 연습<a class="headerlink" href="#11122" title="고유 링크">&para;</a></h2>
<h3 id="1_1">1. &nbsp; 병합 정렬로 배열 정렬하기<a class="headerlink" href="#1_1" title="고유 링크">&para;</a></h3>
<p>정수 배열 <code>nums</code>가 주어진다. 병합 정렬을 직접 구현하여 원소를 비내림차순으로 정렬한 뒤 반환하라. 언어에서 제공하는 정렬 함수를 호출하지 마라.</p>
<details class="tip">
<summary>풀이 힌트</summary>
<ol>
<li>구간 길이가 1 이하면 이미 정렬되어 있다.</li>
<li>중간 지점에서 구간을 둘로 나누고 각각 재귀적으로 정렬한다.</li>
<li>두 포인터로 정렬된 두 구간을 병합한 뒤, 결과를 원래 배열에 다시 쓴다.</li>
</ol>
</details>
<p><a class="rounded-button exercise-button" href="https://leetcode.com/problems/sort-an-array/" rel="noopener noreferrer" target="_blank">LeetCode</a></p>
<h3 id="2_1">2. &nbsp; 계수 정렬로 정수 배열 정렬하기<a class="headerlink" href="#2_1" title="고유 링크">&para;</a></h3>
<p>정수 배열 <code>nums</code>와 음이 아닌 정수 <span class="arithmatex">\(K\)</span>가 주어진다. 배열의 모든 원소는 <span class="arithmatex">\(0\)</span> 이상 <span class="arithmatex">\(K\)</span> 이하이다.</p>
<p>계수 정렬을 구현하여 비내림차순으로 정렬한 결과를 <code>nums</code>에 다시 쓰고 <code>nums</code>를 반환하라.
원소의 대소 비교로 순서를 결정하거나 언어에서 제공하는 정렬 함수를 호출하지 마라.</p>
<details class="tip">
<summary>풀이 힌트</summary>
<ol>
<li>모든 원소가 0 이상 K 이하이므로 원소 값을 계수 배열의 인덱스로 바로 사용할 수 있다.</li>
<li>먼저 nums를 한 번 순회하면서 해당 위치의 계수를 1씩 늘린다.</li>
<li>이어서 계수 배열을 0부터 K까지 순회한다. 값 x가 나타난 횟수만큼 nums에 x를 연속해서 쓴다.</li>
</ol>
</details>
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