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449
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<h2 id="51-N-Queens-N皇后"><a href="#51-N-Queens-N皇后" class="headerlink" title="51.N-Queens(N皇后)"></a>51.N-Queens(N皇后)</h2><h3 id="链接"><a href="#链接" class="headerlink" title="链接"></a>链接</h3><p><a href="https://leetcode-cn.com/problems/n-queens/" target="_blank" rel="noopener">https://leetcode-cn.com/problems/n-queens/</a></p>
<h3 id="题目"><a href="#题目" class="headerlink" title="题目"></a>题目</h3><p><em>n _皇后问题研究的是如何将 _n</em> 个皇后放置在 <em>n</em> × <em>n</em> 的棋盘上，并且使皇后彼此之间不能相互攻击。</p>
<p><img src="https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2018/10/12/8-queens.png" alt></p>
<p>给定一个整数 <em>n</em> ，返回所有不同的 _n _皇后问题的解决方案。</p>
<p>每一种解法包含一个明确的 <em>n</em> 皇后问题的棋子放置方案，该方案中 <code>'Q'</code> 和 <code>'.'</code> 分别代表了皇后和空位。</p>
<p>示例:</p>
<pre><code> 输入: 4
输出: [
[".Q..", // 解法 1
"...Q",
"Q...",
"..Q."],
["..Q.", // 解法 2
"Q...",
"...Q",
".Q.."]
]
解释: 4 皇后问题存在两个不同的解法。</code></pre><h3 id="思路"><a href="#思路" class="headerlink" title="思路"></a>思路</h3><p>这题的思路和之前的N皇后II一样，都是运用回溯法，只是输出较难设置，还有一个重点，是其中存放答案的res，需要在每次计算前clear一下，要不然就无法ac。</p>
<h3 id="代码"><a href="#代码" class="headerlink" title="代码"></a>代码</h3><figure class="highlight plain"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br></pre></td><td class="code"><pre><span class="line"></span><br><span class="line">private static boolean col[];</span><br><span class="line">private static boolean line1[];</span><br><span class="line">private static boolean line2[];</span><br><span class="line">private static int answer[];</span><br><span class="line">private static List<List<String>> res = new LinkedList<>();</span><br><span class="line"></span><br><span class="line">public static List<List<String>> solveNQueens(int n) {</span><br><span class="line"> col = new boolean[n];</span><br><span class="line"> line1 = new boolean[2 * n - 1];</span><br><span class="line"> line2 = new boolean[2 * n - 1];</span><br><span class="line"> answer = new int[n];</span><br><span class="line"> res.clear();</span><br><span class="line"> putQueen(n, 0);</span><br><span class="line"> return res;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line">private static void putQueen(int n, int index) {</span><br><span class="line"> if (index == n) {</span><br><span class="line"> List<String> item = new ArrayList<String>();</span><br><span class="line"> for (int i = 0; i < answer.length; i++) {</span><br><span class="line"> StringBuilder sb = new StringBuilder();</span><br><span class="line"> for (int j = 0; j < answer.length; j++) {</span><br><span class="line"> if (answer[i] != j) {</span><br><span class="line"> sb.append('.');</span><br><span class="line"> } else {</span><br><span class="line"> sb.append('Q');</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> item.add(sb.toString());</span><br><span class="line"> }</span><br><span class="line"> res.add(item);</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> for (int i = 0; i < n; i++) {</span><br><span class="line"> if (!col[i] && !line1[i - index + n - 1] && !line2[i + index]) {</span><br><span class="line"> answer[index] = i;</span><br><span class="line"> col[i] = true;</span><br><span class="line"> line1[i - index + n - 1] = true;</span><br><span class="line"> line2[i + index] = true;</span><br><span class="line"></span><br><span class="line"> col[i] = false;</span><br><span class="line"> line1[i - index + n - 1] = false;</span><br><span class="line"> line2[i + index] = false;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>
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<div class="post-toc-content"><ol class="nav"><li class="nav-item nav-level-2"><a class="nav-link" href="#51-N-Queens-N皇后"><span class="nav-number">1.</span> <span class="nav-text">51.N-Queens(N皇后)</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#链接"><span class="nav-number">1.1.</span> <span class="nav-text">链接</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#题目"><span class="nav-number">1.2.</span> <span class="nav-text">题目</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#思路"><span class="nav-number">1.3.</span> <span class="nav-text">思路</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#代码"><span class="nav-number">1.4.</span> <span class="nav-text">代码</span></a></li></ol></li></ol></div>
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