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Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
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The above copyright notice and this permission notice shall be included in
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FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_backtracking/n_queens_problem.md" title="编辑此页" class="md-content__button md-icon">
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<h1 id="134-n">13.4 N 皇后问题<a class="headerlink" href="#134-n" title="Permanent link">¶</a></h1>
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<p class="admonition-title">Question</p>
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<p>逐行放置 <span class="arithmatex">\(n\)</span> 次,考虑列约束,则从第一行到最后一行分别有 <span class="arithmatex">\(n\)</span>、<span class="arithmatex">\(n-1\)</span>、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span> 个选择,<strong>因此时间复杂度为 <span class="arithmatex">\(O(n!)\)</span></strong> 。实际上,根据对角线约束的剪枝也能够大幅地缩小搜索空间,因而搜索效率往往优于以上时间复杂度。</p>
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<p>数组 <code>state</code> 使用 <span class="arithmatex">\(O(n^2)\)</span> 空间,数组 <code>cols</code>、<code>diags1</code> 和 <code>diags2</code> 皆使用 <span class="arithmatex">\(O(n)\)</span> 空间。最大递归深度为 <span class="arithmatex">\(n\)</span> ,使用 <span class="arithmatex">\(O(n)\)</span> 栈帧空间。因此,<strong>空间复杂度为 <span class="arithmatex">\(O(n^2)\)</span></strong> 。</p>
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Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
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Permission is hereby granted, free of charge, to any person obtaining a copy
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deal in the Software without restriction, including without limitation the
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rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
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sell copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in
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all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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