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chapter_searching/binary_search/index.html
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@@ -3430,7 +3430,32 @@
<div class="md-content" data-md-component="content">
<article class="md-content__inner md-typeset">
<!--
Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to
deal in the Software without restriction, including without limitation the
rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
sell copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
IN THE SOFTWARE.
-->
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_searching/binary_search.md" title="编辑此页" class="md-content__button md-icon">
@@ -3441,6 +3466,13 @@
<!--
Hack: check whether the content contains a h1 headline. If it doesn't, the
page title (or respectively site name) is used as the main headline.
-->
<!-- Page content -->
<h1 id="101">10.1 &nbsp; 二分查找<a class="headerlink" href="#101" title="Permanent link">&para;</a></h1>
<p>「二分查找 binary search」是一种基于分治策略的高效搜索算法。它利用数据的有序性，每轮减少一半搜索范围，直至找到目标元素或搜索区间为空为止。</p>
<div class="admonition question">
@@ -4035,11 +4067,73 @@
<li>小数据量下，线性查找性能更佳。在线性查找中，每轮只需要 1 次判断操作；而在二分查找中，需要 1 次加法、1 次除法、1 ~ 3 次判断操作、1 次加法（减法），共 4 ~ 6 个单元操作；因此，当数据量 <span class="arithmatex">\(n\)</span> 较小时，线性查找反而比二分查找更快。</li>
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@@ -4105,48 +4199,31 @@
</main>
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<a href="../" class="md-footer__link md-footer__link--prev" aria-label="上一页: 第 10 章 &amp;nbsp; 搜索" rel="prev">
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rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
sell copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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@@ -4157,6 +4234,8 @@
</div>
<!-- Social links -->
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chapter_searching/binary_search_edge/index.html
+123 -44
View File
@@ -3478,7 +3478,32 @@
<div class="md-content" data-md-component="content">
<article class="md-content__inner md-typeset">
<!--
Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to
deal in the Software without restriction, including without limitation the
rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
sell copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
IN THE SOFTWARE.
-->
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_searching/binary_search_edge.md" title="编辑此页" class="md-content__button md-icon">
@@ -3489,6 +3514,13 @@
<!--
Hack: check whether the content contains a h1 headline. If it doesn't, the
page title (or respectively site name) is used as the main headline.
-->
<!-- Page content -->
<h1 id="103">10.3 &nbsp; 二分查找边界<a class="headerlink" href="#103" title="Permanent link">&para;</a></h1>
<h2 id="1031">10.3.1 &nbsp; 查找左边界<a class="headerlink" href="#1031" title="Permanent link">&para;</a></h2>
<div class="admonition question">
@@ -3870,11 +3902,73 @@
<li>因为该方法引入了小数，所以需要将函数中的变量 <code>target</code> 改为浮点数类型。</li>
</ul>
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@@ -3940,48 +4034,31 @@
</main>
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<a href="../binary_search_insertion/" class="md-footer__link md-footer__link--prev" aria-label="上一页: 10.2 &amp;nbsp; 二分查找插入点" rel="prev">
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Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to
deal in the Software without restriction, including without limitation the
rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
sell copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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@@ -3992,6 +4069,8 @@
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chapter_searching/binary_search_insertion/index.html
+123 -44
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@@ -3438,7 +3438,32 @@
<div class="md-content" data-md-component="content">
<article class="md-content__inner md-typeset">
<!--
Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to
deal in the Software without restriction, including without limitation the
rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
sell copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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IN THE SOFTWARE.
-->
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_searching/binary_search_insertion.md" title="编辑此页" class="md-content__button md-icon">
@@ -3449,6 +3474,13 @@
<!--
Hack: check whether the content contains a h1 headline. If it doesn't, the
page title (or respectively site name) is used as the main headline.
-->
<!-- Page content -->
<h1 id="102">10.2 &nbsp; 二分查找插入点<a class="headerlink" href="#102" title="Permanent link">&para;</a></h1>
<p>二分查找不仅可用于搜索目标元素，还具有许多变种问题，比如搜索目标元素的插入位置。</p>
<h2 id="1021">10.2.1 &nbsp; 无重复元素的情况<a class="headerlink" href="#1021" title="Permanent link">&para;</a></h2>
@@ -3970,11 +4002,73 @@
<p>总的来看，二分查找无非就是给指针 <span class="arithmatex">\(i\)</span> 和 <span class="arithmatex">\(j\)</span> 分别设定搜索目标，目标可能是一个具体的元素（例如 <code>target</code> ），也可能是一个元素范围（例如小于 <code>target</code> 的元素）。</p>
<p>在不断的循环二分中，指针 <span class="arithmatex">\(i\)</span> 和 <span class="arithmatex">\(j\)</span> 都逐渐逼近预先设定的目标。最终，它们或是成功找到答案，或是越过边界后停止。</p>
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deal in the Software without restriction, including without limitation the
rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
sell copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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@@ -3369,7 +3369,32 @@
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<article class="md-content__inner md-typeset">
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Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to
deal in the Software without restriction, including without limitation the
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sell copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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@@ -3380,6 +3405,13 @@
<!--
Hack: check whether the content contains a h1 headline. If it doesn't, the
page title (or respectively site name) is used as the main headline.
-->
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<h1 id="10">第 10 章 &nbsp; 搜索<a class="headerlink" href="#10" title="Permanent link">&para;</a></h1>
<div class="center-table">
<p><img alt="搜索" src="../assets/covers/chapter_searching.jpg" width="600" /></p>
@@ -3399,11 +3431,73 @@
<li><a href="https://www.hello-algo.com/chapter_searching/summary/">10.6 &nbsp; 小结</a></li>
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<h1 id="104">10.4 &nbsp; 哈希优化策略<a class="headerlink" href="#104" title="Permanent link">&para;</a></h1>
<p>在算法题中，<strong>我们常通过将线性查找替换为哈希查找来降低算法的时间复杂度</strong>。我们借助一个算法题来加深理解。</p>
<div class="admonition question">
@@ -3901,11 +3933,73 @@
<p>此方法通过哈希查找将时间复杂度从 <span class="arithmatex">\(O(n^2)\)</span> 降低至 <span class="arithmatex">\(O(n)\)</span> ，大幅提升运行效率。</p>
<p>由于需要维护一个额外的哈希表，因此空间复杂度为 <span class="arithmatex">\(O(n)\)</span> 。<strong>尽管如此，该方法的整体时空效率更为均衡，因此它是本题的最优解法</strong>。</p>
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<p>「搜索算法 searching algorithm」用于在数据结构（例如数组、链表、树或图）中搜索一个或一组满足特定条件的元素。</p>
<p>搜索算法可根据实现思路分为以下两类。</p>
@@ -3577,11 +3609,73 @@
<li>若使用 AVL 树或红黑树，则各项操作可在 <span class="arithmatex">\(O(\log n)\)</span> 效率下稳定运行，但维护树平衡的操作会增加额外开销。</li>
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@@ -3385,11 +3417,73 @@
<li>用哈希查找替换线性查找是一种常用的优化运行时间的策略，可将时间复杂度从 <span class="arithmatex">\(O(n)\)</span> 降低至 <span class="arithmatex">\(O(1)\)</span> 。</li>
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