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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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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z"/></svg>
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.4.2 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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-->
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<h1 id="142">14.2 动态规划问题特性<a class="headerlink" href="#142" title="Permanent link">¶</a></h1>
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<p>在上一节中，我们学习了动态规划是如何通过子问题分解来求解原问题的。实际上，子问题分解是一种通用的算法思路，在分治、动态规划、回溯中的侧重点不同。</p>
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<div class="md-content" data-md-component="content">
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<article class="md-content__inner md-typeset">
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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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of this software and associated documentation files (the "Software"), to
|
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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:
|
||||
|
||||
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
|
||||
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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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
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FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
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IN THE SOFTWARE.
|
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-->
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z"/></svg>
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.4.2 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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page title (or respectively site name) is used as the main headline.
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-->
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<h1 id="143">14.3 动态规划解题思路<a class="headerlink" href="#143" title="Permanent link">¶</a></h1>
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<p>上两节介绍了动态规划问题的主要特征，接下来我们一起探究两个更加实用的问题。</p>
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<article class="md-content__inner md-typeset">
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<!--
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Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
|
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|
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Permission is hereby granted, free of charge, to any person obtaining a copy
|
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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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FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
|
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IN THE SOFTWARE.
|
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-->
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<!-- Tags -->
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class="md-content__button md-icon"
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z"/></svg>
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.4.2 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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-->
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<h1 id="146">14.6 编辑距离问题<a class="headerlink" href="#146" title="Permanent link">¶</a></h1>
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<p>编辑距离，也称 Levenshtein 距离，指两个字符串之间互相转换的最少修改次数，通常用于在信息检索和自然语言处理中度量两个序列的相似度。</p>
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<div class="md-content" data-md-component="content">
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<!--
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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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FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
|
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IN THE SOFTWARE.
|
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-->
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<!-- Tags -->
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_dynamic_programming/index.md" title="编辑此页" class="md-content__button md-icon">
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title="编辑此页"
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class="md-content__button md-icon"
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z"/></svg>
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||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.4.2 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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<!--
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page title (or respectively site name) is used as the main headline.
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-->
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<h1 id="14">第 14 章 动态规划<a class="headerlink" href="#14" title="Permanent link">¶</a></h1>
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<div class="center-table">
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<div class="md-content" data-md-component="content">
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<!--
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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
|
||||
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
|
||||
IN THE SOFTWARE.
|
||||
-->
|
||||
|
||||
<!-- Tags -->
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<!-- Tags -->
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|
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<!-- Actions -->
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<!-- Edit button -->
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_dynamic_programming/intro_to_dynamic_programming.md" title="编辑此页" class="md-content__button md-icon">
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<a
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href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_dynamic_programming/intro_to_dynamic_programming.md"
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title="编辑此页"
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class="md-content__button md-icon"
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>
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|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z"/></svg>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.4.2 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
|
||||
</a>
|
||||
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||||
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||||
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||||
|
||||
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||||
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||||
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|
||||
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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||||
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||||
|
||||
<!-- Page content -->
|
||||
<h1 id="141">14.1 初探动态规划<a class="headerlink" href="#141" title="Permanent link">¶</a></h1>
|
||||
<p>「动态规划 dynamic programming」是一个重要的算法范式，它将一个问题分解为一系列更小的子问题，并通过存储子问题的解来避免重复计算，从而大幅提升时间效率。</p>
|
||||
|
||||
@@ -3366,48 +3366,29 @@
|
||||
<div class="md-content" data-md-component="content">
|
||||
<article class="md-content__inner md-typeset">
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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
|
||||
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
|
||||
IN THE SOFTWARE.
|
||||
-->
|
||||
|
||||
<!-- Tags -->
|
||||
<!-- Tags -->
|
||||
|
||||
|
||||
<!-- Actions -->
|
||||
<!-- Actions -->
|
||||
|
||||
|
||||
<!-- Edit button -->
|
||||
|
||||
<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_dynamic_programming/knapsack_problem.md" title="编辑此页" class="md-content__button md-icon">
|
||||
<a
|
||||
href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_dynamic_programming/knapsack_problem.md"
|
||||
title="编辑此页"
|
||||
class="md-content__button md-icon"
|
||||
>
|
||||
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z"/></svg>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.4.2 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
|
||||
</a>
|
||||
|
||||
|
||||
<!-- View button -->
|
||||
|
||||
|
||||
|
||||
<!--
|
||||
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="144-0-1">14.4 0-1 背包问题<a class="headerlink" href="#144-0-1" title="Permanent link">¶</a></h1>
|
||||
<p>背包问题是一个非常好的动态规划入门题目，是动态规划中最常见的问题形式。其具有很多变种，例如 0-1 背包问题、完全背包问题、多重背包问题等。</p>
|
||||
|
||||
@@ -3272,48 +3272,29 @@
|
||||
<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.
|
||||
-->
|
||||
|
||||
<!-- Tags -->
|
||||
<!-- Tags -->
|
||||
|
||||
|
||||
<!-- Actions -->
|
||||
<!-- Actions -->
|
||||
|
||||
|
||||
<!-- Edit button -->
|
||||
|
||||
<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_dynamic_programming/summary.md" title="编辑此页" class="md-content__button md-icon">
|
||||
<a
|
||||
href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_dynamic_programming/summary.md"
|
||||
title="编辑此页"
|
||||
class="md-content__button md-icon"
|
||||
>
|
||||
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z"/></svg>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.4.2 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
|
||||
</a>
|
||||
|
||||
|
||||
<!-- View button -->
|
||||
|
||||
|
||||
|
||||
<!--
|
||||
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="147">14.7 小结<a class="headerlink" href="#147" title="Permanent link">¶</a></h1>
|
||||
<ul>
|
||||
|
||||
@@ -3514,48 +3514,29 @@
|
||||
<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.
|
||||
-->
|
||||
|
||||
<!-- Tags -->
|
||||
<!-- Tags -->
|
||||
|
||||
|
||||
<!-- Actions -->
|
||||
<!-- Actions -->
|
||||
|
||||
|
||||
<!-- Edit button -->
|
||||
|
||||
<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_dynamic_programming/unbounded_knapsack_problem.md" title="编辑此页" class="md-content__button md-icon">
|
||||
<a
|
||||
href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_dynamic_programming/unbounded_knapsack_problem.md"
|
||||
title="编辑此页"
|
||||
class="md-content__button md-icon"
|
||||
>
|
||||
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z"/></svg>
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.4.2 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
|
||||
</a>
|
||||
|
||||
|
||||
<!-- View button -->
|
||||
|
||||
|
||||
|
||||
<!--
|
||||
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="145">14.5 完全背包问题<a class="headerlink" href="#145" title="Permanent link">¶</a></h1>
|
||||
<p>在本节中，我们先求解另一个常见的背包问题：完全背包，再了解它的一种特例：零钱兑换。</p>
|
||||
|
||||
Reference in New Issue
Block a user