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krahets
2023-11-09 05:13:54 +08:00
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<div class="tabbed-set tabbed-alternate" data-tabs="1:5"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<p><a class="glightbox" href="../algorithms_are_everywhere.assets/binary_search_dictionary_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="查字典步骤" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step1.png" /></a></p>
<p><a class="glightbox" href="../algorithms_are_everywhere.assets/binary_search_dictionary_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="查字典步骤" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step1.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../algorithms_are_everywhere.assets/binary_search_dictionary_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_dictionary_step2" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step2.png" /></a></p>
<p><a class="glightbox" href="../algorithms_are_everywhere.assets/binary_search_dictionary_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_dictionary_step2" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step2.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../algorithms_are_everywhere.assets/binary_search_dictionary_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_dictionary_step3" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step3.png" /></a></p>
<p><a class="glightbox" href="../algorithms_are_everywhere.assets/binary_search_dictionary_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_dictionary_step3" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step3.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../algorithms_are_everywhere.assets/binary_search_dictionary_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_dictionary_step4" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step4.png" /></a></p>
<p><a class="glightbox" href="../algorithms_are_everywhere.assets/binary_search_dictionary_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_dictionary_step4" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step4.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../algorithms_are_everywhere.assets/binary_search_dictionary_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_dictionary_step5" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step5.png" /></a></p>
<p><a class="glightbox" href="../algorithms_are_everywhere.assets/binary_search_dictionary_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_dictionary_step5" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step5.png" /></a></p>
</div>
</div>
</div>
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<li>在无序部分抽出一张扑克牌,插入至有序部分的正确位置;完成后最左 2 张扑克已经有序。</li>
<li>不断循环步骤 <code>2.</code> ,每一轮将一张扑克牌从无序部分插入至有序部分,直至所有扑克牌都有序。</li>
</ol>
<p><a class="glightbox" href="../algorithms_are_everywhere.assets/playing_cards_sorting.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="扑克排序步骤" src="../algorithms_are_everywhere.assets/playing_cards_sorting.png" /></a></p>
<p><a class="glightbox" href="../algorithms_are_everywhere.assets/playing_cards_sorting.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="扑克排序步骤" class="animation-figure" src="../algorithms_are_everywhere.assets/playing_cards_sorting.png" /></a></p>
<p align="center"> 图 1-2 &nbsp; 扑克排序步骤 </p>
<p>上述整理扑克牌的方法本质上是“插入排序”算法,它在处理小型数据集时非常高效。许多编程语言的排序库函数中都存在插入排序的身影。</p>
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<li>从剩余可选项中拿出最大的 <span class="arithmatex">\(1\)</span> 元,剩余 <span class="arithmatex">\(1 - 1 = 0\)</span> 元。</li>
<li>完成找零,方案为 <span class="arithmatex">\(20 + 10 + 1 = 31\)</span> 元。</li>
</ol>
<p><a class="glightbox" href="../algorithms_are_everywhere.assets/greedy_change.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="货币找零过程" src="../algorithms_are_everywhere.assets/greedy_change.png" /></a></p>
<p><a class="glightbox" href="../algorithms_are_everywhere.assets/greedy_change.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="货币找零过程" class="animation-figure" src="../algorithms_are_everywhere.assets/greedy_change.png" /></a></p>
<p align="center"> 图 1-3 &nbsp; 货币找零过程 </p>
<p>在以上步骤中,我们每一步都采取当前看来最好的选择(尽可能用大面额的货币),最终得到了可行的找零方案。从数据结构与算法的角度看,这种方法本质上是“贪心”算法。</p>

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<!-- Page content -->
<h1 id="1">第 1 章 &nbsp; 初识算法<a class="headerlink" href="#1" title="Permanent link">&para;</a></h1>
<div class="center-table">
<p><a class="glightbox" href="../assets/covers/chapter_introduction.jpg" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="初识算法" src="../assets/covers/chapter_introduction.jpg" width="600" /></a></p>
<p><a class="glightbox" href="../assets/covers/chapter_introduction.jpg" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="初识算法" class="cover-image" src="../assets/covers/chapter_introduction.jpg" /></a></p>
</div>
<div class="admonition abstract">
<p class="admonition-title">Abstract</p>

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<li>算法是数据结构发挥作用的舞台。数据结构本身仅存储数据信息,结合算法才能解决特定问题。</li>
<li>算法通常可以基于不同的数据结构进行实现,但执行效率可能相差很大,选择合适的数据结构是关键。</li>
</ul>
<p><a class="glightbox" href="../what_is_dsa.assets/relationship_between_data_structure_and_algorithm.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="数据结构与算法的关系" src="../what_is_dsa.assets/relationship_between_data_structure_and_algorithm.png" /></a></p>
<p><a class="glightbox" href="../what_is_dsa.assets/relationship_between_data_structure_and_algorithm.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="数据结构与算法的关系" class="animation-figure" src="../what_is_dsa.assets/relationship_between_data_structure_and_algorithm.png" /></a></p>
<p align="center"> 图 1-4 &nbsp; 数据结构与算法的关系 </p>
<p>数据结构与算法犹如图 1-5 所示的拼装积木。一套积木,除了包含许多零件之外,还附有详细的组装说明书。我们按照说明书一步步操作,就能组装出精美的积木模型。</p>
<p><a class="glightbox" href="../what_is_dsa.assets/assembling_blocks.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="拼装积木" src="../what_is_dsa.assets/assembling_blocks.png" /></a></p>
<p><a class="glightbox" href="../what_is_dsa.assets/assembling_blocks.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="拼装积木" class="animation-figure" src="../what_is_dsa.assets/assembling_blocks.png" /></a></p>
<p align="center"> 图 1-5 &nbsp; 拼装积木 </p>
<p>两者的详细对应关系如表 1-1 所示。</p>