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1457/dynamic_programming/intro-to-dp.html

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<ul class="metadata page-metadata" data-bi-name="page info" lang="en-us" dir="ltr">
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<span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-date" title="April 24, 2025 08:34:22">April 24, 2025</span>&emsp;
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<span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-date" title="April 24, 2025 08:39:56">April 24, 2025</span>&emsp;
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<td><a href="/knapsack.md">0-1 Knapsack</a></td>
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<td><a href="/dynamic_programming/knapsack.md">0-1 Knapsack</a></td>
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<td>Given <span class="arithmatex">$W$</span>, <span class="arithmatex">$N$</span>, and <span class="arithmatex">$N$</span> items with weights <span class="arithmatex">$w_i$</span> and values <span class="arithmatex">$v_i$</span>, what is the maximum <span class="arithmatex">$\sum_{i=1}^{k} v_i$</span> for each subset of items of size <span class="arithmatex">$k$</span> (<span class="arithmatex">$1 \le k \le N$</span>) while ensuring <span class="arithmatex">$\sum_{i=1}^{k} w_i \le W$</span>?</td>
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<td>Subset Sum</td>
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<td>Given <span class="arithmatex">$N$</span> integers and <span class="arithmatex">$T$</span>, determine whether there exists a subset of the given set whose elements sum up to the <span class="arithmatex">$T$</span>.</td>
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<td><a href="/longest_increasing_subsequence.md">Longest Increasing Subsequence (LIS)</a></td>
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<td><a href="/dynamic_programming/longest_increasing_subsequence.md">Longest Increasing Subsequence (LIS)</a></td>
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<td>You are given an array containing <span class="arithmatex">$N$</span> integers. Your task is to determine the LIS in the array, i.e., a subsequence where every element is larger than the previous one.</td>
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<h2 id="related-topics">Related Topics<a class="headerlink" href="#related-topics" title="Permanent link">&para;</a></h2>
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<ul>
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<li><a href="/profile-dynamics.md">Bitmask Dynamic Programming</a></li>
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<li><a href="/dynamic_programming/profile-dynamics.md">Bitmask Dynamic Programming</a></li>
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<li>Digit Dynamic Programming</li>
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<li>Dynamic Programming on Trees</li>
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