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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>

<td>Subset Sum</td>

<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>

<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>

<h2 id="related-topics">Related Topics<a class="headerlink" href="#related-topics" title="Permanent link">&para;</a></h2>

<li>Digit Dynamic Programming</li>

<li>Dynamic Programming on Trees</li>