https://milknocandy.github.io/study/ Recent content in Studies on PaperMoon's blog https://milknocandy.github.io/%3Clink%20or%20path%20of%20image%20for%20opengraph,%20twitter-cards%3E https://milknocandy.github.io/%3Clink%20or%20path%20of%20image%20for%20opengraph,%20twitter-cards%3E Hugo -- 0.154.3 en Mon, 23 Mar 2026 12:30:15 +0800 https://milknocandy.github.io/study/20260311_knapsack/ Wed, 11 Mar 2026 21:05:49 +0800 https://milknocandy.github.io/study/20260311_knapsack/ <!-- set id for section manually --> <h2 id="01knapsack-ref">0-1 Knapsack Problem</h2> <div class="highlight-box default"> <div class="box-content"> <p><strong>Description:</strong> There are $N$ items and one knapsack with a maximum capacity of $V$. Each item can be selected at most once (i.e., either take it or leave it). The $i\text{-th}$ item has a volume of $v_i$​ and a value of $w_i$​. Your task is to select a subset of items to put into the knapsack such that:</p> <ol> <li>The total volume of the selected items does not exceed the knapsack's capacity V.</li> <li>The total value of the selected items is maximized.</li> </ol> <p>Output the maximum possible total value achievable under these constraints.</p>