leetcode-problemset/leetcode-cn/originData/collect-coins-in-a-tree.json

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        "question": {
            "questionId": "2717",
            "questionFrontendId": "2603",
            "categoryTitle": "Algorithms",
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            "title": "Collect Coins in a Tree",
            "titleSlug": "collect-coins-in-a-tree",
            "content": "<p>There exists an undirected and unrooted tree with <code>n</code> nodes indexed from <code>0</code> to <code>n - 1</code>. You are given an integer <code>n</code> and a 2D integer array edges of length <code>n - 1</code>, where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that there is an edge between nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code> in the tree. You are also given&nbsp;an array <code>coins</code> of size <code>n</code> where <code>coins[i]</code> can be either <code>0</code> or <code>1</code>, where <code>1</code> indicates the presence of a coin in the vertex <code>i</code>.</p>\n\n<p>Initially, you choose to start at any vertex in&nbsp;the tree.&nbsp;Then, you can perform&nbsp;the following operations any number of times:&nbsp;</p>\n\n<ul>\n\t<li>Collect all the coins that are at a distance of at most <code>2</code> from the current vertex, or</li>\n\t<li>Move to any adjacent vertex in the tree.</li>\n</ul>\n\n<p>Find <em>the minimum number of edges you need to go through to collect all the coins and go back to the initial vertex</em>.</p>\n\n<p>Note that if you pass an edge several times, you need to count it into the answer several times.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/03/01/graph-2.png\" style=\"width: 522px; height: 522px;\" />\n<pre>\n<strong>Input:</strong> coins = [1,0,0,0,0,1], edges = [[0,1],[1,2],[2,3],[3,4],[4,5]]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> Start at vertex 2, collect the coin at vertex 0, move to vertex 3, collect the coin at vertex 5 then move back to vertex 2.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/03/02/graph-4.png\" style=\"width: 522px; height: 522px;\" />\n<pre>\n<strong>Input:</strong> coins = [0,0,0,1,1,0,0,1], edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[5,6],[5,7]]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> Start at vertex 0, collect the coins at vertices 4 and 3, move to vertex 2,  collect the coin at vertex 7, then move back to vertex 0.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == coins.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 3 * 10<sup>4</sup></code></li>\n\t<li><code>0 &lt;= coins[i] &lt;= 1</code></li>\n\t<li><code>edges.length == n - 1</code></li>\n\t<li><code>edges[i].length == 2</code></li>\n\t<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li>\n\t<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>\n\t<li><code>edges</code> represents a valid tree.</li>\n</ul>\n",
            "translatedTitle": "收集树中金币",
            "translatedContent": "<p>给你一个 <code>n</code>&nbsp;个节点的无向无根树，节点编号从&nbsp;<code>0</code>&nbsp;到&nbsp;<code>n - 1</code>&nbsp;。给你整数&nbsp;<code>n</code>&nbsp;和一个长度为 <code>n - 1</code>&nbsp;的二维整数数组 <code>edges</code>&nbsp;，其中&nbsp;<code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code>&nbsp;表示树中节点&nbsp;<code>a<sub>i</sub></code> 和&nbsp;<code>b<sub>i</sub></code>&nbsp;之间有一条边。再给你一个长度为 <code>n</code>&nbsp;的数组&nbsp;<code>coins</code>&nbsp;，其中&nbsp;<code>coins[i]</code> 可能为&nbsp;<code>0</code>&nbsp;也可能为&nbsp;<code>1</code>&nbsp;，<code>1</code>&nbsp;表示节点 <code>i</code>&nbsp;处有一个金币。</p>\n\n<p>一开始，你需要选择树中任意一个节点出发。你可以执行下述操作任意次：</p>\n\n<ul>\n\t<li>收集距离当前节点距离为 <code>2</code>&nbsp;以内的所有金币，或者</li>\n\t<li>移动到树中一个相邻节点。</li>\n</ul>\n\n<p>你需要收集树中所有的金币，并且回到出发节点，请你返回最少经过的边数。</p>\n\n<p>如果你多次经过一条边，每一次经过都会给答案加一。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/03/01/graph-2.png\" style=\"width: 522px; height: 522px;\"></p>\n\n<pre><b>输入：</b>coins = [1,0,0,0,0,1], edges = [[0,1],[1,2],[2,3],[3,4],[4,5]]\n<b>输出：</b>2\n<b>解释：</b>从节点 2 出发，收集节点 0 处的金币，移动到节点 3 ，收集节点 5 处的金币，然后移动回节点 2 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/03/02/graph-4.png\" style=\"width: 522px; height: 522px;\"></p>\n\n<pre><b>输入：</b>coins = [0,0,0,1,1,0,0,1], edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[5,6],[5,7]]\n<b>输出：</b>2\n<b>解释：</b>从节点 0 出发，收集节点 4 和 3 处的金币，移动到节点 2 处，收集节点 7 处的金币，移动回节点 0 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>n == coins.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 3 * 10<sup>4</sup></code></li>\n\t<li><code>0 &lt;= coins[i] &lt;= 1</code></li>\n\t<li><code>edges.length == n - 1</code></li>\n\t<li><code>edges[i].length == 2</code></li>\n\t<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li>\n\t<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>\n\t<li><code>edges</code>&nbsp;表示一棵合法的树。</li>\n</ul>\n",
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