leetcode-problemset/leetcode-cn/originData/find-number-of-coins-to-place-in-tree-nodes.json

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        "question": {
            "questionId": "3218",
            "questionFrontendId": "2973",
            "categoryTitle": "Algorithms",
            "boundTopicId": 2575542,
            "title": "Find Number of Coins to Place in Tree Nodes",
            "titleSlug": "find-number-of-coins-to-place-in-tree-nodes",
            "content": "<p>You are given an <strong>undirected</strong> tree with <code>n</code> nodes labeled from <code>0</code> to <code>n - 1</code>, and rooted at node <code>0</code>. You are given a 2D integer array <code>edges</code> 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.</p>\n\n<p>You are also given a <strong>0-indexed</strong> integer array <code>cost</code> of length <code>n</code>, where <code>cost[i]</code> is the <strong>cost</strong> assigned to the <code>i<sup>th</sup></code> node.</p>\n\n<p>You need to place some coins on every node of the tree. The number of coins to be placed at node <code>i</code> can be calculated as:</p>\n\n<ul>\n\t<li>If size of the subtree of node <code>i</code> is less than <code>3</code>, place <code>1</code> coin.</li>\n\t<li>Otherwise, place an amount of coins equal to the <strong>maximum</strong> product of cost values assigned to <code>3</code> distinct nodes in the subtree of node <code>i</code>. If this product is <strong>negative</strong>, place <code>0</code> coins.</li>\n</ul>\n\n<p>Return <em>an array </em><code>coin</code><em> of size </em><code>n</code><em> such that </em><code>coin[i]</code><em> is the number of coins placed at node </em><code>i</code><em>.</em></p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/11/09/screenshot-2023-11-10-012641.png\" style=\"width: 600px; height: 233px;\" />\n<pre>\n<strong>Input:</strong> edges = [[0,1],[0,2],[0,3],[0,4],[0,5]], cost = [1,2,3,4,5,6]\n<strong>Output:</strong> [120,1,1,1,1,1]\n<strong>Explanation:</strong> For node 0 place 6 * 5 * 4 = 120 coins. All other nodes are leaves with subtree of size 1, place 1 coin on each of them.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/11/09/screenshot-2023-11-10-012614.png\" style=\"width: 800px; height: 374px;\" />\n<pre>\n<strong>Input:</strong> edges = [[0,1],[0,2],[1,3],[1,4],[1,5],[2,6],[2,7],[2,8]], cost = [1,4,2,3,5,7,8,-4,2]\n<strong>Output:</strong> [280,140,32,1,1,1,1,1,1]\n<strong>Explanation:</strong> The coins placed on each node are:\n- Place 8 * 7 * 5 = 280 coins on node 0.\n- Place 7 * 5 * 4 = 140 coins on node 1.\n- Place 8 * 2 * 2 = 32 coins on node 2.\n- All other nodes are leaves with subtree of size 1, place 1 coin on each of them.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/11/09/screenshot-2023-11-10-012513.png\" style=\"width: 300px; height: 277px;\" />\n<pre>\n<strong>Input:</strong> edges = [[0,1],[0,2]], cost = [1,2,-2]\n<strong>Output:</strong> [0,1,1]\n<strong>Explanation:</strong> Node 1 and 2 are leaves with subtree of size 1, place 1 coin on each of them. For node 0 the only possible product of cost is 2 * 1 * -2 = -4. Hence place 0 coins on node 0.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n &lt;= 2 * 10<sup>4</sup></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>cost.length == n</code></li>\n\t<li><code>1 &lt;= |cost[i]| &lt;= 10<sup>4</sup></code></li>\n\t<li>The input is generated such that <code>edges</code> represents a valid tree.</li>\n</ul>\n",
            "translatedTitle": "树中每个节点放置的金币数目",
            "translatedContent": "<p>给你一棵&nbsp;<code>n</code>&nbsp;个节点的&nbsp;<strong>无向</strong>&nbsp;树，节点编号为&nbsp;<code>0</code>&nbsp;到&nbsp;<code>n - 1</code>&nbsp;，树的根节点在节点&nbsp;<code>0</code>&nbsp;处。同时给你一个长度为 <code>n - 1</code>&nbsp;的二维整数数组&nbsp;<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。</p>\n\n<p>给你一个长度为 <code>n</code>&nbsp;下标从 <strong>0</strong>&nbsp;开始的整数数组&nbsp;<code>cost</code>&nbsp;，其中&nbsp;<code>cost[i]</code>&nbsp;是第 <code>i</code>&nbsp;个节点的 <b>开销</b>&nbsp;。</p>\n\n<p>你需要在树中每个节点都放置金币，在节点 <code>i</code>&nbsp;处的金币数目计算方法如下：</p>\n\n<ul>\n\t<li>如果节点 <code>i</code>&nbsp;对应的子树中的节点数目小于&nbsp;<code>3</code>&nbsp;，那么放&nbsp;<code>1</code>&nbsp;个金币。</li>\n\t<li>否则，计算节点 <code>i</code> 对应的子树内 <code>3</code> 个不同节点的开销乘积的 <strong>最大值</strong> ，并在节点 <code>i</code> 处放置对应数目的金币。如果最大乘积是 <b>负数</b>&nbsp;，那么放置 <code>0</code>&nbsp;个金币。</li>\n</ul>\n\n<p>请你返回一个长度为 <code>n</code>&nbsp;的数组<em>&nbsp;</em><code>coin</code>&nbsp;，<code>coin[i]</code>是节点&nbsp;<code>i</code>&nbsp;处的金币数目。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/11/09/screenshot-2023-11-10-012641.png\" style=\"width: 600px; height: 233px;\" /></p>\n\n<pre>\n<b>输入：</b>edges = [[0,1],[0,2],[0,3],[0,4],[0,5]], cost = [1,2,3,4,5,6]\n<b>输出：</b>[120,1,1,1,1,1]\n<b>解释：</b>在节点 0 处放置 6 * 5 * 4 = 120 个金币。所有其他节点都是叶子节点，子树中只有 1 个节点，所以其他每个节点都放 1 个金币。\n</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/11/09/screenshot-2023-11-10-012614.png\" style=\"width: 800px; height: 374px;\" /></p>\n\n<pre>\n<b>输入：</b>edges = [[0,1],[0,2],[1,3],[1,4],[1,5],[2,6],[2,7],[2,8]], cost = [1,4,2,3,5,7,8,-4,2]\n<b>输出：</b>[280,140,32,1,1,1,1,1,1]\n<b>解释：</b>每个节点放置的金币数分别为：\n- 节点 0 处放置 8 * 7 * 5 = 280 个金币。\n- 节点 1 处放置 7 * 5 * 4 = 140 个金币。\n- 节点 2 处放置 8 * 2 * 2 = 32 个金币。\n- 其他节点都是叶子节点，子树内节点数目为 1 ，所以其他每个节点都放 1 个金币。\n</pre>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/11/09/screenshot-2023-11-10-012513.png\" style=\"width: 300px; height: 277px;\" /></p>\n\n<pre>\n<b>输入：</b>edges = [[0,1],[0,2]], cost = [1,2,-2]\n<b>输出：</b>[0,1,1]\n<b>解释：</b>节点 1 和 2 都是叶子节点，子树内节点数目为 1 ，各放置 1 个金币。节点 0 处唯一的开销乘积是 2 * 1 * -2 = -4 。所以在节点 0 处放置 0 个金币。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n &lt;= 2 * 10<sup>4</sup></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>cost.length == n</code></li>\n\t<li><code>1 &lt;= |cost[i]| &lt;= 10<sup>4</sup></code></li>\n\t<li><code>edges</code>&nbsp;一定是一棵合法的树。</li>\n</ul>\n",
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                "If there are more than three values in total, we can sort them. Let’s call the resultant array <code>A</code>, the maximum product of three is <code>max(A[0] * A[1] * A[n - 1], A[n - 1] * A[n - 2] * A[n - 3])</code>. Don’t forget to set the result to <code>0</code> if the value is negative.",
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