mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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182 lines
20 KiB
JSON
182 lines
20 KiB
JSON
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"questionId": "3058",
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"title": "Maximum Number of K-Divisible Components",
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"content": "<p>There is an undirected tree with <code>n</code> nodes labeled from <code>0</code> to <code>n - 1</code>. You are given the integer <code>n</code> and 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>values</code> of length <code>n</code>, where <code>values[i]</code> is the <strong>value</strong> associated with the <code>i<sup>th</sup></code> node, and an integer <code>k</code>.</p>\n\n<p>A <strong>valid split</strong> of the tree is obtained by removing any set of edges, possibly empty, from the tree such that the resulting components all have values that are divisible by <code>k</code>, where the <strong>value of a connected component</strong> is the sum of the values of its nodes.</p>\n\n<p>Return <em>the <strong>maximum number of components</strong> in any valid split</em>.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/08/07/example12-cropped2svg.jpg\" style=\"width: 1024px; height: 453px;\" />\n<pre>\n<strong>Input:</strong> n = 5, edges = [[0,2],[1,2],[1,3],[2,4]], values = [1,8,1,4,4], k = 6\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> We remove the edge connecting node 1 with 2. The resulting split is valid because:\n- The value of the component containing nodes 1 and 3 is values[1] + values[3] = 12.\n- The value of the component containing nodes 0, 2, and 4 is values[0] + values[2] + values[4] = 6.\nIt can be shown that no other valid split has more than 2 connected components.</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/08/07/example21svg-1.jpg\" style=\"width: 999px; height: 338px;\" />\n<pre>\n<strong>Input:</strong> n = 7, edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]], values = [3,0,6,1,5,2,1], k = 3\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> We remove the edge connecting node 0 with 2, and the edge connecting node 0 with 1. The resulting split is valid because:\n- The value of the component containing node 0 is values[0] = 3.\n- The value of the component containing nodes 2, 5, and 6 is values[2] + values[5] + values[6] = 9.\n- The value of the component containing nodes 1, 3, and 4 is values[1] + values[3] + values[4] = 6.\nIt can be shown that no other valid split has more than 3 connected components.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= n <= 3 * 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 <= a<sub>i</sub>, b<sub>i</sub> < n</code></li>\n\t<li><code>values.length == n</code></li>\n\t<li><code>0 <= values[i] <= 10<sup>9</sup></code></li>\n\t<li><code>1 <= k <= 10<sup>9</sup></code></li>\n\t<li>Sum of <code>values</code> is divisible by <code>k</code>.</li>\n\t<li>The input is generated such that <code>edges</code> represents a valid tree.</li>\n</ul>\n",
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"code": "class Solution(object):\n def maxKDivisibleComponents(self, n, edges, values, k):\n \"\"\"\n :type n: int\n :type edges: List[List[int]]\n :type values: List[int]\n :type k: int\n :rtype: int\n \"\"\"\n ",
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"code": "# @param {Integer} n\n# @param {Integer[][]} edges\n# @param {Integer[]} values\n# @param {Integer} k\n# @return {Integer}\ndef max_k_divisible_components(n, edges, values, k)\n \nend",
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"Root the tree at node <code>0</code>.",
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"If a leaf node is not divisible by <code>k</code>, it must be in the same component as its parent node so we merge it with its parent node.",
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"If a leaf node is divisible by <code>k</code>, it will be in its own components so we separate it from its parent node.",
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"In each step, we either cut a leaf node down or merge a leaf node. The number of nodes on the tree reduces by one. Repeat this process until only one node is left."
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