mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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181 lines
18 KiB
JSON
181 lines
18 KiB
JSON
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"questionId": "2583",
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"title": "Divide Nodes Into the Maximum Number of Groups",
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"content": "<p>You are given a positive integer <code>n</code> representing the number of nodes in an <strong>undirected</strong> graph. The nodes are labeled from <code>1</code> to <code>n</code>.</p>\n\n<p>You are also given a 2D integer array <code>edges</code>, where <code>edges[i] = [a<sub>i, </sub>b<sub>i</sub>]</code> indicates that there is a <strong>bidirectional</strong> edge between nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code>. <strong>Notice</strong> that the given graph may be disconnected.</p>\n\n<p>Divide the nodes of the graph into <code>m</code> groups (<strong>1-indexed</strong>) such that:</p>\n\n<ul>\n\t<li>Each node in the graph belongs to exactly one group.</li>\n\t<li>For every pair of nodes in the graph that are connected by an edge <code>[a<sub>i, </sub>b<sub>i</sub>]</code>, if <code>a<sub>i</sub></code> belongs to the group with index <code>x</code>, and <code>b<sub>i</sub></code> belongs to the group with index <code>y</code>, then <code>|y - x| = 1</code>.</li>\n</ul>\n\n<p>Return <em>the maximum number of groups (i.e., maximum </em><code>m</code><em>) into which you can divide the nodes</em>. Return <code>-1</code> <em>if it is impossible to group the nodes with the given conditions</em>.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/10/13/example1.png\" style=\"width: 352px; height: 201px;\" />\n<pre>\n<strong>Input:</strong> n = 6, edges = [[1,2],[1,4],[1,5],[2,6],[2,3],[4,6]]\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> As shown in the image we:\n- Add node 5 to the first group.\n- Add node 1 to the second group.\n- Add nodes 2 and 4 to the third group.\n- Add nodes 3 and 6 to the fourth group.\nWe can see that every edge is satisfied.\nIt can be shown that that if we create a fifth group and move any node from the third or fourth group to it, at least on of the edges will not be satisfied.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 3, edges = [[1,2],[2,3],[3,1]]\n<strong>Output:</strong> -1\n<strong>Explanation:</strong> If we add node 1 to the first group, node 2 to the second group, and node 3 to the third group to satisfy the first two edges, we can see that the third edge will not be satisfied.\nIt can be shown that no grouping is possible.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= n <= 500</code></li>\n\t<li><code>1 <= edges.length <= 10<sup>4</sup></code></li>\n\t<li><code>edges[i].length == 2</code></li>\n\t<li><code>1 <= a<sub>i</sub>, b<sub>i</sub> <= n</code></li>\n\t<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>\n\t<li>There is at most one edge between any pair of vertices.</li>\n</ul>\n",
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"If the graph is not bipartite, it is not possible to group the nodes.",
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"Notice that we can solve the problem for each connected component independently, and the final answer will be just the sum of the maximum number of groups in each component.",
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"Finally, to solve the problem for each connected component, we can notice that if for some node v we fix its position to be in the leftmost group, then we can also evaluate the position of every other node. That position is the depth of the node in a bfs tree after rooting at node v."
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