mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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183 lines
22 KiB
JSON
183 lines
22 KiB
JSON
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"questionId": "2803",
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"title": "Modify Graph Edge Weights",
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"content": "<p>You are given an <strong>undirected weighted</strong> <strong>connected</strong> graph containing <code>n</code> nodes labeled from <code>0</code> to <code>n - 1</code>, and an integer array <code>edges</code> where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>, w<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> with weight <code>w<sub>i</sub></code>.</p>\n\n<p>Some edges have a weight of <code>-1</code> (<code>w<sub>i</sub> = -1</code>), while others have a <strong>positive</strong> weight (<code>w<sub>i</sub> > 0</code>).</p>\n\n<p>Your task is to modify <strong>all edges</strong> with a weight of <code>-1</code> by assigning them <strong>positive integer values </strong>in the range <code>[1, 2 * 10<sup>9</sup>]</code> so that the <strong>shortest distance</strong> between the nodes <code>source</code> and <code>destination</code> becomes equal to an integer <code>target</code>. If there are <strong>multiple</strong> <strong>modifications</strong> that make the shortest distance between <code>source</code> and <code>destination</code> equal to <code>target</code>, any of them will be considered correct.</p>\n\n<p>Return <em>an array containing all edges (even unmodified ones) in any order if it is possible to make the shortest distance from </em><code>source</code><em> to </em><code>destination</code><em> equal to </em><code>target</code><em>, or an <strong>empty array</strong> if it's impossible.</em></p>\n\n<p><strong>Note:</strong> You are not allowed to modify the weights of edges with initial positive weights.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<p><strong class=\"example\"><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/04/18/graph.png\" style=\"width: 300px; height: 300px;\" /></strong></p>\n\n<pre>\n<strong>Input:</strong> n = 5, edges = [[4,1,-1],[2,0,-1],[0,3,-1],[4,3,-1]], source = 0, destination = 1, target = 5\n<strong>Output:</strong> [[4,1,1],[2,0,1],[0,3,3],[4,3,1]]\n<strong>Explanation:</strong> The graph above shows a possible modification to the edges, making the distance from 0 to 1 equal to 5.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<p><strong class=\"example\"><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/04/18/graph-2.png\" style=\"width: 300px; height: 300px;\" /></strong></p>\n\n<pre>\n<strong>Input:</strong> n = 3, edges = [[0,1,-1],[0,2,5]], source = 0, destination = 2, target = 6\n<strong>Output:</strong> []\n<strong>Explanation:</strong> The graph above contains the initial edges. It is not possible to make the distance from 0 to 2 equal to 6 by modifying the edge with weight -1. So, an empty array is returned.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<p><strong class=\"example\"><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/04/19/graph-3.png\" style=\"width: 300px; height: 300px;\" /></strong></p>\n\n<pre>\n<strong>Input:</strong> n = 4, edges = [[1,0,4],[1,2,3],[2,3,5],[0,3,-1]], source = 0, destination = 2, target = 6\n<strong>Output:</strong> [[1,0,4],[1,2,3],[2,3,5],[0,3,1]]\n<strong>Explanation:</strong> The graph above shows a modified graph having the shortest distance from 0 to 2 as 6.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= n <= 100</code></li>\n\t<li><code><font face=\"monospace\">1 <= edges.length <= n * (n - 1) / 2</font></code></li>\n\t<li><code>edges[i].length == 3</code></li>\n\t<li><code>0 <= a<sub>i</sub>, b<sub>i </sub>< n</code></li>\n\t<li><code><font face=\"monospace\">w<sub>i</sub> = -1 </font></code>or <code><font face=\"monospace\">1 <= w<sub>i </sub><= 10<sup><span style=\"font-size: 10.8333px;\">7</span></sup></font></code></li>\n\t<li><code>a<sub>i </sub>!= b<sub>i</sub></code></li>\n\t<li><code>0 <= source, destination < n</code></li>\n\t<li><code>source != destination</code></li>\n\t<li><code><font face=\"monospace\">1 <= target <= 10<sup>9</sup></font></code></li>\n\t<li>The graph is connected, and there are no self-loops or repeated edges</li>\n</ul>\n",
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"Firstly, check that it’s actually possible to make the shortest path from source to destination equal to the target.",
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"If the shortest path from source to destination without the edges to be modified, is less than the target, then it is not possible.",
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"If the shortest path from source to destination including the edges to be modified and assigning them a temporary weight of 1, is greater than the target, then it is also not possible.",
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"Suppose we can find a modifiable edge (u, v) such that the length of the shortest path from source to u (dis1) plus the length of the shortest path from v to destination (dis2) is less than target (dis1 + dis2 < target), then we can change its weight to “target - dis1 - dis2”.",
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"For all the other edges that still have the weight “-1”, change the weights into sufficient large number (target, target + 1 or 200000000 etc.)."
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