mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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201 lines
20 KiB
JSON
201 lines
20 KiB
JSON
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"title": "Path with Maximum Probability",
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"content": "<p>You are given an undirected weighted graph of <code>n</code> nodes (0-indexed), represented by an edge list where <code>edges[i] = [a, b]</code> is an undirected edge connecting the nodes <code>a</code> and <code>b</code> with a probability of success of traversing that edge <code>succProb[i]</code>.</p>\n\n<p>Given two nodes <code>start</code> and <code>end</code>, find the path with the maximum probability of success to go from <code>start</code> to <code>end</code> and return its success probability.</p>\n\n<p>If there is no path from <code>start</code> to <code>end</code>, <strong>return 0</strong>. Your answer will be accepted if it differs from the correct answer by at most <strong>1e-5</strong>.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2019/09/20/1558_ex1.png\" style=\"width: 187px; height: 186px;\" /></strong></p>\n\n<pre>\n<strong>Input:</strong> n = 3, edges = [[0,1],[1,2],[0,2]], succProb = [0.5,0.5,0.2], start = 0, end = 2\n<strong>Output:</strong> 0.25000\n<strong>Explanation:</strong> There are two paths from start to end, one having a probability of success = 0.2 and the other has 0.5 * 0.5 = 0.25.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2019/09/20/1558_ex2.png\" style=\"width: 189px; height: 186px;\" /></strong></p>\n\n<pre>\n<strong>Input:</strong> n = 3, edges = [[0,1],[1,2],[0,2]], succProb = [0.5,0.5,0.3], start = 0, end = 2\n<strong>Output:</strong> 0.30000\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2019/09/20/1558_ex3.png\" style=\"width: 215px; height: 191px;\" /></strong></p>\n\n<pre>\n<strong>Input:</strong> n = 3, edges = [[0,1]], succProb = [0.5], start = 0, end = 2\n<strong>Output:</strong> 0.00000\n<strong>Explanation:</strong> There is no path between 0 and 2.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 <= n <= 10^4</code></li>\n\t<li><code>0 <= start, end < n</code></li>\n\t<li><code>start != end</code></li>\n\t<li><code>0 <= a, b < n</code></li>\n\t<li><code>a != b</code></li>\n\t<li><code>0 <= succProb.length == edges.length <= 2*10^4</code></li>\n\t<li><code>0 <= succProb[i] <= 1</code></li>\n\t<li>There is at most one edge between every two nodes.</li>\n</ul>\n",
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"hints": [
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"Multiplying probabilities will result in precision errors.",
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"Take log probabilities to sum up numbers instead of multiplying them.",
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"Use Dijkstra's algorithm to find the minimum path between the two nodes after negating all costs."
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