leetcode-problemset/leetcode-cn/originData/path-with-maximum-probability.json

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        "question": {
            "questionId": "1325",
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            "categoryTitle": "Algorithms",
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            "title": "Path with Maximum Probability",
            "titleSlug": "path-with-maximum-probability",
            "content": "<p>You are given an undirected weighted graph of&nbsp;<code>n</code>&nbsp;nodes (0-indexed), represented by an edge list where&nbsp;<code>edges[i] = [a, b]</code>&nbsp;is an undirected edge connecting the nodes&nbsp;<code>a</code>&nbsp;and&nbsp;<code>b</code>&nbsp;with a probability of success of traversing that edge&nbsp;<code>succProb[i]</code>.</p>\r\n\r\n<p>Given two nodes&nbsp;<code>start</code>&nbsp;and&nbsp;<code>end</code>, find the path with the maximum probability of success to go from&nbsp;<code>start</code>&nbsp;to&nbsp;<code>end</code>&nbsp;and return its success probability.</p>\r\n\r\n<p>If there is no path from&nbsp;<code>start</code>&nbsp;to&nbsp;<code>end</code>, <strong>return&nbsp;0</strong>. Your answer will be accepted if it differs from the correct answer by at most <strong>1e-5</strong>.</p>\r\n\r\n<p>&nbsp;</p>\r\n<p><strong>Example 1:</strong></p>\r\n\r\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2019/09/20/1558_ex1.png\" style=\"width: 187px; height: 186px;\" /></strong></p>\r\n\r\n<pre>\r\n<strong>Input:</strong> n = 3, edges = [[0,1],[1,2],[0,2]], succProb = [0.5,0.5,0.2], start = 0, end = 2\r\n<strong>Output:</strong> 0.25000\r\n<strong>Explanation:</strong>&nbsp;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.\r\n</pre>\r\n\r\n<p><strong>Example 2:</strong></p>\r\n\r\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2019/09/20/1558_ex2.png\" style=\"width: 189px; height: 186px;\" /></strong></p>\r\n\r\n<pre>\r\n<strong>Input:</strong> n = 3, edges = [[0,1],[1,2],[0,2]], succProb = [0.5,0.5,0.3], start = 0, end = 2\r\n<strong>Output:</strong> 0.30000\r\n</pre>\r\n\r\n<p><strong>Example 3:</strong></p>\r\n\r\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2019/09/20/1558_ex3.png\" style=\"width: 215px; height: 191px;\" /></strong></p>\r\n\r\n<pre>\r\n<strong>Input:</strong> n = 3, edges = [[0,1]], succProb = [0.5], start = 0, end = 2\r\n<strong>Output:</strong> 0.00000\r\n<strong>Explanation:</strong>&nbsp;There is no path between 0 and 2.\r\n</pre>\r\n\r\n<p>&nbsp;</p>\r\n<p><strong>Constraints:</strong></p>\r\n\r\n<ul>\r\n\t<li><code>2 &lt;= n &lt;= 10^4</code></li>\r\n\t<li><code>0 &lt;= start, end &lt; n</code></li>\r\n\t<li><code>start != end</code></li>\r\n\t<li><code>0 &lt;= a, b &lt; n</code></li>\r\n\t<li><code>a != b</code></li>\r\n\t<li><code>0 &lt;= succProb.length == edges.length &lt;= 2*10^4</code></li>\r\n\t<li><code>0 &lt;= succProb[i] &lt;= 1</code></li>\r\n\t<li>There is at most one edge between every two nodes.</li>\r\n</ul>",
            "translatedTitle": "概率最大的路径",
            "translatedContent": "<p>给你一个由 <code>n</code> 个节点（下标从 0 开始）组成的无向加权图，该图由一个描述边的列表组成，其中 <code>edges[i] = [a, b]</code> 表示连接节点 a 和 b 的一条无向边，且该边遍历成功的概率为 <code>succProb[i]</code> 。</p>\n\n<p>指定两个节点分别作为起点 <code>start</code> 和终点 <code>end</code> ，请你找出从起点到终点成功概率最大的路径，并返回其成功概率。</p>\n\n<p>如果不存在从 <code>start</code> 到 <code>end</code> 的路径，请 <strong>返回 0</strong> 。只要答案与标准答案的误差不超过 <strong>1e-5 </strong>，就会被视作正确答案。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/07/12/1558_ex1.png\" style=\"height: 186px; width: 187px;\"></strong></p>\n\n<pre><strong>输入：</strong>n = 3, edges = [[0,1],[1,2],[0,2]], succProb = [0.5,0.5,0.2], start = 0, end = 2\n<strong>输出：</strong>0.25000\n<strong>解释：</strong>从起点到终点有两条路径，其中一条的成功概率为 0.2 ，而另一条为 0.5 * 0.5 = 0.25\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/07/12/1558_ex2.png\" style=\"height: 186px; width: 189px;\"></strong></p>\n\n<pre><strong>输入：</strong>n = 3, edges = [[0,1],[1,2],[0,2]], succProb = [0.5,0.5,0.3], start = 0, end = 2\n<strong>输出：</strong>0.30000\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/07/12/1558_ex3.png\" style=\"height: 191px; width: 215px;\"></strong></p>\n\n<pre><strong>输入：</strong>n = 3, edges = [[0,1]], succProb = [0.5], start = 0, end = 2\n<strong>输出：</strong>0.00000\n<strong>解释：</strong>节点 0 和 节点 2 之间不存在路径\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;= 10^4</code></li>\n\t<li><code>0 &lt;= start, end &lt; n</code></li>\n\t<li><code>start != end</code></li>\n\t<li><code>0 &lt;= a, b &lt; n</code></li>\n\t<li><code>a != b</code></li>\n\t<li><code>0 &lt;= succProb.length == edges.length &lt;= 2*10^4</code></li>\n\t<li><code>0 &lt;= succProb[i] &lt;= 1</code></li>\n\t<li>每两个节点之间最多有一条边</li>\n</ul>\n",
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                "Multiplying probabilities will result in precision errors.",
                "Take log probabilities to sum up numbers instead of multiplying them.",
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