{ "data": { "question": { "questionId": "1912", "questionFrontendId": "1786", "categoryTitle": "Algorithms", "boundTopicId": 635606, "title": "Number of Restricted Paths From First to Last Node", "titleSlug": "number-of-restricted-paths-from-first-to-last-node", "content": "

There is an undirected weighted connected graph. You are given a positive integer n which denotes that the graph has n nodes labeled from 1 to n, and an array edges where each edges[i] = [ui, vi, weighti] denotes that there is an edge between nodes ui and vi with weight equal to weighti.

\n\n

A path from node start to node end is a sequence of nodes [z0, z1, z2, ..., zk] such that z0 = start and zk = end and there is an edge between zi and zi+1 where 0 <= i <= k-1.

\n\n

The distance of a path is the sum of the weights on the edges of the path. Let distanceToLastNode(x) denote the shortest distance of a path between node n and node x. A restricted path is a path that also satisfies that distanceToLastNode(zi) > distanceToLastNode(zi+1) where 0 <= i <= k-1.

\n\n

Return the number of restricted paths from node 1 to node n. Since that number may be too large, return it modulo 109 + 7.

\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: n = 5, edges = [[1,2,3],[1,3,3],[2,3,1],[1,4,2],[5,2,2],[3,5,1],[5,4,10]]\nOutput: 3\nExplanation: Each circle contains the node number in black and its distanceToLastNode value in blue. The three restricted paths are:\n1) 1 --> 2 --> 5\n2) 1 --> 2 --> 3 --> 5\n3) 1 --> 3 --> 5\n
\n\n

Example 2:

\n\"\"\n
\nInput: n = 7, edges = [[1,3,1],[4,1,2],[7,3,4],[2,5,3],[5,6,1],[6,7,2],[7,5,3],[2,6,4]]\nOutput: 1\nExplanation: Each circle contains the node number in black and its distanceToLastNode value in blue. The only restricted path is 1 --> 3 --> 7.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "从第一个节点出发到最后一个节点的受限路径数", "translatedContent": "

现有一个加权无向连通图。给你一个正整数 n ,表示图中有 n 个节点,并按从 1n 给节点编号;另给你一个数组 edges ,其中每个 edges[i] = [ui, vi, weighti] 表示存在一条位于节点 uivi 之间的边,这条边的权重为 weighti

\n\n

从节点 start 出发到节点 end 的路径是一个形如 [z0, z1, z2, ..., zk] 的节点序列,满足 z0 = startzk = end 且在所有符合 0 <= i <= k-1 的节点 zizi+1 之间存在一条边。

\n\n

路径的距离定义为这条路径上所有边的权重总和。用 distanceToLastNode(x) 表示节点 nx 之间路径的最短距离。受限路径 为满足 distanceToLastNode(zi) > distanceToLastNode(zi+1) 的一条路径,其中 0 <= i <= k-1

\n\n

返回从节点 1 出发到节点 n受限路径数 。由于数字可能很大,请返回对 109 + 7 取余 的结果。

\n\n

 

\n\n

示例 1:

\n\"\"\n
\n输入:n = 5, edges = [[1,2,3],[1,3,3],[2,3,1],[1,4,2],[5,2,2],[3,5,1],[5,4,10]]\n输出:3\n解释:每个圆包含黑色的节点编号和蓝色的 distanceToLastNode 值。三条受限路径分别是:\n1) 1 --> 2 --> 5\n2) 1 --> 2 --> 3 --> 5\n3) 1 --> 3 --> 5\n
\n\n

示例 2:

\n\"\"\n
\n输入:n = 7, edges = [[1,3,1],[4,1,2],[7,3,4],[2,5,3],[5,6,1],[6,7,2],[7,5,3],[2,6,4]]\n输出:1\n解释:每个圆包含黑色的节点编号和蓝色的 distanceToLastNode 值。唯一一条受限路径是:1 --> 3 --> 7 。
\n\n

 

\n\n

提示:

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