Package g1701_1800.s1786_number_of_restricted_paths_from_first_to_last_node

Class Solution

  • public class Solution
extends Object
    1786 - Number of Restricted Paths From First to Last Node.

    Medium

    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.

    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.

    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.

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

    Example 1:

    Input: n = 5, edges = [[1,2,3],[1,3,3],[2,3,1],[1,4,2],[5,2,2],[3,5,1],[5,4,10]]

    Output: 3

    Explanation: Each circle contains the node number in black and its distanceToLastNode value in blue. The three restricted paths are:

    1. 1 –> 2 –> 5

    2. 1 –> 2 –> 3 –> 5

    3. 1 –> 3 –> 5

    Example 2:

    Input: 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]]

    Output: 1

    Explanation: Each circle contains the node number in black and its distanceToLastNode value in blue. The only restricted path is 1 –> 3 –> 7.

    Constraints:

    • 1 <= n <= 2 * 104
    • n - 1 <= edges.length <= 4 * 104
    • edges[i].length == 3
    • 1 <= ui, vi <= n
    • ui != vi
    • 1 <= weighti <= 105
    • There is at most one edge between any two nodes.
    • There is at least one path between any two nodes.

    • Constructor Detail

      • Solution

        public Solution()

    • Method Detail

      • countRestrictedPaths

        public int countRestrictedPaths​(int n,
                                int[][] edges)