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.