# 1786. Number of Restricted Paths From First to Last Node

https://leetcode.com/problems/number-of-restricted-paths-from-first-to-last-node

## Description

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:**

![](https://assets.leetcode.com/uploads/2021/02/17/restricted_paths_ex1.png)

```
**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:**

![](https://assets.leetcode.com/uploads/2021/02/17/restricted_paths_ex22.png)

```
**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.

## ac

```java
```
