# 0882. Reachable Nodes In Subdivided Graph

<https://leetcode.com/problems/reachable-nodes-in-subdivided-graph>

## Description

You are given an undirected graph (the **"original graph"**) with `n` nodes labeled from `0` to `n - 1`. You decide to **subdivide** each edge in the graph into a chain of nodes, with the number of new nodes varying between each edge.

The graph is given as a 2D array of `edges` where `edges[i] = [ui, vi, cnti]` indicates that there is an edge between nodes `ui` and `vi` in the original graph, and `cnti` is the total number of new nodes that you will **subdivide** the edge into. Note that `cnti == 0` means you will not subdivide the edge.

To **subdivide** the edge `[ui, vi]`, replace it with `(cnti + 1)` new edges and `cnti` new nodes. The new nodes are `x1`, `x2`, ..., `xcnti`, and the new edges are `[ui, x1]`, `[x1, x2]`, `[x2, x3]`, ..., `[xcnti-1, xcnti]`, `[xcnti, vi]`.

In this **new graph**, you want to know how many nodes are **reachable** from the node `0`, where a node is **reachable** if the distance is `maxMoves` or less.

Given the original graph and `maxMoves`, return *the number of nodes that are **reachable** from node* `0` *in the new graph*.

**Example 1:**

![](https://s3-lc-upload.s3.amazonaws.com/uploads/2018/08/01/origfinal.png)

```
**Input:** edges = [[0,1,10],[0,2,1],[1,2,2]], maxMoves = 6, n = 3
**Output:** 13
**Explanation:** The edge subdivisions are shown in the image above.
The nodes that are reachable are highlighted in yellow.
```

**Example 2:**

```
**Input:** edges = [[0,1,4],[1,2,6],[0,2,8],[1,3,1]], maxMoves = 10, n = 4
**Output:** 23
```

**Example 3:**

```
**Input:** edges = [[1,2,4],[1,4,5],[1,3,1],[2,3,4],[3,4,5]], maxMoves = 17, n = 5
**Output:** 1
**Explanation:** Node 0 is disconnected from the rest of the graph, so only node 0 is reachable.
```

**Constraints:**

* `0 <= edges.length <= min(n * (n - 1) / 2, 104)`
* `edges[i].length == 3`
* `0 <= ui < vi < n`
* There are **no multiple edges** in the graph.
* `0 <= cnti <= 104`
* `0 <= maxMoves <= 109`
* `1 <= n <= 3000`

## ac

```java
```
