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g0801_0900.s0882_reachable_nodes_in_subdivided_graph.readme.md Maven / Gradle / Ivy

882\. Reachable Nodes In Subdivided Graph

Hard

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`