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 <code>edgesi = u_i, v_i, cnt_i</code> indicates that there is an edge between nodes <code>u_i</code> and <code>v_i</code> in the original graph, and <code>cnt_i</code> is the total number of new nodes that you will subdivide the edge into. Note that <code>cnt_i == 0</code> means you will not subdivide the edge.

To subdivide the edge <code>u_i, v_i</code>, replace it with <code>(cnt_i + 1)</code> new edges and <code>cnt_i</code> new nodes. The new nodes are <code>x₁</code>, <code>x₂</code>, ..., <code>x_{cnt_i}</code>, and the new edges are <code>u_i, x₁</code>, <code>x₁, x₂</code>, <code>x₂, x₃</code>, ..., <code>x_{cnt_i-1}, x_{cnt_i}</code>, <code>x_{cnt_i}, v_i</code>.

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:

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:

• <code>0 <= edges.length <= min(n * (n - 1) / 2, 10⁴)</code>

• edges[i].length == 3

• <code>0 <= u_i< v_i< n</code>

• There are no multiple edges in the graph.

• <code>0 <= cnt_i<= 10⁴</code>

• <code>0 <= maxMoves <= 10⁹</code>

• 1 <= n <= 3000