Given two trees and an integer , connect one node from the first tree to one node from the second tree. For each node in the first tree, count how many nodes in the combined graph are within distance at most after the connection, and maximize that count.
Problem
You are given two undirected trees, tree1 and tree2, with n and m nodes respectively. Each tree is described by its edges.
You may add exactly one edge connecting any node in tree1 to any node in tree2.
For a chosen node u in tree1, define its target nodes as the nodes whose distance from u in the new combined graph is at most k.
Return an array where the i-th value is the maximum possible number of target nodes for node i in tree1 after choosing the best connection edge between the two trees.
Key idea
The connection between the trees changes distances only through the newly added bridge. The task is to count nodes reachable within a distance limit and maximize the contribution from the second tree by placing the bridge strategically.
Input Format
edges1: edges of the first tree, whereedges1.length = n - 1edges2: edges of the second tree, whereedges2.length = m - 1k: non-negative integer distance limit
Each edge is an undirected pair of nodes using 0-based labels.
Output Format
- Return an integer array
ansof lengthn ans[i]is the maximum number of nodes with distance<= kfrom nodeiintree1after connecting the two trees with one edge
Constraints
- Both
tree1andtree2are valid trees. - Node labels are distinct within each tree and start at 0.
- The added edge must connect one node from
tree1to one node fromtree2. - The exact input sizes are not provided in the source metadata.
Example 1
Input
edges1 = [[0,1],[1,2],[1,3]], edges2 = [[0,1],[0,2],[2,3]], k = 2
Output
[6,6,6,5]
Explanation
For each node in tree1, count nodes within distance 2 after choosing the best edge between the trees.
- Node 0 can reach nodes 0,1,2,3 in tree1 and 2 nodes in tree2 through a good connection, for a total of 6.
- Node 1 can reach all 4 nodes in tree1 and 2 nodes in tree2, for a total of 6.
- Node 2 can also reach 4 nodes in tree1 and 2 nodes in tree2, for a total of 6.
- Node 3 can reach 3 nodes in tree1 and 2 nodes in tree2, for a total of 5.
Example 2
Input
edges1 = [[0,1]], edges2 = [[0,1]], k = 1
Output
[3,3]
Explanation
Each node in tree1 can always count itself and its direct neighbor in tree1. By connecting the trees through either endpoint, one node from tree2 becomes reachable within distance 1 from the chosen endpoint in tree1, giving a total of 3 for each node.
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