Maximum weighted edge in path between two nodes in an N-ary tree using binary lifting
Given an N-ary tree with weighted edge and Q queries where each query contains two nodes of the tree. The task is to find the maximum weighted edge in the simple path between these two nodes.
Naive Approach: A simple solution is to traverse the whole tree for each query and find the path between the two nodes.
Efficient Approach: The idea is to use binary lifting to pre-compute the maximum weighted edge from every node to every other node at distance of some
. We will store the maximum weighted edge till
- j is the node and
- i is the distance of
- dp[i][j] stores the parent of j at
- distance if present, else it will store 0
- mx[i][j] stores the maximum edge from node j to the parent of this node at
We’ll do a depth-first search to find all the parents at
distance and their weight and then precompute parents and maximum edges at every
Below is the implementation of the above approach:
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Time Complexity: O(N*logN).
Auxiliary Space: O(N*logN).