How to Solve Number of Good Paths Problem
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Number of Good Paths
There is a tree (i.e. a connected, undirected graph with no cycles) consisting of n nodes numbered from 0 to n - 1 and exactly n - 1 edges. You are given a 0-indexed integer array vals of length n where vals[i] denotes the value of the ith node. You are also given a 2D integer array edges where edges[i] = [ai, bi] denotes that there exists an undirected edge connecting nodes ai and bi. A good path is a simple path that satisfies the following conditions: Return the number of distinct good paths. Note that a path and its reverse are counted as the same path. For example, 0 -> 1 is considered to be the same as 1 -> 0. A single node is also considered as a valid path.
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Understanding the Number of Good Paths Problem
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Problem Statement
There is a tree (i.e. a connected, undirected graph with no cycles) consisting of n nodes numbered from 0 to n - 1 and exactly n - 1 edges. You are given a 0-indexed integer array vals of length n where vals[i] denotes the value of the ith node. You are also given a 2D integer array edges where edges[i] = [ai, bi] denotes that there exists an undirected edge connecting nodes ai and bi. A good path is a simple path that satisfies the following conditions: Return the number of distinct good paths. Note that a path and its reverse are counted as the same path. For example, 0 -> 1 is considered to be the same as 1 -> 0. A single node is also considered as a valid path.
Number of Good Paths
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Examples
# Example 1
vals = [1,3,2,1,3], edges = [[0,1],[0,2],[2,3],[2,4]]
6
# Example 2
vals = [1,1,2,2,3], edges = [[0,1],[1,2],[2,3],[2,4]]
7
# Example 3
vals = [1], edges = []
1
Constraints
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Solve Number of Good Paths — There is a tree (i.e. a connected, undirected graph with no cycles) consisting o...
Here's the optimal approach using Array:
Time: O(n) | Space: O(n)
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