Practice Number of Good Paths
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Number of Good Paths
A tree has node values vals and undirected edges. Count its simple paths whose two endpoints have equal values and whose intermediate nodes have values no greater than those endpoints. A one-node path counts. A path and the same path traversed backwards count only once. Practice approach: Process node values in increasing groups. Union edges through already allowed values, then count nodes with the current value in each connected component. A component with c such nodes contributes c*(c+1)/2 paths, including single-node paths. Sorting dominates at O(n log n); disjoint-set operations are nearly linear.
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Understanding the Number of Good Paths Problem
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Problem Statement
A tree has node values vals and undirected edges. Count its simple paths whose two endpoints have equal values and whose intermediate nodes have values no greater than those endpoints. A one-node path counts. A path and the same path traversed backwards count only once. Practice approach: Process node values in increasing groups. Union edges through already allowed values, then count nodes with the current value in each connected component. A component with c such nodes contributes c*(c+1)/2 paths, including single-node paths. Sorting dominates at O(n log n); disjoint-set operations are nearly linear.
Source: Number of Good Paths on LeetCode. Use the original task for its coding environment and submissions.
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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