How to Solve Minimum Increments to Equalize Leaf Paths Problem
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Minimum Increments to Equalize Leaf Paths
You are given an integer n and an undirected tree rooted at node 0 with n nodes numbered from 0 to n - 1. This is represented by a 2D array edges of length n - 1, where edges[i] = [ui, vi] indicates a...
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Understanding the Minimum Increments to Equalize Leaf Paths Problem
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Problem Statement
You are given an integer n and an undirected tree rooted at node 0 with n nodes numbered from 0 to n - 1. This is represented by a 2D array edges of length n - 1, where edges[i] = [ui, vi] indicates an edge from node ui to vi . Each node i has an associated cost given by cost[i], representing the cost to traverse that node. The score of a path is defined as the sum of the costs of all nodes along the path. Your goal is to make the scores of all root-to-leaf paths equal by increasing the cost of any number of nodes by any non-negative amount. Return the minimum number of nodes whose cost must be increased to make all root-to-leaf path scores equal.
Minimum Increments to Equalize Leaf Paths
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Examples
n = 3, edges = [[0,1],[0,2]], cost = [2,1,3]1There are two root-to-leaf paths: Path 0 → 1 has a score of 2 + 1 = 3. Path 0 → 2 has a score of 2 + 3 = 5. To make all root-to-leaf path scores equal to 5, increase the cost of node 1 by 2. Only one node is increased, so the output is 1.
n = 3, edges = [[0,1],[1,2]], cost = [5,1,4]0There is only one root-to-leaf path: Path 0 → 1 → 2 has a score of 5 + 1 + 4 = 10. Since only one root-to-leaf path exists, all path costs are trivially equal, and the output is 0.
n = 5, edges = [[0,4],[0,1],[1,2],[1,3]], cost = [3,4,1,1,7]1There are three root-to-leaf paths: Path 0 → 4 has a score of 3 + 7 = 10. Path 0 → 1 → 2 has a score of 3 + 4 + 1 = 8. Path 0 → 1 → 3 has a score of 3 + 4 + 1 = 8. To make all root-to-leaf path scores equal to 10, increase the cost of node 1 by 2. Thus, the output is 1.
Constraints
2 <= n <= 105edges.length == n - 1edges[i] == [ui, vi]0 <= ui, vi < ncost.length == n1 <= cost[i] <= 109The input is generated such that edges represents a valid tree.How Interview Coder Helps with Leetcode Problems
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