How to Solve Number of Ways to Assign Edge Weights I Problem
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Number of Ways to Assign Edge Weights I
There is an undirected tree with n nodes labeled from 1 to n, rooted at node 1. The tree is represented by a 2D integer array edges of length n - 1, where edges[i] = [ui, vi] indicates that there is a...
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Understanding the Number of Ways to Assign Edge Weights I Problem
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Problem Statement
There is an undirected tree with n nodes labeled from 1 to n, rooted at node 1. The tree is represented by a 2D integer array edges of length n - 1, where edges[i] = [ui, vi] indicates that there is an edge between nodes ui and vi. Initially, all edges have a weight of 0. You must assign each edge a weight of either 1 or 2. The cost of a path between any two nodes u and v is the total weight of all edges in the path connecting them. Select any one node x at the maximum depth. Return the number of ways to assign edge weights in the path from node 1 to x such that its total cost is odd. Since the answer may be large, return it modulo 109 + 7. Note: Ignore all edges not in the path from node 1 to x.
Number of Ways to Assign Edge Weights I
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Examples
edges = [[1,2]]1The path from Node 1 to Node 2 consists of one edge (1 → 2). Assigning weight 1 makes the cost odd, while 2 makes it even. Thus, the number of valid assignments is 1.
edges = [[1,2],[1,3],[3,4],[3,5]]2The maximum depth is 2, with nodes 4 and 5 at the same depth. Either node can be selected for processing. For example, the path from Node 1 to Node 4 consists of two edges (1 → 3 and 3 → 4). Assigning weights (1,2) or (2,1) results in an odd cost. Thus, the number of valid assignments is 2.
Constraints
2 <= n <= 105edges.length == n - 1edges[i] == [ui, vi]1 <= ui, vi <= nedges represents a valid tree.How Interview Coder Helps with Leetcode Problems
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