How to Solve Shortest Path in a Weighted Tree Problem
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Shortest Path in a Weighted Tree
You are given an integer n and an undirected, weighted tree rooted at node 1 with n nodes numbered from 1 to n. This is represented by a 2D array edges of length n - 1, where edges[i] = [ui, vi, wi] i...
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Understanding the Shortest Path in a Weighted Tree Problem
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Problem Statement
You are given an integer n and an undirected, weighted tree rooted at node 1 with n nodes numbered from 1 to n. This is represented by a 2D array edges of length n - 1, where edges[i] = [ui, vi, wi] indicates an undirected edge from node ui to vi with weight wi. You are also given a 2D integer array queries of length q, where each queries[i] is either: [1, u, v, w'] – Update the weight of the edge between nodes u and v to w', where (u, v) is guaranteed to be an edge present in edges. [2, x] – Compute the shortest path distance from the root node 1 to node x. Return an integer array answer, where answer[i] is the shortest path distance from node 1 to x for the ith query of [2, x].
Shortest Path in a Weighted Tree
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Examples
n = 2, edges = [[1,2,7]], queries = [[2,2],[1,1,2,4],[2,2]][7,4]Query [2,2]: The shortest path from root node 1 to node 2 is 7. Query [1,1,2,4]: The weight of edge (1,2) changes from 7 to 4. Query [2,2]: The shortest path from root node 1 to node 2 is 4.
n = 3, edges = [[1,2,2],[1,3,4]], queries = [[2,1],[2,3],[1,1,3,7],[2,2],[2,3]][0,4,2,7]Query [2,1]: The shortest path from root node 1 to node 1 is 0. Query [2,3]: The shortest path from root node 1 to node 3 is 4. Query [1,1,3,7]: The weight of edge (1,3) changes from 4 to 7. Query [2,2]: The shortest path from root node 1 to node 2 is 2. Query [2,3]: The shortest path from root node 1 to node 3 is 7.
n = 4, edges = [[1,2,2],[2,3,1],[3,4,5]], queries = [[2,4],[2,3],[1,2,3,3],[2,2],[2,3]][8,3,2,5]Query [2,4]: The shortest path from root node 1 to node 4 consists of edges (1,2), (2,3), and (3,4) with weights 2 + 1 + 5 = 8. Query [2,3]: The shortest path from root node 1 to node 3 consists of edges (1,2) and (2,3) with weights 2 + 1 = 3. Query [1,2,3,3]: The weight of edge (2,3) changes from 1 to 3. Query [2,2]: The shortest path from root node 1 to node 2 is 2. Query [2,3]: The shortest path from root node 1 to node 3 c
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