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Solution: Path with Maximum Probability

Explore how to apply graph theory and Dijkstra's algorithm variation to determine the path with maximum success probability between two nodes in a weighted graph. Understand the construction of adjacency lists, use of a max heap for prioritizing paths, and evaluate time and space complexities of this algorithm.

Statement

You are given an undirected weighted graph of n nodes, represented by a 0-indexed list, edges, where edges[i] = [a, b] is an undirected edge connecting the nodes a and b. There is another list succProb, where succProb[i] is the probability of success of traversing the edge edges[i].

Additionally, you are given two nodes, start and end. Your task is to find the path with the maximum probability of success to go from start to end and return its success probability. If there is no path from start to end, return 0.

Constraints:

  • 22 \leq n 103\leq 10^3

  • 00 \leq start, end << n

  • start \neq ...