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Solution: Path with Maximum Probability

Explore how to solve the maximum probability path problem in undirected weighted graphs. Understand constructing adjacency lists and applying a max-heap based version of Dijkstra's algorithm to maximize traversal success probability between two nodes. This lesson helps you implement efficient graph algorithms and analyze their time and space complexity for coding interviews.

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 ...