Solution: Path with Maximum Probability

Explore how to implement a modified Dijkstra's algorithm to find the path with the highest probability of success between two nodes in an undirected weighted graph. This lesson guides you through constructing a graph adjacency list, using a max heap for traversal, and updating probabilities to determine the most reliable path. You will understand the algorithm's steps, analyze its time and space complexities, and apply graph traversal techniques to real coding interview problems.

We'll cover the following...

Statement
Solution
- Time complexity
- Space complexity

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:

$2 \leq$ n $\leq 10^3$
$0 \leq$ start, end $<$ n
start $\neq$ ...