# Leetcode 1514. Path with Maximum Probability

[medium]

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

Given two nodes `start` and `end`, 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. Your answer will be accepted if it differs from the correct answer by at most 1e-5.

Example 1:

`Input: n = 3, edges = [[0,1],[1,2],[0,2]], succProb = [0.5,0.5,0.2], start = 0, end = 2Output: 0.25000Explanation: There are two paths from start to end, one having a probability of success = 0.2 and the other has 0.5 * 0.5 = 0.25.`

Example 2:

`Input: n = 3, edges = [[0,1],[1,2],[0,2]], succProb = [0.5,0.5,0.3], start = 0, end = 2Output: 0.30000`

Example 3:

`Input: n = 3, edges = [[0,1]], succProb = [0.5], start = 0, end = 2Output: 0.00000Explanation: There is no path between 0 and 2.`

Constraints:

• `2 <= n <= 10^4`
• `0 <= start, end < n`
• `start != end`
• `0 <= a, b < n`
• `a != b`
• `0 <= succProb.length == edges.length <= 2*10^4`
• `0 <= succProb[i] <= 1`
• There is at most one edge between every two nodes.

[Think]

1. using Dijkstra algorithm to find the highest prob in the graph
2. create a class “state” to track each node best prob
3. create a hashmap to put all undirect edge into the map with prob
4. priority queue to show the highest prob in the front
5. start with the first node, if we meet the end node, we can return the best prob
6. Else, check the map with linked edge and check the new prob. If the new prob is lower than current best record, no need to update
7. if could not find the end node, return 0;

[Java]

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CS new grad, 6 years experience related to supply chain management. Located in Bay area