# 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 = 2

**Output:** 0.25000

**Explanation:** 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 = 2

**Output:** 0.30000

**Example 3:**

**Input:** n = 3, edges = [[0,1]], succProb = [0.5], start = 0, end = 2

**Output:** 0.00000

**Explanation:** 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]

- using Dijkstra algorithm to find the highest prob in the graph
- create a class “state” to track each node best prob
- create a hashmap to put all undirect edge into the map with prob
- priority queue to show the highest prob in the front
- start with the first node, if we meet the end node, we can return the best prob
- 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
- if could not find the end node, return 0;

[Java]