# Leetcode 1514. Path with Maximum Probability

`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.`
`Input: n = 3, edges = [[0,1],[1,2],[0,2]], succProb = [0.5,0.5,0.3], start = 0, end = 2Output: 0.30000`
`Input: n = 3, edges = [[0,1]], succProb = [0.5], start = 0, end = 2Output: 0.00000Explanation: There is no path between 0 and 2.`
• `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.
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;

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