# Path With Maximum Probability

Moderate
0/80
Average time to solve is 25m
Contributed by

## Problem statement

You are given an undirected unweighted graph and an array 'sProability' which denotes the probability of traversing edges such that 'sProability[i]' denotes the probability of traversing ith edge. You are given the start and end vertex, You need to determine the maximum path probability on going from start to end vertex if there is no path from start to end return 0.

Detailed explanation ( Input/output format, Notes, Images )
Constraints
``````1 <= T <= 10
1 <= N <= 5 * 10 ^ 4
1 <= M <= min((N * (N - 1) / 2),10^5)
0 <= VERTEX VALUE, START, END <= N - 1
0 <= sProability[i] <= 1

Time Limit: 1 second
``````
Sample Input 1
``````1
3 3 0 2
0 1
1 2
0 2
0.9 0.9 0.75
``````
Sample Output 1
``````0.810000
``````
Explanation for Sample Output 1:
``````For the test case 1:

The graph is as follows:
``````

``````Path with maximum probability from 0 to 1 is 0->2->1. Hence the maximum probability is 0.90 * 0.90 = 0.81.
``````
Sample Input 2
``````1
4 2 0 2
0 1
2 3
0.8 0.8
``````
Sample Output 2
``````0.000000
``````
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