## Microsoft Interview Question for SDE-2s

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AnswersYou are given a directed cyclic graph represented by an adjacency matrix. The graph has at least one terminal node (i.e. the node with no outgoing edges).

Each edge of the graph is assigned a positive integer representing a probability of taking this edge. E.g. if you have 3 outgoing edges with numbers 3, 2, and 4, this means that the prob. of taking these edges are: 3/9, 2/9 and 4/9, respectively.

You need to find the probability of reaching each terminal node from the starting node 0.

Example:

adjacency matrix 5x5:`m = {{0 1 0 0 1}, {0 0 3 2 0}, {4 0 0 1 0}, {0 0 0 0 0}, {0 0 0 0 0}}`

so we have two terminal nodes here: 3 and 4

- pavel.emeliyanenko@toptal.com May 11, 2021 in United States

we can take the following paths:

0 -> 1 -> 3 = probability: 1/2*2/5 = 1/5

0 -> 1 -> 2 -> 3 = probability: 1/2*3/5*1/5 = 3/50

0 -> 1 -> 2 -> 0 -> 1 -> 3 ... and so on

or to the node 4:

0 -> 4: probability: 1/2

0 -> 1 -> 2 -> 0 -> 4: probability 1/2*3/5*4/5*1/2 = 3/25

and so on, summing up probabilities of all possible paths we get:

total probability to reach node 3: 13/38

total probability to reach node 4: 25/38| Report Duplicate | Flag | PURGE

Microsoft SDE-2 Algorithm

**Country:**United States

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