pavel.emeliyanenko@toptal.com
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13of 13 votes
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 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
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