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Finding terminal states in markov chain matrix (Simple project)

This project was awarded to quantmacro for $30 USD.

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Project Budget
$10 - $30 USD
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Project Description

I want someone to solve this problem in either Java/python.

Write a function answer(m) that takes an array of array of nonnegative ints representing how many times that state has gone to the next state and return an array of ints for each terminal state giving the exact probabilities of each terminal state, represented as the numerator for each state, then the denominator for all of them at the end and in simplest form. The matrix is at most 10 by 10. It is guaranteed that no matter which state the elements is in, there is a path from that state to a terminal state. That is, the processing will always eventually end in a stable state. The elements starts in state 0. The denominator will fit within a signed 32-bit integer during the calculation, as long as the fraction is simplified regularly. For example, consider the matrix m:

[

[0,1,0,0,0,1], # s0, the initial state, goes to s1 and s5 with equal probability

[4,0,0,3,2,0], # s1 can become s0, s3, or s4, but with different probabilities

[0,0,0,0,0,0], # s2 is terminal, and unreachable (never observed in practice)

[0,0,0,0,0,0], # s3 is terminal

[0,0,0,0,0,0], # s4 is terminal

[0,0,0,0,0,0], # s5 is terminal

]

So, we can consider different paths to terminal states, such as:

s0 -> s1 -> s3

s0 -> s1 -> s0 -> s1 -> s0 -> s1 -> s4

s0 -> s1 -> s0 -> s5

Tracing the probabilities of each, we find that

s2 has probability 0

s3 has probability 3/14

s4 has probability 1/7

s5 has probability 9/14

Function format:

Java:

public static int[] calculate(int[][] m) {

// Your code goes here.

}

Python:

def answer(m):

Your program will be tested for custom inputs.

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