Probability of a Path in an HMM

[hamidgasmi]

Compute the probability of a hidden path in an HMM.

Input: A hidden path π in an HMM (Σ, States, Transition, Emission).

Output: The probability of this path, Pr(π).

Input Format.
The 1st line of the input contains the path π in the HMM
The 2nd line of the input is “--------” (a delimiter).
The 3rd line of the input is the list of states States (space-separated).
The 4th line of the input is “--------” (a delimiter).
The remaining lines are the transition matrix Transition, depicted as a tab-delimited |States| by |States| matrix.
You may assume that transitions from the initial state occur with equal probability.

Output Format.
The probability of this path, Pr(π), to at least 3 significant figures.

Constraints. 50 ≤ |π| ≤ 100; |States| = 10