Codeforces 16E Fish - Problem Statement

There are $n$ fish in a lake. Each second, two fish meet uniformly at random, and one eats the other. You're given a matrix where $a[i][j]$ is the probability that fish $i$ eats fish $j$ when they meet.

Find the probability that each fish is the last survivor. Output $n$ probabilities.

Constraints: $n \le 18$. This hints at bitmask DP since $2^{18}$ states are manageable.

Simulating all meeting sequences grows factorially. Instead, track the set of surviving fish as state since transitions only depend on which fish remain.