Editorial for CTU Open Contest 2018 - Numbers Generator

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Keep track of current state with Finite automaton.
We can use Aho-Corasick algorithm to achieve this.
We create matrix $A$ ~A~ with probabilities of transitions.
We can achieve this by giving each edge in Aho-Corasick $\frac 1 2$ ~\frac 1 2~ probability of traversal, and creating edges with probability $1$ ~1~ from all final states to one common final state.
Now find the expected number of steps before ending in absorbing state.
After solving $(E-A)x = 1$ ~(E-A)x = 1~, the answer can be found in $x_0$ ~x_0~.
To solve this equation, we can use Gaussian Elimination.
Complexity $\mathcal O((WB)^3)$ ~\mathcal O((WB)^3)~

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