Extra Credit. Hex Game Hex Game is a board game played by two players. It is pla

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Extra Credit. Hex Game Hex Game is a board game played by two players. It is played on a graph G- (V,E) with two specified vertices s,teV. The players alternate choosing a vertex from V- s.t with those chosen by player 1 being colored blue and those chosen by player 2 being colored red. Play continues until all vertices except s and t are being colored. Player 1 wins, if and only if there is a path from s to t that passes through blue vertices Hex Game" problem Input: graph G, vertices s,t Question: Can Player 1 win? Prove, that "Hex Game" e NP. Explain each step of the proof

Explanation / Answer

Answer

given by

In "Hex Game"

the first player contain the captivating strategy. To establish that "Hex Game" f NP.

The proof is explain using NP. Generally proving any crisis that belongs to confident dilemma to a complexity classes is to transform the other predicament using a polynomial conversion that original quandary is straightly translatable to the way out to extra.

For NP complete quantify Boolean formula (QBF) is been used for conversion.

By this attestation Hex is equal to revolution of any quantified Boolean formula.

this carried out by more number of straightforward alteration via a polynomial time. The over statement prove that Hex belongs to NP inclusive, and hence it must also NP• entire. The QBF is logical phrase.

The layout of QBF Q_1X_1Q_2X_2………Q_Mx_m

here x_i is Boolean patchy is a cooperative or existential quantifier.

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