Prove that each of following problems is in P by sketching a polynomial time alg

Question

Prove that each of following problems is in P by sketching a polynomial time algorithm that solves it. Briefly justify that your algorithm runs in polynomial. (1) EASY SOLUTION = {(F) | F is a formula in 3cnf which is satisfied by assigning the same truth value to all of its variables (i.e., all variables are true or all variables are false)} (2) LARGE-SUBSET = {(S, k, t) | S = {x_1, ..., x_n} is a set of positive numbers such there exists a set {y_1, .., y_k} subsetoforequalto S where sigma^k_i = 1 y_i greaterthanorequalto t} (3) COMPLETE = {(G) | G is a complete graph (i.e., it contains a clique of size n where n is the number of nodes in the graph)} SPATH = {(G, s, t, k) | G is an undirected graph with a simple path from s to t with length at most k}

Explanation / Answer

4)Answer:

4.

For SPATH = {<G, s, t, k> | G is an undirected graph by means of a simple path from s to t with distance end to end at most k}

The length of the direct paths exposed.

On input <G, s, t, k> wherever m-node graph G has nodes a and b:

                     Unmarked node b, spot node t by “i + 1”.

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