Show that if P=NP then there is a polynomial-time algorithm for the following search problem: given...

Show that if P=NP then there is a polynomial-time algorithm for the following search problem: given a graph, find its largest clique.

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Prove that the partition problem is NP-complete by giving a polynomial time reduction of the subset-sum...

Prove that the partition problem is NP-complete by giving a polynomial time reduction of the subset-sum problem to the partition problem.

What is P-Problem? What is NP-Problem? What is NP-Complete problem?

Given the pseudocode for Binary Search Algorithm as below: BinarySearch(A, p, r, V) if p...

Given the pseudocode for Binary Search Algorithm as below: BinarySearch(A, p, r, V) if p < r q = (p + r)/2 if V = A[q] return q else if V > A[q] return BinarySearch(A, q+1, r, V) else return BinarySearch(A, p, q-1) else if p = r, if V = A[p] return p else return -1 return -1 end function Using this pseudocode, write a function for BinarySearch and also complete the program, by...

Show that the following problem is NP-hard. Input: A boolean function in CNF such that every...

Show that the following problem is NP-hard. Input: A boolean function in CNF such that every clause has at most three literals and every variable appears in at most three clauses. Output: An assignment that evaluates the given function TRUE.

Show that if G is a group of order np where p is prime and 1...

Show that if G is a group of order np where p is prime and 1 < n < p, then G is not simple. (Please do not use Sylow theorem)

Given: Polynomial P(x) of degree 6 Given: x=3 is a zero for the Polynomial above List...

Given: Polynomial P(x) of degree 6 Given: x=3 is a zero for the Polynomial above List all combinations of real and complex zeros, but do not consider multiplicity for the zeros.

Let T∈ L(V), and let p ∈ P(F) be a polynomial. Show that if p(λ) is...

Let T∈ L(V), and let p ∈ P(F) be a polynomial. Show that if p(λ) is an eigenvalue of p(T), then λ is an eigenvalue of T. Under the additional assumption that V is a complex vector space, and conclude that {μ | λ an eigenvalue of p(T)} = {p(λ) | λan eigenvalue of T}.

Let X be a Bin(n, p) random variable. Show that Var(X) = np(1 − p). Hint:...

Let X be a Bin(n, p) random variable. Show that Var(X) = np(1 − p). Hint: First compute E[X(X − 1)] and then use (c) and (d). (c) Var(X) = E(X^2 ) − (E X)^ 2 (d) E(X + Y ) = E X + E Y

What is the Average time complexity of sequential search algorithm in a linked list?

(a) Assume that a polynomial-time primality testing algorithm, calledPrimes is available, which takes as input a...

(a) Assume that a polynomial-time primality testing algorithm, calledPrimes is available, which takes as input a single numbern >1 and outputs whethernis a primenumber or not. Now consider the following algorithm: Input: A natural number n > 1 Algorithm Mystery(n) if ( n mod 2 == 0 ) then if (n == 2) then output ‘‘Input is a prime number’’ else ‘‘Input is not a prime number’’ else Primes(n) What is Algorithm Mystery trying to achieve? What is tightest...

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