greedy algorithm to the travelling salesman problem
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- Use the Repeated Nearest Neighbor Algorithm to find an approximation for the optimal Hamiltonian circuit. 1. The Hamiltonian circuit given by the Nearest Neighbor Algorithm starting at vertex A is . The sum of it's edges is . 2. The Hamiltonian circuit given by the Nearest Neighbor Algorithm starting at vertex B is . The sum of it's edges is . 3. The Hamiltonian circuit given by the Nearest Neighbor Algorithm starting at vertex C is . The sum of its edges is . 4. The Hamiltonian circuit given by the Nearest Neighbor Algorithm starting at vertex D is . The sum of it's edges is . 5. The Hamiltonian circuit giving the approximate optimal solution using the Repeated Nearest Neighbor Algorithm is . The approximate optimal solution is . IMAGE BELOWThis question concerns computational complexity.In this question, the perfect square problem is the problem of determining if a positive integer, n, is a perfect square i.e. if n = x^2 where x is a positive integer.(a) The following decision algorithm, A, is proposed for the perfect square problem:Compute x^2 for integer x starting at x = 1 until x2 either equals or exceeds n. n is accepted in the former case and rejected otherwise.Based on A, what is the complexity class of the perfect square problem? Show your reasoning. (b) What is Heron's algorithm for finding the square root of a number?Using Wilson's Theorm, Fermat's Little Theorm and The Pollard Factorization Metod how could I solve Quetion 2 in Section 6.1