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NP - Completeness Minimization Problem

Please show me the detailed solution and explanation to the question attached.

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Solution Preview

The basic idea of my algorithm is binary search. Suppose A(x,k) is the algorithm that solves the decision version of P with instance x and size k. We define the cost function with instance x and size n as follows:

int CostOfP(x, n)
// The cost of instance x is between 1 and n^4
start = 1;

Solution Summary

Determines algorithm's complexity and completes response to questions.