Abstract
Abstract: The P vs NP problem is one of the most significant open problems in computer science and mathematics. This problem asks whether every problem that can be solved in polynomial time can also be verified in polynomial time. The purpose of this research paper is to explore the P vs NP problem and its relevance in the analysis of algorithms. We will discuss the techniques used to design and analyze algorithms, such as divide-and-conquer, dynamic programming, and greedy algorithms, and their relation to the P vs NP problem. We will also examine some examples of polynomial-time algorithms and NP-hard problems and analyze their time and space complexity, addition to which we will analyze the NP-Complete Problem and finally looking the current scenario of the P & NP and stating its significance.
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