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Prove that the following problem, given a set S of integers and a number t, is of the NP class. Is there a subset of S whose elements add up to t?

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Concept explainers

Eight puzzle problem

The N-puzzle problem contains N tiles (N+1 including empty tiles) where the value of N can be 8, 15, 24, etc. The puzzle is divided into the square root of (N+1) rows and the square root of (N+1) columns. These problems have an initial state or configuration and a goal state or configuration. The puzzle can be solved by shifting the tiles one by one in the empty space. The objective is to place the numbers on the tiles to match the final state using the empty space. The other name for the N-puzzle problem is the sliding puzzle.

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Prove that the following problem, given a set S of integers and a number t, is of the NP class. Is there a subset of S whose elements add up to t?
Note: An issue with data structures and algorithms

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