Algorithms Analysis Practice Test

Integer Factorization is categorized as a problem that is believed to be difficult and falls into the NP (nondeterministic polynomial time) problems. This means that, as of the current understanding in computational complexity theory, there is no polynomial-time algorithm known that can solve all instances of this problem efficiently. This stems from the nature of integer factorization, where the task is to decompose a large integer into its prime factors. While it is quick to verify a solution if one is provided (by multiplying the factors back together), finding those factors directly remains a computationally challenging problem. In contrast, sorting algorithms and graph traversal problems like depth-first search and breadth-first search can all be solved in polynomial time. Linear programming is also efficient, with methods such as the Simplex algorithm and Interior-Point methods offering polynomial time solutions for practical sizes of input. Thus, Integer Factorization stands out as a problem not classified as P, making it the correct choice here.