Which of the following problems should be solved using dynamic programming?1 pointMergesortBinary searchLongest common subsequenceQuicksort

The problem that should be solved using dynamic programming from the given options is the Longest Common Subsequence problem.

Dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems. It is used when the subproblems are not independent, i.e., when the solution to one subproblem can be used to solve other subproblems.

The Longest Common Subsequence (LCS) problem is a classic computer science problem that can be solved using dynamic programming. The LCS problem is to find the longest subsequence common to all sequences in a set of sequences (often just two sequences). It differs from problems of finding common substrings: unlike substrings, subsequences are not required to occupy consecutive positions within the original sequences.

On the other hand, Mergesort, Binary search, and Quicksort are algorithms that are more related to sorting and searching in data structures and do not typically involve dynamic programming.