hich of the following problems should be solved using dynamic programming? Mergesort  Binary search Longest common subsequence Quicksort

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

Here's why:

1. Mergesort and Quicksort are sorting algorithms, they are not typically solved using dynamic programming. They have their own specific algorithms to solve them.

2. Binary search is a search algorithm, which is used to find the position of a specific value within a sorted array. It also does not require dynamic programming.

3. The Longest Common Subsequence (LCS) problem, however, 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. Dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems. It is applicable to problems exhibiting the properties of overlapping subproblems and optimal substructure.