Discuss the Characteristics and features of Problems which are solved using following Design Techniques i. Divide and Conquer ii. Greedy iii. Dynamic Programming Also Compare these Design Techniques

 The divide and conquer design technique involves dividing a large problem into smaller subproblems, solving each of the subproblems individually, and then combining the solutions to the subproblems to get a solution to the original problem. This technique is typically used for problems that can be divided into subproblems that are similar in nature and can be solved independently of each other. Examples of problems that can be solved using the divide and conquer technique include sorting algorithms, such as quicksort and mergesort, and certain mathematical algorithms, such as the fast Fourier transform.

The greedy design technique involves making a series of decisions that are locally optimal in the hope of finding a global optimal solution to a problem. This technique is typically used for optimization problems, where the goal is to find the best solution among a set of possible solutions. Examples of problems that can be solved using the greedy technique include the knapsack problem and the minimum spanning tree problem.

The dynamic programming design technique involves breaking a problem down into smaller subproblems, storing the solutions to these subproblems in a table, and then using the solutions in the table to solve the original problem. This technique is typically used for problems that have overlapping subproblems, where the solution to one subproblem can be used to solve other subproblems. Examples of problems that can be solved using dynamic programming include the longest common subsequence problem and the traveling salesmanperson problem.

In comparison, the divide and conquer technique is generally more effective for problems that can be divided into independent subproblems, while the greedy technique is more effective for optimization problems. Dynamic programming, on the other hand, is more effective for problems with overlapping subproblems. Additionally, the divide and conquer and dynamic programming techniques typically require more time and space complexity, while the greedy technique has lower time and space complexity.