Question

Explain the general procedure of divide and conquer method

Answer 1

The Divide and Conquer method is the most widely applicable technique for designing efficient algorithms. It works in three stages, as shown below:

1. Divide: Recursively divide the bigger problem of size n into smaller sub-problems of size n/2.
2. Solve: Sub-problems are solved independently.
3. Combine: Combine solutions of smaller sub-problems to derive the solution of the larger big problem of size n.

Smaller sub-problems are similar to the larger problem with smaller arguments. Hence, such problems can be solved easily using recursion. Divide and conquer is a multi-branched, top-down recursive approach. Each branch indicates one sub-problem and it calls itself with the smaller argument.

 

 

Above diagram shows the working of Divide and Conquer method

 

 

 

 

Comments

The Divide and Conquer method is a problem-solving technique that involves dividing a large problem into smaller sub-problems that are easier to solve, solving each sub-problem independently, and then combining the solutions to get the solution for the original problem.

This technique is based on the idea that a problem can be broken down into smaller problems that are similar to the original problem but easier to solve. By recursively dividing the original problem into smaller sub-problems, we can solve each sub-problem independently, which reduces the complexity of the problem.

Once the sub-problems are solved, their solutions are combined to derive the solution for the larger big problem of size n. This combining step involves merging the solutions of smaller sub-problems to form a solution for the original problem.

Divide and conquer is a recursive approach that involves breaking down a problem into sub-problems and solving each sub-problem independently. This approach is widely used in many algorithms, including sorting algorithms like merge sort and quicksort, and in finding the closest pair of points in a plane.