DAA - Divide & Conquer

Many algorithms are recursive in nature to solve a given problem recursively dealing with sub-problems.

In divide and conquer approach, a problem is divided into smaller problems, then the smaller problems are solved independently, and finally the solutions of smaller problems are combined into a solution for the large problem.

Generally, divide-and-conquer algorithms have three parts −

• Divide the problem into a number of sub-problems that are smaller instances of the same problem.

• Conquer the sub-problems by solving them recursively. If they are small enough, solve the sub-problems as base cases.

• Combine the solutions to the sub-problems into the solution for the original problem.

Pros and cons of Divide and Conquer Approach

Divide and conquer approach supports parallelism as sub-problems are independent. Hence, an algorithm, which is designed using this technique, can run on the multiprocessor system or in different machines simultaneously.

In this approach, most of the algorithms are designed using recursion, hence memory management is very high. For recursive function stack is used, where function state needs to be stored.

Application of Divide and Conquer Approach

Following are some problems, which are solved using divide and conquer approach.

• Finding the maximum and minimum of a sequence of numbers
• Strassen’s matrix multiplication
• Merge sort
• Binary search