Divide & Conquer
Divide & Conquer
The Divide & Conquer algorithm design approach is a problem-solving technique that involves breaking down a complex problem into smaller, more manageable subproblems. It follows a recursive approach where each subproblem is solved independently, and their solutions are combined to obtain the final solution to the original problem.
The divide and conquer approach typically consists of three steps: divide, conquer, and combine.
1. Divide: The first step involves dividing the original problem into smaller, more manageable subproblems. This division is performed recursively until the subproblems become simple enough to be solved directly. The division can be based on various criteria, such as splitting the problem into halves, dividing it based on a specific property, or partitioning the input data.
2. Conquer: Once the problem is divided into subproblems, the next step is to solve each subproblem independently. This is done by applying the same algorithm recursively to each subproblem until a base case is reached. The base case represents the simplest form of the problem that can be solved directly without further division.
3. Combine: After solving the subproblems, the final step is to combine their solutions to obtain the solution to the original problem. This involves merging or integrating the results from the subproblems in a way that produces the desired output for the overall problem.
The key idea behind the divide and conquer approach is that by breaking down a complex problem into smaller, more manageable parts, it becomes easier to solve each part individually. This can lead to improved efficiency and can often result in more concise and elegant algorithms.
Common examples of algorithms that use the divide and conquer approach include merge sort, quicksort, binary search, and the fast Fourier transform (FFT). These algorithms demonstrate how dividing the problem, solving the subproblems, and combining the results can lead to efficient solutions for a wide range of problems.
The links below opens Jupyter Notebook pages on Google Colab (https://colab.research.google.com/) and presents how to solve the corresponding computer science problem using the Divide & Conquer algorithmic design approach.
List of a computer science problem that can be solved using Divide and Conquer: