Stages of Divide and Conquer Algorithm
Divide and Conquer Algorithm can be divided into three stages: Divide, Conquer and Merge.
1. Divide:
- Break down the original problem into smaller subproblems.
- Each subproblem should represent a part of the overall problem.
- The goal is to divide the problem until no further division is possible.
2. Conquer:
- Solve each of the smaller subproblems individually.
- If a subproblem is small enough (often referred to as the “base case”), we solve it directly without further recursion.
- The goal is to find solutions for these subproblems independently.
3. Merge:
- Combine the sub-problems to get the final solution of the whole problem.
- Once the smaller subproblems are solved, we recursively combine their solutions to get the solution of larger problem.
- The goal is to formulate a solution for the original problem by merging the results from the subproblems.
Divide and Conquer Algorithm
Divide and Conquer algorithm is a problem-solving strategy that involves breaking down a complex problem into smaller, more manageable parts, solving each part individually, and then combining the solutions to solve the original problem. It is a widely used algorithmic technique in computer science and mathematics.
Example: In the Merge Sort algorithm, the “Divide and Conquer” strategy is used to sort a list of elements. Below image illustrate the dividing and merging states to sort the array using Merge Sort.
Table of Content
- What is Divide and Conquer?
- Stages of Divide and Conquer
- Applications of Divide and Conquer
- Basics of Divide and Conquer
- Standard Algorithms on Divide and Conquer
- Binary Search based problems
- Practice problems on Divide and Conquer
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