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Data Structures Divide and Conquer

The divide and conquer approach involves breaking a problem into smaller sub-problems, solving each independently, and then merging the solutions to form the final answer. This process consists of three main steps: Divide, Conquer, and Merge. Examples of algorithms that utilize this approach include Merge Sort, Quick Sort, and Binary Search.

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47 views2 pages

Data Structures Divide and Conquer

The divide and conquer approach involves breaking a problem into smaller sub-problems, solving each independently, and then merging the solutions to form the final answer. This process consists of three main steps: Divide, Conquer, and Merge. Examples of algorithms that utilize this approach include Merge Sort, Quick Sort, and Binary Search.

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10/11/2018 Data Structures Divide and Conquer

DATA STRUCTURES - DIVIDE AND CONQUER


https://www.tutorialspoint.com/data_structures_algorithms/divide_and_conquer.htm Copyright © tutorialspoint.com

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In divide and conquer approach, the problem in hand, is divided into smaller sub-problems and then each problem is solved
independently. When we keep on dividing the subproblems into even smaller sub-problems, we may eventually reach a stage where no
more division is possible. Those "atomic" smallest possible sub-problem f ractions are solved. The solution of all sub-problems is finally
merged in order to obtain the solution of an original problem.

Broadly, we can understand divide-and-conquer approach in a three-step process.

Divide/Break
This step involves breaking the problem into smaller sub-problems. Sub-problems should represent a part of the original problem. This
step generally takes a recursive approach to divide the problem until no sub-problem is further divisible. At this stage, sub-problems
become atomic in nature but still represent some part of the actual problem.

Conquer/Solve
This step receives a lot of smaller sub-problems to be solved. Generally, at this level, the problems are considered 'solved' on their own.

Merge/Combine
When the smaller sub-problems are solved, this stage recursively combines them until they formulate a solution of the original problem.
This algorithmic approach works recursively and conquer & merge steps works so close that they appear as one.

Examples
The following computer algorithms are based on divide-and-conquer programming approach −

Merge Sort
Quick Sort
Binary Search
Strassen's Matrix Multiplication
Closest pair points

There are various ways available to solve any computer problem, but the mentioned are a good example of divide and conquer approach.

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