Design and Analysis of Algorithms
Selected Reading
- DAA - Discussion
- DAA - Useful Resources
- DAA - Quick Guide
- DAA - Hill Climbing Algorithm
- NP Hard & NP-Complete Classes
- DAA - Cook’s Theorem
- DAA - P and NP Class
- DAA - Vertex Cover
- DAA - Max Cliques
- Deterministic vs. Nondeterministic Computations
- DAA - Sublist Search
- DAA - Fibonacci Search
- DAA - Exponential Search
- DAA - Jump Search
- DAA - Interpolation Search
- DAA - Binary Search
- DAA - Linear Search
- Searching Techniques Introduction
- DAA - Radix Sort
- DAA - Counting Sort
- DAA - Bucket Sort
- DAA - Heap Sort
- DAA - Shell Sort
- DAA - Selection Sort
- DAA - Insertion Sort
- DAA - Bubble Sort
- DAA - Extract Method
- DAA - Heapify Method
- DAA - Insert Method
- DAA - Binary Heap
- Optimal Cost Binary Search Trees
- DAA - Multistage Graph
- DAA - Shortest Paths
- DAA - Spanning Tree
- Travelling Salesperson Approximation Algorithm
- Set Cover Problem
- Vertex Cover Problem
- Approximation Algorithms
- Fisher-Yates Shuffle
- Karger’s Minimum Cut
- Randomized Quick Sort
- Randomized Algorithms
- Travelling Salesman Problem | Dynamic Programming
- Longest Common Subsequence
- DAA - 0-1 Knapsack
- Floyd Warshall Algorithm
- Matrix Chain Multiplication
- DAA - Dynamic Programming
- DAA - Optimal Merge Pattern
- DAA - Job Sequencing with Deadline
- DAA - Fractional Knapsack
- Map Colouring Algorithm
- Dijkstra’s Shortest Path Algorithm
- Kruskal’s Minimal Spanning Tree
- Travelling Salesman Problem
- DAA - Greedy Method
- Towers of Hanoi
- Karatsuba Algorithm
- Strassen’s Matrix Multiplication
- DAA - Binary Search
- DAA - Merge Sort
- DAA - Max-Min Problem
- DAA - Divide & Conquer
- DAA - Space Complexities
- Master’s Theorem
- Time Complexity
- Asymptotic Notations & Apriori Analysis
- DAA - Methodology of Analysis
- DAA - Analysis of Algorithms
- DAA - Introduction
- Home
Selected Reading
- Who is Who
- Computer Glossary
- HR Interview Questions
- Effective Resume Writing
- Questions and Answers
- UPSC IAS Exams Notes
DAA - Divide & Conquer
Design and Analysis - Divide and Conquer
Using spanide and conquer approach, the problem in hand, is spanided into smaller sub-problems and then each problem is solved independently. When we keep spaniding the sub-problems into even smaller sub-problems, we may eventually reach a stage where no more spanision is possible. Those smallest possible sub-problems are solved using original solution because it takes lesser time to compute. The solution of all sub-problems is finally merged in order to obtain the solution of the original problem.
Broadly, we can understand spanide-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 spanide the problem until no sub-problem is further spanisible. At this stage, sub-problems become atomic in size 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.
Pros and cons of Divide and Conquer Approach
Divide and conquer approach supports parallepsm 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.
Examples of Divide and Conquer Approach
The following computer algorithms are based on spanide-and-conquer programming approach −
Merge Sort
Quick Sort
Binary Search
Strassen s Matrix Multippcation
Closest pair (points)
Karatsuba
There are various ways available to solve any computer problem, but the mentioned are a good example of spanide and conquer approach.
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