- Design and Analysis of Algorithms
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- Basics of Algorithms
- DAA - Introduction
- DAA - Analysis of Algorithms
- DAA - Methodology of Analysis
- Asymptotic Notations & Apriori Analysis
- DAA - Space Complexities

- Design Strategies
- DAA - Divide & Conquer
- DAA - Max-Min Problem
- DAA - Merge Sort
- DAA - Binary Search
- Strassen’s Matrix Multiplication
- DAA - Greedy Method
- DAA - Fractional Knapsack
- DAA - Job Sequencing with Deadline
- DAA - Optimal Merge Pattern
- DAA - Dynamic Programming
- DAA - 0-1 Knapsack
- Longest Common Subsequence

- Graph Theory
- DAA - Spanning Tree
- DAA - Shortest Paths
- DAA - Multistage Graph
- Travelling Salesman Problem
- Optimal Cost Binary Search Trees

- Heap Algorithms
- DAA - Binary Heap
- DAA - Insert Method
- DAA - Heapify Method
- DAA - Extract Method

- Sorting Methods
- DAA - Bubble Sort
- DAA - Insertion Sort
- DAA - Selection Sort
- DAA - Quick Sort
- DAA - Radix Sort

- Complexity Theory
- Deterministic vs. Nondeterministic Computations
- DAA - Max Cliques
- DAA - Vertex Cover
- DAA - P and NP Class
- DAA - Cook’s Theorem
- NP Hard & NP-Complete Classes
- DAA - Hill Climbing Algorithm

- DAA Useful Resources
- DAA - Quick Guide
- DAA - Useful Resources
- DAA - Discussion

- Selected Reading
- UPSC IAS Exams Notes
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# Design and Analysis Divide and 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