Algorithm

Getting Started with AlgorithmWhat is an Algorithm?

Characteristics of Algorithm1 Topic

Analysis Framework

Performance Analysis3 Topics

Mathematical Analysis2 Topics

Sorting AlgorithmSorting Algorithm10 Topics

Searching Algorithm6 Topics

Fundamental of Data StructuresStacks

Queues

Graphs

Trees

Sets

Dictionaries

Divide and ConquerGeneral Method

Binary Search

Recurrence Equation for Divide and Conquer

Finding the Maximum and Minimum

Merge Sort

Quick Sort

Stassen’s Matrix Multiplication

Advantages and Disadvantages of Divide and Conquer

Decrease and ConquerInsertion Sort

Topological Sort

Greedy MethodGeneral Method

Coin Change Problem

Knapsack Problem

Job Sequencing with Deadlines

Minimum Cost Spanning Trees2 Topics

Single Source Shortest Paths1 Topic

Optimal Tree Problem1 Topic

Transform and Conquer Approach1 Topic

Dynamic ProgrammingGeneral Method with Examples

Multistage Graphs

Transitive Closure1 Topic

All Pairs Shortest Paths6 Topics

BacktrackingGeneral Method

NQueens Problem

Sum of Subsets problem

Graph Coloring

Hamiltonian Cycles

Branch and Bound2 Topics

0/1 Knapsack problem2 Topics

NPComplete and NPHard Problems1 Topic
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As another example of divideandconquer, we investigate a sorting algorithm that has the nice property that in the worst case its complexity is 0(n logn). This algorithm is called merge sort. We assume throughout that the elements are to be sorted in non decreasing order.Given a sequence of n elements( also called keys) a[l],… ,a[n], the general idea is to imagine them split into two sets a[l],… ,a[[n/2]] and a[[n/2]+ 1],… ,a[n]. Each set is individually sorted,and the resulting sorted sequences are merged to produce a single sorted sequence of n elements. Thus we have another ideal example of the divideandconquer strategy in which the splitting is into two equalsized sets and the combining operation is the merging of two sorted sets into one.
MergeSort (Algorithm 6) describes this process very succinctly using recursion and a function Merge (Algorithm 7)which merges two sorted sets. Before executing Merge Sort,the n element should be placed in a[1 :n]. Then MergeSort (1,n) causes the keys to be rearranged into non decreasing order in a.
Below figure shows the diagram of working of merge sort algorithm in divide and conquer approach.