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
Analysis Framework
Once the algorithm is built, the next step is to analyze how efficient the algorithm is ?
In order to analyze the algorithm, we actually consider two parameters.
TIME & SPACE
We measure efficiency of an algorithm in terms of how fast it runs (executes) and we refer to it as time efficiency.
And we also measure efficiency of an algorithm in terms of how much extra (more) space the algorithm requires to run(executes).
Time efficiency can be analyzed on following 2 factors:
1)Based on number of inputs the algorithm accepts.
It is known fact that as number of inputs given to the algorithm increases , the consumed to execute the same would also increase .
For Example, it always takes a longer time to solve a tower of Hanoi problem with 5 discs when compared it with 3 discs
2)Measuring Unit of Time.
An Algorithm running time can be measured in several units of time
For Example, we may use a few standard units such as milliseconds, microseconds etc.
But we have drawbacks with these units such as speed of computer , the programming language used to implement the algorithm etc.,makes it difficult to measure algorithms efficiency . we would like to have a parameter (unit) which does not depend on above factors.
#ONE WAY IS TO COUNT THE NUMBER OF TIMES THE BASIC OPERATION IS EXECUTED.
Hence , the time efficiency is analyses by determining the number of times the basic operation is repeated as a function of input size (number of inputs accepted)
i.e. T(n) ≈ Cop C(n)
Where,
T> running time Cop>Execution time of basic operation
C>number of times basic operation is executed n>size of input.