Algorithm Design & Analysis For Problem Solving

In life we are faced with a lot of problems. Sometimes the problems are simple and easy to solve but in a lot of other cases the problems are of mathematical type. We need to solve the problems in order to come to a solution. This is where algorithms come handy. By using algorithms we know how to divide the complex problems into small parts and solve them efficiently. In this application you will be seeing different types of algorithms which will help you in solving different types of mathematical problems.

In theoretical analysis of algorithms, it is common to estimate their complexity in the asymptotic sense, i.e., to estimate the complexity function for arbitrarily large input. The term "analysis of algorithms"was coined by Donald Knuth.

Algorithm analysis is an important part of computational complexity theory, which provides theoretical estimation for the required resources of an algorithm to solve a specific computational problem. Most algorithms are designed to work with inputs of arbitrary length. Analysis of algorithms is the determination of the amount of time and space resources required to execute it.

Usually, the efficiency or running time of an algorithm is stated as a function relating the input length to the number of steps, known as time complexity, or volume of memory, known as space complexity.

The various topics that you will find in this application are as follows.

Chapter: BASICS OF ALGORITHMS

1) INTRODUCTION

2) ANALYSIS OF ALGORITHMS

3) METHODOLOGY OF ANALYSIS

4) ASYMPTOTIC NOTATIONS & APRIORI ANALYSIS

5) SPACE COMPLEXITIES

Chapter : DESIGN STRATEGIES

6) DIVIDE & CONQUER

7 ) MAX-MIN PROBLEM

8 ) MERGE SORT

9 ) BINARY SEARCH

10) STRASSEN’S MATRIX MULTIPLICATION

11) GREEDY METHOD

12 ) FRACTIONAL KNAPSACK

13 ) JOB SEQUENCING WITH DEADLINE

14 ) OPTIMAL MERGE PATTERN

15 ) DYNAMIC PROGRAMMING

16 )KNAPSACK

17 )LONGEST COMMON SUBSEQUENCE

Chapter: GRAPH THEORY

18) SPANNING TREE

19) SHORTEST PATHS

20) MULTISTAGE GRAPH

21) TRAVELLING SALESMAN PROBLEM

22) OPTIMAL COST BINARY SEARCH TREES

Chapter: HEAP ALGORITHMS

23) BINARY HEAP

24) INSERT METHOD

25) HEAPIFY METHOD

26) EXTRACT METHOD

Chapter SORTING METHODS

27) BUBBLE SORT

28) INSERTION SORT

29) SELECTION SORT

30) QUICK SORT

31) RADIX SORT

Chapter: COMPLEXITY THEORY

32) DETERMINISTIC VS. NONDETERMINISTIC COMPUTATIONS

33) MAX CLIQUES

34) VERTEX COVER

35) P AND NP CLASS

36) COOK’S THEOREM

37) NP HARD & NP-COMPLETE CLASSES

38) HILL CLIMBING ALGORITHM

By considering an algorithm for a specific problem, we can begin to develop pattern recognition so that similar types of problems can be solved by the help of this algorithm.

Algorithms are often quite different from one another, though the objective of these algorithms is the same. For example, we know that a set of numbers can be sorted using different algorithms. Number of comparisons performed by one algorithm may vary with others for the same input. Hence, time complexity of those algorithms may differ. At the same time, we need to calculate the memory space required by each algorithm.

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