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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