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

Stassenâ€™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
Basic Concepts
The theory of NPcompleteness which we present here does not provide a
method of obtaining polynomial time algorithms for problems in the second
group. Nor does it say that algorithms of this complexity do not exist.
Instead,what we do is show that many of the problems for which there are no known polynomial time algorithms are computationally related. In fact,
we establish two classes of problems. These are given the names NPhard
and NPcomplete. A problem that is NPcomplete has the property that
it can be solved in polynomial time if and only if all other NPcomplete
problems can also be solved in polynomial time. If an NPhard problem
can be solved in polynomial time,then all NPcomplete problems can be
solved in polynomial time. All NPcomplete problems are NPhard, but
some NPhard problems are not known to be NPcomplete.
Although one can define many distinct problem classes having the
properties stated above for the NP hard and NP complete classes,the classes we study are related to nondeterministic computations(to be defined later). The relationship of these classes to nondeterministic computations together with the apparent power of nondeterminism leads to the intuitive (though as yet unproved)conclusion that no NPcomplete or NPhard problem is polynomially solvable.
We see that the class of NPhard problems(and the subclass of NV complete problems)is very rich as it contains many interesting problems from
a wide variety of disciplines. First,we formalize the preceding discussion of
the classes.