- Design and Analysis of Algorithms
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- Basics of Algorithms
- DAA - Introduction to Algorithms
- DAA - Analysis of Algorithms
- DAA - Methodology of Analysis
- DAA - Asymptotic Notations & Apriori Analysis
- DAA - Time Complexity
- DAA - Master's Theorem
- DAA - Space Complexities
- Divide & Conquer
- DAA - Divide & Conquer Algorithm
- DAA - Max-Min Problem
- DAA - Merge Sort Algorithm
- DAA - Strassen's Matrix Multiplication
- DAA - Karatsuba Algorithm
- DAA - Towers of Hanoi
- Greedy Algorithms
- DAA - Greedy Algorithms
- DAA - Travelling Salesman Problem
- DAA - Prim's Minimal Spanning Tree
- DAA - Kruskal's Minimal Spanning Tree
- DAA - Dijkstra's Shortest Path Algorithm
- DAA - Map Colouring Algorithm
- DAA - Fractional Knapsack
- DAA - Job Sequencing with Deadline
- DAA - Optimal Merge Pattern
- Dynamic Programming
- DAA - Dynamic Programming
- DAA - Matrix Chain Multiplication
- DAA - Floyd Warshall Algorithm
- DAA - 0-1 Knapsack Problem
- DAA - Longest Common Subsequence Algorithm
- DAA - Travelling Salesman Problem using Dynamic Programming
- Randomized Algorithms
- DAA - Randomized Algorithms
- DAA - Randomized Quick Sort Algorithm
- DAA - Karger's Minimum Cut Algorithm
- DAA - Fisher-Yates Shuffle Algorithm
- Approximation Algorithms
- DAA - Approximation Algorithms
- DAA - Vertex Cover Problem
- DAA - Set Cover Problem
- DAA - Travelling Salesperson Approximation Algorithm
- Sorting Techniques
- DAA - Bubble Sort Algorithm
- DAA - Insertion Sort Algorithm
- DAA - Selection Sort Algorithm
- DAA - Shell Sort Algorithm
- DAA - Heap Sort Algorithm
- DAA - Bucket Sort Algorithm
- DAA - Counting Sort Algorithm
- DAA - Radix Sort Algorithm
- DAA - Quick Sort Algorithm
- Searching Techniques
- DAA - Searching Techniques Introduction
- DAA - Linear Search
- DAA - Binary Search
- DAA - Interpolation Search
- DAA - Jump Search
- DAA - Exponential Search
- DAA - Fibonacci Search
- DAA - Sublist Search
- DAA - Hash Table
- Graph Theory
- DAA - Shortest Paths
- DAA - Multistage Graph
- DAA - Optimal Cost Binary Search Trees
- Heap Algorithms
- DAA - Binary Heap
- DAA - Insert Method
- DAA - Heapify Method
- DAA - Extract Method
- Complexity Theory
- DAA - Deterministic vs. Nondeterministic Computations
- DAA - Max Cliques
- DAA - Vertex Cover
- DAA - P and NP Class
- DAA - Cook's Theorem
- DAA - NP Hard & NP-Complete Classes
- DAA - Hill Climbing Algorithm
- DAA Useful Resources
- DAA - Quick Guide
- DAA - Useful Resources
- DAA - Discussion
Deterministic vs. Nondeterministic Computations
To understand class P and NP, first we should know the computational model. Hence, in this chapter we will discuss two important computational models.
Deterministic Computation and the Class P
The deterministic computation always provides the same output during the initial state with all the data available. As long as there is no change in the computation, there is no randomness involved with it.
There are various models available to perform deterministic computation −
Deterministic Turing Machine
One of these models is deterministic one-tape Turing machine. This machine consists of a finite state control, a read-write head and a two-way tape with infinite sequence.
Following is the schematic diagram of a deterministic one-tape Turing machine.
A program for a deterministic Turing machine specifies the following information −
- A finite set of tape symbols (input symbols and a blank symbol)
- A finite set of states
- A transition function
In algorithmic analysis, if a problem is solvable in polynomial time by a deterministic one tape Turing machine, the problem belongs to P class.
Nondeterministic Computation and the Class NP
Nondeterministic Turing Machine
To solve the computational problem, another model is the Non-deterministic Turing Machine (NDTM). The structure of NDTM is similar to DTM, however here we have one additional module known as the guessing module, which is associated with one write-only head.
Following is the schematic diagram.
If the problem is solvable in polynomial time by a non-deterministic Turing machine, the problem belongs to NP class.
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