The NP problems set of problems whose solutions are hard to find but easy to verify and are solved by Non-Deterministic Machine in polynomial time.
Any decision problem Pi is called NP-Hard if and only if every problem of NP(say P<subj) is reducible to Pi in polynomial time.
NP-Complete Problem: Any problem is NP-Complete if it is a part of both NP and NP-Hard Problem.
Difference between NP-Hard and NP-Complete:
|NP-Hard problems(say X) can be solved if and only if there is a NP-Complete problem(say Y) can be reducible into X in polynomial time.||NP-Complete problems can be solved by deterministic algorithm in polynomial time.|
|To solve this problem, it must be a NP problem.||To solve this problem, it must be both NP and NP-hard problem.|
|It is not a Decision problem.||It is exclusively Decision problem .|
|Example: Halting problem, Vertex cover problem, Circuit-satisfiability problem, etc.||Example: Determine whether a graph has a Hamiltonian cycle, Determine whether a Boolean formula is satisfiable or not, etc.|
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
- Proof that traveling salesman problem is NP Hard
- Difference between Hard Disk Drive (HDD) and Solid State Drive (SSD)
- Difference between Soft Computing and Hard Computing
- Difference between Hard link and Soft link
- Difference between Hard real time and Soft real time system
- Difference between Hard Disk and Floppy Disk
- Difference between Hard Copy and Soft Copy
- Difference between Hard drives and Flash drives
- Difference between Memory and Hard Disk
- Proof that Clique Decision problem is NP-Complete | Set 2
- Proof that Subgraph Isomorphism problem is NP-Complete
- Proof that Clique Decision problem is NP-Complete
- Hitting Set problem is NP Complete
- Proof that Collinearity Problem is NP Complete
- Algorithms | NP Complete | Question 1
- Algorithms | NP Complete | Question 2
- Algorithms | NP Complete | Question 3
- Algorithms | NP Complete | Question 4
- Algorithms | NP Complete | Question 5
- Algorithms | NP Complete | Question 6
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.