How do you prove knapsack is NP-complete?
Theorem 1 Knapsack is NP-complete. Proof: First of all, Knapsack is NP. The proof is the set S of items that are chosen and the verification process is to compute ∑i∈S si and ∑i∈S vi, which takes polynomial time in the size of input.
Is knapsack problem an example of an NP-complete problem?
Computational complexity The decision problem form of the knapsack problem (Can a value of at least V be achieved without exceeding the weight W?) is NP-complete, thus there is no known algorithm both correct and fast (polynomial-time) in all cases. There is a pseudo-polynomial time algorithm using dynamic programming.
Are NP-hard problems NP-complete?
The complexity class of problems of this form is called NP, an abbreviation for “nondeterministic polynomial time”. A problem is said to be NP-hard if everything in NP can be transformed in polynomial time into it even though it may not be in NP. Conversely, a problem is NP-complete if it is both in NP and NP-hard.
Which problems are NP-complete?
NP-complete problem, any of a class of computational problems for which no efficient solution algorithm has been found. Many significant computer-science problems belong to this class—e.g., the traveling salesman problem, satisfiability problems, and graph-covering problems.
Is Floyd warshall NP hard?
It is not NP-complete, because it is not a decision problem. In weighted complete graphs with non-negative edge weights, the weighted longest path problem is the same as the Travelling salesman path problem, because the longest path always includes all vertices.
Is shortest path problem NP-complete?
We show that the following variation of the single-source shortest path problem is NP-complete. Let a weighted, directed, acyclic graph G=(V,E,w) with source and sink vertices s and t be given. It is NP-complete by reduction from 3SAT. …
What is NP hard problem with example?
An example of an NP-hard problem is the decision subset sum problem: given a set of integers, does any non-empty subset of them add up to zero? That is a decision problem and happens to be NP-complete.
Which of the following is not NP hard?
Which of the following problems is not NP complete? Explanation: Hamiltonian circuit, bin packing, partition problems are NP complete problems.