The Stanford researchers apply Grover’s algorithm to the number partitioning problem by encoding each possible partition of the integer list as a quantum state. They also formulate an oracle that can ...

For Mario, the team also prove that the games are NP-complete, an additional property with important consequences. Many difficult problems can be converted into any problem in the NP-complete ...

He then uses graph theory to prove that any game exhibiting both location traversal and single-use paths is NP-hard, that’s the same class of complexity as the travelling salesman problem.