For example, you can verify that a given solution to the TSP visits every city.These problems are referred to as Non-deterministic Polynomial problems or NP-type problems.The challenge for programmers is to find a P-type solution to NP-type problems.
Algorithms of the class O(n are solutions to tractable problems.
Some problems can only be solved with algorithms whose execution time grows too quickly in relation to their input to be solved in polynomial time. The Travelling Salesperson Problem is the example most used to describe intractability.
For example, finding the factors of a number or finding the n prime number.
A counting problem requires a total of the solutions to a search problem.
What we do is pick a place to start from, try every possible route, store the total cost of each journey and compare them when all routes have been found.
For a map with 4 cities, it's quite easy to see what we would have to do, All this means that there are (n-1)! Fine if we start with a small number of cities but not workable when the number of cities increases.
Looking back at how we compare algorithms, we know that algorithms that execute in exponential time grow too quickly to be useful with large inputs. There are many intractable problems that still get solved by computer. Producing a timetable for a school is an intractable problem - an optimal solution is likely to require a program that executes in exponential time.
Quicker answers are required so a different approach to solving the problem tends to be used.
For example, 'how many of the first 100 integers are prime? Optimization problems require the identification of the best solution to a search problem from a given set of solutions. Info) ,mentioned in the page on Abstraction, is a good example of this.
This program was designed to find optimal and suboptimal solutions to the Rubik's cube from given states.