Computational Theory Questions
Decision problems and optimization problems are two different types of computational problems.
Decision problems are concerned with determining whether a given input satisfies a certain property or condition. The answer to a decision problem is either "yes" or "no". For example, given a list of numbers, a decision problem could be to determine whether there exists a pair of numbers in the list that sum up to a specific target value.
On the other hand, optimization problems involve finding the best solution among a set of possible solutions. The goal is to optimize a certain objective function, which could be maximizing or minimizing a certain value. Unlike decision problems, optimization problems do not have a simple "yes" or "no" answer. Instead, they require finding the optimal solution that satisfies certain constraints. For example, in the traveling salesman problem, the objective is to find the shortest possible route that visits a set of cities and returns to the starting city.
In summary, the main difference between decision problems and optimization problems lies in the nature of the answer they seek. Decision problems aim to determine whether a certain condition is satisfied, while optimization problems aim to find the best solution among a set of possibilities.