# A Simple Definition

The formal definition of “*NP*-Complete” uses reductions, or transformations, of one problem to another. Suppose we want to solve a problem **P** and we already have an algorithm for another problem **Q**. Suppose we also have a function *T* that takes an input *x* for **P** and produces *T(x)*, an input for **Q** such that the correct answer for **P** on *x* is *yes* if and only if the correct answer for **Q** on *T(x)* is *yes*. Then, by composing *T* and the algorithm for **Q**, we have an algorithm for **P**.

Simple. Right?