Polynomial time

Polynomial time is a way to measure the amount of time it takes to solve a problem using a computer. Imagine you have a big puzzle with lots of pieces to put together. If you have to check every single piece to see where it fits, it would take you a really long time. But if you have a trick to quickly eliminate pieces that don't fit, it would be much faster.

Just like that, some problems can be solved quickly using a special trick that helps the computer eliminate some wrong answers. These problems are said to be "solvable in polynomial time." A polynomial is a mathematical function that involves adding, subtracting, multiplying, and raising a number to a power. If a problem can be solved in polynomial time, it means that the amount of time it takes to find the answer increases at most as a polynomial function of the problem's size.

For example, let's say you have to sort a list of numbers. If you had to compare every single number to every other number to sort the list, it would take a really long time as the size of list increases. But a special trick called "quicksort" eliminates lots of unnecessary comparisons, allowing the computer to sort the list much faster, and in polynomial time.

In summary, "polynomial time" means that we have a way to solve a problem quickly, using a special trick that eliminates unnecessary work, and the amount of time it takes to solve the problem increases at most as a polynomial function of the problem's size.