>>11543196Not quite. Big O notation is how a function scales in relation to the size of the input. Take the following:
O(n^5000), polynomial time
O(2^n), exponential time
For most numbers n we'd deal with in a computer situation, the latter would be faster. But eventually, if n becomes great enough, the exponential would exceed the former.
So essentially, P = NP would be true if it takes O(n^2) to check a filled out sodoku puzzle's correctness and O(n^100) to find the solution to a sodoku puzzle.
