You are given a collection of n bolts of different widths and n corresponding nuts. You are allowed to try a pair of a nut and a bolt together, from which you can determine whether the nut is larger or smaller than the bolt, or matches the bolt exactly. However, there is no way to compare two nuts together or two bolts together. The problem is to match each bolt to its nut. Design an algorithm for solving this problem and show that the time complexity of your algorithm is O(n^2) in the worst case and O(n log K ) in the average case.