Checking for Matching Nuts and Bolts Algorithm

How can we check if there is a nut and a bolt that have the same size?

Given a collection of n nuts and a collection of n bolts, each arranged in an increasing order of size, how can we efficiently determine if there is a nut and a bolt that have the same size?

Solution: Matching Nuts and Bolts Algorithm

To check if there is a nut and a bolt that have the same size, we can use the following O(n) time algorithm:

The algorithm works by iterating through the sizes of both the nuts and bolts arrays simultaneously. Here is a step-by-step explanation of how the algorithm functions:

1. Keep two iterators, i (for nuts array) and j (for bolts array).

2. While i < n and j < n:

a. If nuts[i] == bolts[j], there is a case where sizes match, and we can output/return the result.

b. If nuts[i] < bolts[j], it means that the size of the nut is smaller than that of the bolt. In this case, we should move to the next bigger nut by incrementing i (i.e., i += 1).

c. If nuts[i] > bolts[j], it means that the size of the bolt is smaller than that of the nut. In this case, we should move to the next bigger bolt by incrementing j (i.e., j += 1).

3. Repeat step 2 until either a matching pair is found or all elements have been compared.

Since the algorithm only goes through each index in both arrays once, it runs in O(n) time complexity, making it an efficient solution for checking if there is a nut and a bolt that have the same size.