Given an array nums containing n + 1 integers where each integer is between 1 and n (inclusive), prove that at least one duplicate number must exist. Assume that there is only one duplicate number, ...

The main purpose of these assignments is to learn to implement some number theory algorithms and learn how we can use them with big data. Number theory has important applications in computer ...

We do scan the unique items list for each entry in the main list, but even in a worst case this greatly reduces the number of comparisons. Those two examples let us check for duplicates. The improved ...