Given numbers from 1 to 2^32-1, one is missing. How to find the missing number optimally?

Question

You are given 2^32-2 unique numbers that range from 1 to 2^32-1. It\'s impossible to fit all the numbers into memory (thus sorting is not an option). You are asked to find t

Answer 1

Add all the numbers you are given up using your favourite big integer library, and subtract that total from the sum of all the numbers from 1 to 2^32-1 as obtained from the sum of arithmetic progression formula