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

Use bitwise operator XOR. Here are example in JavaScript:

var numbers = [6, 2, 4, 5, 7, 1]; //2^3 exclude one, starting from 1
var result = 0;

//xor all values in numbers
for (var i = 0, l = numbers.length; i < l; i++) {
    result ^= numbers[i]; 
}

console.log(result); //3

numbers[0] = 3; //replace 6 with 3
//same as above in functional style
result = numbers.reduce(function (previousValue, currentValue, index, array) {return currentValue ^= previousValue;});

console.log(result); //6

The same in C#:

int[] numbers = {3, 2, 4, 5, 7, 1};

int missing = numbers.Aggregate((result, next) => result ^ next);

Console.WriteLine(missing);