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Find integer not occurring twice in an array
Accenture interview question – find the only unpaired element in the array

Given an array of integers of odd size. All the integers in the array appear twice except for a single integer. How to find this uncoupled integer in most efficient (both memory and complexity-wise) way?

Answer 1

If you XOR all of them together, you’ll end up with the lone (uncoupled) value.

That’s because x XOR x is zero for all x values, and 0 XOR x is x.

By way of example, the following program outputs 99:

#include <stdio.h>
int main (void) {
    int num[] = { 1, 2, 3, 4, 5, 99, 1, 2, 3, 4, 5};
    unsigned int i;
    int accum;

    for (accum = 0, i = 0; i < sizeof(num)/sizeof(*num); i++)
        accum ^= num[i];

    printf ("%d\n", accum);

    return 0;
}

In terms of efficiency, it’s basically O(1) space and O(n) time complexity, minimal, average and worst case.