In less-than-linear time, find the duplicate in a sorted array

Question

Today, an interviewer asked me this question. My immediate response was that we could simply do a linear search, comparing the current element with the previous element in t

Answer 1

The example array is a little bit different from your question. Since n is the length of array and there are one and only duplicate in array, the value of each element in array should be in [0,n-1].

If that is true, then this question is the same one with How to find a duplicate element in an array of shuffled consecutive integers?

The following code should find the duplicate in O(n) time and O(1) space.

public static int findOnlyDuplicateFromArray(int[] a, boolean startWithZero){
    int xor = 0;
    int offset = 1;
    for(int i=0; i < a.length; i++){
        if(startWithZero)
            xor = xor ^ (a[i] + offset) ^ i;
        else
            xor = xor ^ a[i] ^ i;
        }
        if(startWithZero)
            xor = xor - offset;
    return xor;
}