I recently had an interview and was given a small problem that I was to code up.
The problem was basically find duplicates in an array of length n, using constant space in O(n). Each element is in the range 1-(n-1) and guaranteed to be a duplicate. This is what I came up with:
public int findDuplicate(int[] vals) {
int indexSum=0;
int valSum=0;
for (int i=0; i< vals.length; i++) {
indexSum += i;
valSum += vals[i];
}
return valSum - indexSum;
}
Then we got into a discussion about the runtime of this algorithm. A sum of series from 0 -> n = (n^2 + n)/2 which is quadratic. However, isn't the algorithm O(n) time? The number of operations are bound by the length of the array right?
What am I missing? Is this algorithm O(n^2)?
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