Question

Given an Array arr of size 100000, each element 0 <= arr[i] < 100. (not sorted, contains duplicates)

Find out how many triplets (i,j,k) are present such that arr[i] ^ arr[j] ^ arr[k] == 0
Note : ^ is the Xor operator. also 0 <= i <= j <= k <= 100000

I have a feeling i have to calculate the frequencies and do some calculation using the frequency, but i just can’t seem to get started.

Any algorithm better than the obvious O(n^3) is welcome. 🙂

It’s not homework. 🙂

Answer 1

I think the key is you don’t need to identify the i,j,k, just count how many.

Initialise an array size 100

Loop though arr, counting how many of each value there are – O(n)

Loop through non-zero elements of the the small array, working out what triples meet the condition – assume the counts of the three numbers involved are A, B, C – the number of combinations in the original arr is (A+B+C)/!A!B!C! – 100**3 operations, but that’s still O(1) assuming the 100 is a fixed value.

So, O(n).