The problem belongs to Codility, here is the link to the problem

Following code segment contains the description in the class comments, followed by fully working solution

/**
 * A pair of integers (P, Q), such that 0 ≤ P ≤ Q < N, is called a slice of array A. The slice consists of the elements A[P], A[P + 1], ..., A[Q]. A distinct slice is a slice consisting of only unique numbers. That is, no individual number occurs more than once in the slice.
 *
 * For example, consider integer M = 6 and array A such that:
 *
 *     A[0] = 3
 *     A[1] = 4
 *     A[2] = 5
 *     A[3] = 5
 *     A[4] = 2
 * There are exactly nine distinct slices: (0, 0), (0, 1), (0, 2), (1, 1), (1, 2), (2, 2), (3, 3), (3, 4) and (4, 4).
 *
 * The goal is to calculate the number of distinct slices.
 */

public int solution(int[] A) {
        Arrays.sort(A);
        int tr=0;
        for(int p=0;p < A.length-2;p++){
            int q=p+1;
            int r=p+2;
            while(r < A.length){
                if(A[p]+A[q] > A[r]){
                    // if it works for p,q and r.. then it should work for all q's in between q and r.. hence r-q
                    tr+=(r-q);
                    r++;
                }else if (q < r-1){
                    // ELSE of the condition.. meaning it didn't work for R, now start incrementing Q for this new R.
                    q++;
                }else{
                    // Q==R-1 , and p,q,r doesn't work.. try moving both q and r now.. or else P itself in the for then
                    r++;
                    q++;
                }
            }
        }
        return tr;
    }