====================================================================================================================== Problem description
A non-empty zero-indexed array A consisting of N integers is given. A prefix_suffix_set is a pair of indices (P, S) such that 0 ≤ P, S < N and such that:
every value that occurs in the sequence A[0], A[1], ..., A[P] also occurs in the sequence A[S], A[S + 1], ..., A[N − 1],
every value that occurs in the sequence A[S], A[S + 1], ..., A[N − 1] also occurs in the sequence A[0], A[1], ..., A[P].
The goal is to calculate the number of prefix_suffix_sets in the array.
For example, consider array A such that:
A[0] = 3
A[1] = 5
A[2] = 7
A[3] = 3
A[4] = 3
A[5] = 5
There are exactly fourteen prefix_suffix_sets: (1, 4), (1, 3), (2, 2), (2, 1), (2, 0), (3, 2), (3, 1), (3, 0), (4, 2), (4, 1), (4, 0), (5, 2), (5, 1), (5, 0).
Write a function:
int solution(int A[], int N);
that, given a non-empty zero-indexed array A of N integers, returns the number of prefix_suffix_sets.
If the number of prefix_suffix_sets is greater than 1,000,000,000, the function should return 1,000,000,000.
For example, given:
A[0] = 3
A[1] = 5
A[2] = 7
A[3] = 3
A[4] = 3
A[5] = 5
the function should return 14, as explained above.
Assume that:
N is an integer within the range [1..40,000];
each element of array A is an integer within the range [−1,000,000,000..1,000,000,000].
Complexity:
expected worst-case time complexity is O(N*log(N));
expected worst-case space complexity is O(N), beyond input storage (not counting the storage required for input arguments).
Elements of input arrays can be modified.