count distinct slices in an array

The solution is not correct because your algorithm is wrong.

First of all, let me show you a counter example. Let A = {2, 1, 2}. The first iteration: base = 0, fibot = 0, sum += 1. That's right. The second one: base = 0, fibot = 1, sum += 2. That's correct, too. The last step: fibot = 2, check[A[fibot]] is true, thus, base = 2. But it should be 1. So your code returns1 + 2 + 1 = 4 while the right answer 1 + 2 + 2 = 5.

The right way to do it could be like this: start with L = 0. For each R from 0 to n - 1, keep moving the L to the right until the subarray contais only distinct values (you can maintain the number of occurrences of each value in an array and use the fact that A[R] is the only element that can occur more than once).

There is one more issue with your code: the sum variable may overflow if int is 32-bit type on the testing platform (for instance, if all elements of A are distinct).

As for the question WHY your algorithm is incorrect, I have no idea why it should be correct in the first place. Can you prove it? The base = fibot assignment looks quite arbitrary to me.