Algorithm to compute minimum number of visible buildings?

You can find the lowest number from the given array and account for all occurances of this number. This will split the array into multiple subarrays and now you need to recursively solve the problem for each of them.

In the example:

1 2 3 1 2 3 (total = 0)

Smallest number is 1:

x 2 3 x 2 3 (total = 1)

Now you have 2 subarrays. Solve for the first one - the smallest number is 2:

  x 3       (total = 2)

Finally you have a single element: total = 3 Solving the other subarray makes it 5.

Here is some code in C#:

int Solve(int[] ar, int start, int end){
    //base for the recursion -> the subarray has single element
    if(end-start == 1) return 1;

    //base for the recursion -> the subarray is empty
    if(end-start < 1) return 0;

    //find min
    int m = int.MaxValue;
    for(int i = start; i < end; i++)
        if (ar[i] < m) m = ar[i];

    int total = 1;
    //find the subarrays and their contribution recursively
    int subStart = start;
    for(int subEnd = start; subEnd < end; subEnd++){
        if(ar[subEnd] == m) {
            total += Solve(ar, subStart, subEnd);
            subStart = subEnd + 1;
        }
    }
    total += Solve(ar, subStart, ar.Length);

    return total;
}