Given the following recursive binary search algorithm for finding an element in a sorted array of integers:

Given the following recursive binary search algorithm for finding an element in a sorted array of integers:

int recursiveBinarySearch(int[] array, int target, int left, int right)

{

  if (left > right)    

return -1;

  int middle = (left + right) / 2; 

 if (array[middle] == target)

   return middle;  

if (array[middle] > target)

    return recursiveBinarySearch(array, target, left, middle - 1);  

return recursiveBinarySearch(array, target, middle + 1, right);

}

Assume n is the length of the array. Find the initial condition and recurrence equation that expresses the execution time for the worst case of this algorithm and then solve that recurrence.