Binary search if array contains duplicates

Question

Hi,

what is the index of the search key if we search for 24 in the following array using binary search.

array = [10,20,21,24,24,24,24,24,30,40,45]
         


        

Answer 1

As pointed out by @Pleepleus it will return the index 5 from the first level of recursion itself. However I would like to point out few things about binary search :

1. Instead of using mid = (left + right)/2 , use mid = left + (right-left)/2

2. If you want to search for lower_bound or upper_bound of an element use the following algorithms:

   binLowerBound(a, lo, hi, x)
     if (lo > hi)
       return lo;
   
     mid = lo +  (hi - lo) / 2;
     if (a[mid] == x)
       return binLowerBound(a, lo, mid-1, x);
     else if (a[mid] > x)
       return binLowerBound(a, lo, mid-1, x);
     else
       return binLowerBound(a, mid+1, hi, x);
   
   binHigherBound(a, lo, hi, x)
     if (lo > hi)
       return lo;
     mid = lo + (hi - lo) / 2;
     if (a[mid] == x)
       return binHigherBound(a, mid+1, hi, x);
     else if (a[mid] > x)
       return binHigherBound(a, lo, mid-1, x);
     else
       return binHigherBound(a, mid+1, hi, x);