Efficient way to count occurrences of a key in a sorted array

Question

This was asked in on-site Microsoft interview.

Count the number of occurrences of a given key in an array.

I answered linear search because the elements may be s

Answer 1

For unsorted array there is not much we can do other than linear search.

For sorted array you can do it in O(logN) using a slightly modified binary search:

• Find the index of first occurrence of key, call it f.
• Find the index of last occurrence of key, call it l.
• If the key exists in the array l-f+1 is the answer.

Finding the first occurrence:

arr[i] is the first occurrence of key iff

• arr[i] == key and either
  • i == 0 ( it's the first element of the array) or
  • arr[i-1] != key (it's not the first element of the array and element to it's left is different)

You can slightly modify the binary search to find the first occurrence.
In a binary search you terminate the search when you find arr[mid] == key.
Modify the condition such that you terminate the search when you find the first occurrence instead of any occurrence.

Algorithm:

low = 0
high = arrSize - 1 

while low <=  high

  mid = (low + high) / 2

  //if arr[mid] == key         // CHANGE
  if arr[mid] == key AND ( mid == 0 OR arr[mid-1] != key )
    return mid
  //else if ( key < arr[mid] ) // CHANGE
  else if ( key <= arr[mid] ) 
    high = mid - 1
  else
    low = mid + 1        
  end-if

end-while

return -1

Similarly you can find the last occurrence.