Binary Search

Look at middle element of sorted array in range [first, last) until the target is found or run out of elements. Return index of target or last.

Analysis (same parameters as Sequential Search)

Objects	Type	Kind	Movement	Name
array of values	int[ ]	varying	received	arr
index of lower bound	int	varying	received	first
index of upper bound	int	varying	received	last
search target	int	varying	received	target
index of target	int	varying	returned	---
index of midpoint	int	varying	local	mid
value at midpoint	int	varying	local	midValue
original last index	int	varying	local	origLast

Algorithm

1. Initialize origLast to last
2. While first < last do

   2.1

   Compute mid = (first+last)/2

   2.2

   Set midValue to arr[mid]

   2.3

   If target equals midValue then (found a match)

   2.3.1 Return mid

   2.4

   Else if target less than midValue then (in lower half)

   2.4.1 Set last to mid

   2.5

   Else (in upper half)

   2.5.1 Set first to mid+1

3. Return origLast (target not found)

Code

// Precondition: first <= last
int BinSearch (const int arr[], int first, int last, int target)
{
   int mid,              // index of midpoint
       midValue,         // value at midpoint
       origLast = last;  // save original value of last

   // while the sublist is not empty
   while (first < last)
   {
      mid = (first+last)/2;
      midValue = arr[mid];
      if (target==midValue)        // found a match
         return mid;
      else if (target < midValue)  // search lower half
         last = mid;
      else                         // search upper half
         first = mid+1;
   }  // end while

   return origLast;                // target not found
}  // end BinSearch