If the data is sorted, a binary search may be done (Figure 1-3). Variables Lb and Ub keep
track of the lower bound and upper bound of the array, respectively. We begin by examining the
middle element of the array. If the key we are searching for is less than the middle element, then
it must reside in the top half of the array. Thus, we set Ub to (M – 1). This restricts our next
iteration through the loop to the top half of the array. In this way, each iteration halves the size
of the array to be searched. For example, the first iteration will leave 3 items to test. After the
second iteration, there will be one item left to test. Therefore it takes only three iterations to find
This is a powerful method. Given an array of 1023 elements, we can narrow the search to
511 elements in one comparison. After another comparison, and we’re looking at only 255
elements. In fact, we can search the entire array in only 10 comparisons.
In addition to searching, we may wish to insert or delete entries. Unfortunately, an array is
not a good arrangement for these operations. For example, to insert the number 18 in Figure 1-1,
we would need to shift A…A down by one slot. Then we could copy number 18 into A.
A similar problem arises when deleting numbers. To improve the efficiency of insert and delete
operations, linked lists may be used.
int function BinarySearch (Array A , int Lb , int Ub , int Key );
M = ( Lb + Ub )/2;
if ( Key < A[M]) then
Ub = M – 1;
else if (Key > A[M]) then
Lb = M + 1;
return M ;
if (Lb > Ub) then
end;- 6 -