Binary Search

Algorithm 4.6:  (Binary Search)  BINARY(DATA, LB, UB, ITEM, LOC)

Here DATA ia a sorted array with lower bound LB and upper bound UB, and ITEM is a given item of information. The variables BEG, END and MID denote, respectively, the beginning, end and middle locations of a segment of elements of DATA.This algorithm finds the location LOC of ITEM in DATA or sets LOC = NULL.

1.  [Initialize segment variables.]
      Set BEG : = LB, END  : = UB and MID = INT((BEG+END)/2).

2.  Repeat Steps 3 and 4 while BEG < END and DATA[MID] != ITEM

3.  If ITEM < DATA[MID], then:

      Set END : = MID - 1.

Else:
    Set BEG : = MID + 1.
[End of Structure.]

4. Set MID : = INT((BEG + END)/2).
     [End of Step 2 Loop.]

5. If DATA[MID] = ITEM, then:
Set LOC : = MID.

Else:
Set LOC : = NULL.
   [End of If Structure.]

6. Exit.

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