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Another example of a computer searching algorithm is binary search. This is a more complex algorithm than linear search and requires all items to be in order.

With each loop that is run, half of the data is removed from the search. To do this, the algorithm uses the index of items in the list - an index is the number given to the position of an item in a list.

To determine the next item to be checked in a list, the midpoint has to be identified. This is found by adding the lowest index to the highest index and dividing by two, then rounding either up or down to the nearest integer if needed. Whether we round up or down does not matter, as long as within a particular search the same method is applied. For example, if the highest index in a list is 8 and the lowest is 0, the midpoint can be found using the following sum:

Highest index (8) + lowest index (0) = 8

8/2 = 4

The algorithm runs as follows:

1. Start by setting the counter to the middle position in the list.
2. If the value held there is a match, the search ends.
3. If the value at the midpoint is less than the value to be found, the list is divided in half, the lower half of the list is ignored and the search keeps to the upper half of the list.
4. Otherwise, if the value at the midpoint is greater than the value to be found, the upper half of the list is ignored and the search keeps to the lower half of the list.
5. The search moves to the midpoint of the remaining items. Steps 2 through 4 continue until a match is made or there are no more items to be found.

Binary search example

This algorithm could be used to search the following list for the number 7:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10

In a trace table, this would look like:

In pseudo-code, this would look like:

Find <-- 7
Found <-- False
Start <-- 0
End <-- length(list)

WHILE Found = False AND Start <= End
     Mid <-- (Start + End) DIV 2

     IF list[Mid] = Find THEN
        OUTPUT 'Found at' +  Mid
        Found <-- True
     ELSE
        IF List[Mid] > Find THEN
           End <-- Mid - 1
        ELSE
          Start <-- Mid + 1
        ENDIF
     ENDIF
ENDWHILE

IF Found = False THEN
     OUTPUT 'Not found'
ENDIF