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# Getting a Program Right (3)

Posted

This is the third article about a seemingly naïve question: how do we write a binary search program? The first article appeared here.

The first program attempt was wrong. The second article introduced a new one:

—  Program attempt #2.

from

i := 1 ; j := n

until i = j or Result > 0  loop

m := (i + j) // 2         — Integer division

if t [m] ≤ x then

i := m  + 1

elseif t [m] = x then

Result := m

else                         — In this case t [m] > x

j := m – 1

end

end

The question was: it right?

Again no.  A trivial example disproves it: n = 1, the array t contains a single element t [1] = 0, x = 0. Then the initialization sets both i and j to 1, i = j holds on entry to the loop which stops immediately, but Result is zero whereas it should be 1 (the place where x appears).

Here now is attempt #3, let us see it if fares better:

—  Program attempt #3.

from

i := 1 ; j := n

until i = j loop

m := (i + j + 1) // 2

if t [m] ≤ x then

i := m  + 1

else

j := m

end

end

if ≤ i  and i n then Result := i end

— If not, Result remains 0.

Post-publication note: the  announced fourth ("Wednesday") article was published here.

Bertrand Meyer is chief technology officer of Eiffel Software (Goleta, CA), professor and provost at the Schaffhausen Institute of Technology (Switzerland), and head of the software engineering lab at Innopolis University (Russia).

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