GATE CS 2015 Set 1 — Question 65
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Programming & Data Structures → C Programming
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Question
Consider the following pseudo code, where and are positive integers.The post condition that needs to be satisfied after the program terminates is
begin
q := 0
r := x
while r >= y do
begin
r := r - y
q := q + 1
end
end
Correct answer
(B) \x = qy + r ∧ r < y\
Solution
The code implements the division algorithm using repeated subtraction to find the quotient and remainder when is divided by .
- Initially, , so holds ().
- In each iteration, is decreased by and is increased by 1. The invariant is maintained because .
- The loop terminates when the condition becomes false, i.e., .
- Since and are positive integers and we subtract only when , remains non-negative.
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