GATE CS 2017 Set 2 — Question 37
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Programming & Data Structures → C Programming → Control Flow
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Question
Consider the C program fragment below which is meant to divide by using repeated subtractions. The variables and are all unsigned int.Which of the following conditions on the variables and before the execution of the fragment will ensure that the loop terminates in a state satisfying the condition ?
while (r >= y) {
r = r - y;
q = q + 1;
}
Correct answer
(C) (q == 0) && (r == x) && (y 0)
Solution
The loop implements division by repeated subtraction. The loop invariant is . For the loop to terminate in a state where , this condition must hold initially.
1.Invariant Check: If we start with and , then . The invariant holds.
2.Termination: For the loop
while (r >= y) to terminate, must be greater than 0. If , since is an unsigned integer, is always true, leading to an infinite loop.3.Standard Initialization: In a typical division algorithm, we initialize the quotient to 0 and the remainder to the dividend .
Comparing with options:- (A) requires initially.
- (B) does not specify .
- (C) specifies , which is sufficient.
- (D) does not specify .
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