GATE CS 2016 Set 2 — Question 45
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Programming & Data Structures → C Programming → Control Flow
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Question
The following function computes for positive integers X and Y.Which one of the following conditions is TRUE before every iteration of the loop?
int exp(int X, int Y) {
int res = 1, a = X, b = Y;
while ( b != 0 ){
if ( b%2 == 0) { a = a*a; b = b/2; }
else { res = res*a; b = b-1; }
}
return res;
}
Correct answer
(C) X^Y = res a^b
Solution
We analyze the loop invariant. We want to compute . The variables are initialized as
res = 1, a = X, b = Y.Initially: . This holds.Inside the loop, there are two cases:1.b is even:
a becomes and b becomes . The term becomes . The value remains unchanged.2.b is odd:
Thus, the invariant holds before every iteration.res becomes and b becomes . The term becomes . The value remains unchanged.Continue learning with Success Tracker
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