GATE CSE 2016 | Set 2 | Question: 35

Question

The following function computes $X^{Y}$ for positive integers $X$ and $Y$.

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; 
}

Which one of the following conditions is TRUE before every iteration of the loop?

• A. $X^{Y} = a^{b}$
• B. $(res * a)^{Y} = (res * X)^{b}$
• C. $X^{Y} = res * a^{b}$
• D. $X^{Y} = (res * a)^{b}$

Comments

take X = 2,  Y = 3
 

---

I took the Opposite and got the same Answer

---

How to choose value of X & Y?
Please anyone teach me

Answer 1

by taking exmple we can solve it. Here i took X=4 & Y=2

Answer 2

Here's another good method.

Take X:2 and Y:3 (I choose them because they are prime) 

X power Y is 8

The program will have output as: But keep track of res, variable a and variable b as they are given in the option.

Now the program will run as like this:

Time 1 (after 1st iteration)	res:2	a:2	b:2
Time 2	res:2	a:4	b:1
Time 3	res:8	a:4	b:0

 

On every time in each row the combination of res, a and b values is equal to X power Y for only option C.

Answer 3

take x=2,y=3