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GATE | Gate IT 2007 | Question 27

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The function f is defined as follows: 

C




int f (int n) {
    if (n <= 1) return 1;
    else if (n % 2  ==  0) return f(n/2);
    else return f(3n - 1);
}


Assuming that arbitrarily large integers can be passed as a parameter to the function, consider the following statements.
1. The function f terminates for finitely many different values of n ≥ 1. 
ii. The function f terminates for infinitely many different values of n ≥ 1. 
iii. The function f does not terminate for finitely many different values of n ≥ 1. 
iv. The function f does not terminate for infinitely many different values of n ≥ 1. 
Which one of the following options is true of the above?

(A)

(i) and (iii)

(B)

(i) and (iv)

(C)

(ii) and (iii)

(D)

(ii) and (iv)



Answer: (D)

Explanation:

The function terminates for all values having a factor of 2 {(2.x)2==0}
So, (i) is false and (ii) is TRUE.
Let n = 3, it will terminate in 2nd iteration.
Let n=5, it will go like 5 – 14 – 7 – 20 – 10 – 5 – and now it will repeat.
And any number with a factor of 5 and 2, there are infinite recursions possible.
So, (iv) is TRUE and (iii) is false.

Hence Option(D) is the correct Option.


Quiz of this Question
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Last Updated : 28 Jun, 2021
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