GATE CSE 1998 | Question: 2.12

Question

What value would the following function return for the input $x=95$?

Function fun (x:integer):integer;
Begin
    If x > 100 then fun = x – 10
    Else fun = fun(fun (x+11))
End;

• A. $89$
• B. $90$
• C. $91$
• D. $92$

Comments

But how to say that fun = x- 10 is a return statement? I assumed it as an assignment and got nothing.

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@Tushar Rana it's just when x >100 it just return and end for fun(100)=fun(fun(111))=fun(101) so x >100 came so it just return x-10 which is 91 

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Also asked in ISRO 2017 https://gateoverflow.in/182123/isro-dec2017-73

Answer 1

Value returned by $\text{fun}(95) = \text{fun}(\text{fun}(106))$
$\qquad\qquad= \text{fun}(96)$
$\qquad\qquad= \text{fun}(\text{fun}(107))$
$\qquad\qquad= \text{fun}(97)$
$\qquad\qquad= \text{fun}(\text{fun}(108))$
$\qquad\qquad= \text{fun}(98)$
$\qquad\qquad = \text{fun}(\text{fun}(109))$
$\qquad\qquad= \text{fun}(99)$
$\qquad\qquad= \text{fun}(\text{fun}(110))$
$\qquad\qquad= \text{fun}(100) $
$\qquad\qquad= \text{fun}(\text{fun}(111)) $
$\qquad\qquad= \text{fun}(101) = 91.$

Correct Answer: $C$

Comments

@neel19 how after 91 the fucntion is not calling fun(102) ?? can u plz elaborate it 

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If you see the 3^rd last step, we have fun(100). The code says :- 

If x > 100 then fun = x – 10
    Else fun = fun(fun (x+11))

 

Now fun(100) = fun(fun(111)) // Since 100 is not > 100.

= fun(101) // since 111 > 100

 now this is unlike the other terms which were < 100, so we need to add 11. 

Here 101 > 100, thus we again subtract 10 from 101

→ fun = 101-10 = $91$

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yeah thanks bro understood @Abhrajyoti00

Answer 2

Yes 91 is correct.

step 1: when fun=111 -> fun(fun(111))

step 2:  fun=101 ->fun(101)

step 3:As 101>100 fun=fun -10 =101-10=91

step 4: as there is no fun function call remaining ,it will exit.

Comments

how can we understand this is stop codition.

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Because when value is 111, there are no further function call. Just the return.

Answer 3

It might help.

int fun(int x)
{
     if(x>100)
     return (x-10);
     else
     return fun(fun(x+11));
}

Equivalent function.

Answer 4

I think the answer is 91.

Comments

Thanks Ahsanul

Answer 5

Initially x=95

hence, IF becomes FALSE

1. fun(fun(106))

fun(96)

2. fun(fun(107))

fun(97)

3. fun(fun(108))

fun(98)

4. fun(fun(109))

fun(99)

5. fun(fun(110))

fun(100)

6. fun(fun(111))

fun(101)

therefore now, IF condition becomes TRUE

return(x-10) ,i.e, return(101-10)

=91

ANSWER IS 91

Answer 6

Answer is 91.

For fun(95) -> fun(fun(106)) is called.

The inside fun(106) is evaluated first which returns 96, hence fun(96) is called.

Similarly for fun(96) -> fun(fun(107)) is called which evaluates to the call of fun(97).

Similarly, fun(97) -> fun(fun(108)) = fun(98) and so on. 

For last call fun(100) calls fun(fun(111)) which evaluates to fun(101) which further returns 91(101-10)