MadeEasy Full Length Test: Programming & DS - Programming in C

Question

Consider the following function foo()

void foo(int n)
{
    if(n<=0) printf("Bye");
    else
    {
        printf("Hi");
        foo(n-3);
        printf("Hi");
        foo(n-1);
    }
}

Let P(n) represent the recurrence relation indicating the number of times the print statement (both “Hi” and “Bye” included) is executed. Then which of the following is the best match for P(n)?

• A. $\text{P(n)=P(n-1)+P(n-3)+2 for n>=0;1 for n=0}$
• B. $\text{P(n)=P(n-1)+P(n-3)+2 for n>0;2 for n=0}$
• C. $\text{P(n)=P(n-1)+P(n-3)+2 for n>0;0 for n=0}$
• D. $\text{P(n)=P(n-1)+P(n-3)+1 for n>0;2 for n=0}$

Ans. A

But when n=1, the o/p will be “Hi Bye Hi Bye” i.e 4 times printed.

From A, P(1)=P(0)+P(-2)+2 = 1+P(-2)+2=3+P(-2)

But nothing is mentioned about P value when n<0.

How to solve for P(-2) and other negative values?

 

Comments

if(n<=0) printf("Bye")

this statement is given

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@Deepanshu

I asked from the recurrence relation what to take for P(negative values)..not from the code snippet..

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i think by p(n) they mean foo(n) bczz thats only function here........

now foo(n) when n<=0 it is  print bye just as code

so for p(-2) i think bye will be taken

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You are not getting me @Deepanshu

From P(n)=P(n-1)+P(n-3)+2 for n>=0;1 for n=0 , show me what will be the value of P(1).

 

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okk okk got u they should have mention something for less than 0   ...

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we all know there are mistakes in MADEEASY solutions, it is also one of them

the correct recurrance would be

P(n)=P(n-1)+P(n-3)+2 for n>0 ; 1 for n ≤ 0