Problems Requiring the Analysis of Recursive Functions

The following problems will give you another excellent opportunity to
hone your recursive skills. These problems do not require to you write 
recursive functions. Instead they require you to study some functions 
(all of which happen to be recursive), decide what each function does, 
and then use that knowledge to deduce what output or return value the 
function produces for the given input. At least this is the best 
approach to take. If you cannot decide what the function does by 
studying it, you should still be able to trace the function for the 
given input to find the necessary output or return value, but doing so 
should be regarded as a last-ditch method of attack.


----- Problem ----------------------------------------------------------
void DoIt(/* in */ int n)
{
    if (n < 10)
        cout << n << n;
    else
    {
        cout << n % 10;
        DoIt(n / 10);
        cout << n % 10;
    }
}

What is this function doing? ___________________________________________

________________________________________________________________________

Give the output from each of the following function calls:

a) DoIt(34567) --> ____________________

b) DoIt(300)   --> ____________________

c) DoIt(2442)  --> ____________________


----- Problem ----------------------------------------------------------
void DoIt(/* in */ int n)
{
    if (n < 10)
    {
        if (n % 2 == 1)
            cout << n;
    }
    else
    {
        int t;
        t = n % 10;
        DoIt(n / 10);
        if (t % 2 == 1) cout << t;
    }
}

What is this function doing? ___________________________________________

________________________________________________________________________

Give the output from each of the following function calls:

a) DoIt(6798)   --> ____________________

b) DoIt(73591)  --> ____________________

c) DoIt(824163) --> ____________________


----- Problem ----------------------------------------------------------
bool f(/* in */ int n)
{
    if (n < 10)
        return true;
    else if (n < 100)
        return (n / 10) == (n % 10);
    else
    {
        int a;
        int c;
        int b;

        int d = 1;
        while (n / d >= 10) d *= 10;

        a =  n / d;
        b = (n % d) % 10;
        c = (n % d) / 10;

        return (a == b) && f(c);
    }
}

What is this function computing? _______________________________________

________________________________________________________________________

Give the value of each of the following:

a) f(3629263)   --> ____________

b) f(6546)      --> ____________

c) f(6)         --> ____________

d) f(12324)     --> ____________

e) f(123454321) --> ____________


----- Problem ----------------------------------------------------------
int f(/* in */ int n)
{
    if (n < 100)
        return 10 * (n % 10) + (n / 10);
    else
        return f(n / 100) * 100 + f(n % 100);
}

What is this function computing? _______________________________________

________________________________________________________________________

Give the value of each of the following:

a) f(362974) --> ____________

b) f(358)    --> ____________

c) f(6)      --> ____________



----- Problem ----------------------------------------------------------
int f(/* in */ int n)
{
    if (n < 10)
    {
        if (n % 2 == 0)
            return 1;
        else
            return 0;
    }
    else
    {
        if ((n % 10) % 2 == 0)
            return 1 + f(n / 10);
        else
            return f(n / 10);
    }
}

What is this function computing? _______________________________________

________________________________________________________________________

Give the value of each of the following:

a) f(654321)  --> ____________

b) f(42622)   --> ____________

c) f(7319531) --> ____________


----- Problem ----------------------------------------------------------
void Doit(/* in */ int n)
{
    if (n < 10)
        cout << n << n;
    else
    {
        int a;
        int b;

        int c = 1;
        while (n / c >= 10) c *= 10;

        a   = n / c;
        b = n % c;

        cout << a;
        Doit(b);
        cout << a;
    }
}

What is this function doing? ___________________________________________

________________________________________________________________________

Give the output from each of the following function calls:

a) DoIt(72549) --> ____________________

b) DoIt(60)   --> ____________________

c) DoIt(2563)  --> ____________________


----- Problem ----------------------------------------------------------
void DoIt()
{
    char ch;
    cin.get(ch);
    if (ch >= 'A' && ch <= 'Z')
        cout << ch;
    if (cin.peek() != '\n')
        DoIt();
}

What is this function doing? ___________________________________________

________________________________________________________________________

Give the output when the input is each of the following:

a) To be or NOT to be --> ______________________________________________

b) The House of the Rising Sun --> _____________________________________

c) A, B and C are the 1st 3 and X, Y and Z the last 3 --> ______________


----- Problem ----------------------------------------------------------
void DoIt(/* in */ int n)
{
    if (n < 10)
        cout << n * n;
    else
    {
        cout << (n % 10) * (n % 10);
        DoIt(n / 10);
    }
}

What is this function doing? ___________________________________________

________________________________________________________________________

Give the output from each of the following function calls:

a) DoIt(432) --> ____________________

b) DoIt(5348)   --> ____________________

c) DoIt(70)  --> ____________________


----- Problem ----------------------------------------------------------
int f(/* in */ int n)
{
    if (n < 3)
        return n;
    else
    {
        return f(n / 3) * 10 + (n % 3);
    }
}

What is this function computing? _______________________________________

________________________________________________________________________

Give the value of each of the following:

a) f(37)  --> ____________

b) f(101) --> ____________

c) f(14)  --> ____________