convert iterative function to recursive function

Question

i have a problem on iterative function and recursive function. i have a iterative function and i have to convert it into a recursive one. could you give me some advice on my code?thanks so much

the code is to determine if the array of data points correspond to a concave function using recursion.

Here is the code of the iterative version:

bool isConcave(double a[], int n)
{
int slope = 1;
bool concave = true;

for (int i = 1; i < n && concave; i++)
{
    double delta = a[i] - a[i-1];

    if (slope > 0)
    {
        if (delta < 0)
            slope = -1;
    }
    else if (delta > 0)  
        concave = false; // slope == -1 and delta > 0
}
return concave;
}

And, here is the code of my recursive version which can't work:

bool isConcave_r(double a[], int n, int& slope)  
{
//Implement this function using recursion
double delta = a[n] - a[n-1];
bool concave = true;

if (n == 0)
    return false;
if (slope > 0)
{
    if (delta < 0)
    {
        slope = -1;
    }
    else
        concave = true;
}else
    return 0;

//dummy return statement
return isConcave_r(a, n, slope);

}

Answer 1

Not necessary the best/cleanest way, but you may replace any loop

for (int i = 0; i != N; ++i) {
    body(i, localVars);
}

by

void body_rec(int N, int i, LocalVars& localVars)
{
    if (i == N) return;
    body(i, localvars);
    body_rec(N, i + 1, localVars);
}

or

int body_rec(int N, int i, LocalVars& localVars)
{
    if (i == N) return localVars.res; // or any correct value
    body(i, localvars);
    if (localVars.end) { // break the "loop", and so stop the recursion.
        return localVars.res; // or any correct value
    }
    return body_rec(N, i + 1, localVars);
}

So, in your case, you forget to pass slope into the recursion.

[edit]

Full solution:

bool isConcave_r(int N, int i, double a[], int slope)
{
    if (i >= N) return true;

    const double delta = a[i] - a[i-1];

    if (slope > 0) {
        if (delta < 0) {
            slope = -1;
        }
    }
    else if (delta > 0) {
        return false;
    }
    return isConcave_r(N, i + 1, a, slope);
}

bool isConcave(double a[], int n)
{
    int i = 1;
    int slope = 1;
    return isConcave_r(n, i, a, slope);
}

Note also that the name seems "incorrect", you don't check if the "curve" is concave, case where delta == 0 should be specific I think...

Answer 2

In the iterative version of your program, the computation moves from 1 to n-1, but in the recursive version computation moves form n-1 to 1. So, instead of tail recursion, use head recursion. And slope should be static variable. So, declare slope as static variable. It will work.