finding nth root of a number by using divide and conquer method

Question

I need help on how to get nth root of some number.

User enters number n and number he wants root of. I need to solve this without cmath lib and with divide and conquer method.

Here's my code that doesn't work yet:

#include<iostream>
using namespace std;

float pow(float a,float c){
    if (a == 0)
        return 0;
    else if(a == 1)
        return 1;
    else{
        float p = pow(a,(c/2));
        if(c%2)
            return p*p*a;
        else
            return p*p;
    }
}

int main(){
    float a,b;
    float c;
    cout << "Enter positive number:(base)" << endl;
    do{
        cin >> a;
    }while (a < 0);
    cout << "Enter number: (root)" << endl;
    cin >> b;
    c = 1/b;
    cout << "Result:"<<pow(a,c) << endl;
    system("pause");
    return 0;
}

Any ideas on how to approach this problem would be more than useful.

Answer 1

Let me tell you how you can use divide and conquer for finding square root. The nth root would be similar.

For a given number x, you need to search for it's square root between 0 and x. Divide it by 2 = x2. If the x2 * x2 < x then your search space moves to x2 -> x or else it will be 0 -> x2. If x2 * x2 matches x then your square root is x2. Similar technique for nth root.

Answer 2

For those not doing numerical experiments: use the <cmath> functions sqrt and cbrt (cube-root) to construct the any root that is factorable by 2 and 3. For example, the 4th root is sqrt(sqrt(x)) and the 6th root is sqrt(cbrt(x)). If you need something for general use you can construct a recursive function which calls sqrt and cbrt appropriately.

I'm guessing this will give a faster and more accurate answer than pow, if that matters. If it doesn't, just use pow.