power of an integer in c++ [duplicate]

Answer 1

There are two alternatives here, when we want to count power(a,n) we may write code which is very short and works in O(logn) time, but is recursively and therefore requires creating new stackframe for each call and needs a bit more time than loop iteration. So short code is:

int power(int a, int n){
    if(n == 0) return 1;
    int keep = power(a,n/2);
    if(n & 1) return keep*keep*a;   // (n & 1) is and operation of 1 and the 
    return keep*keep;               // last bit of n
}

and as for the faster code, here it is using while loop:

int power(int a, int n) {
    int res = 1;
    while (n) {
        if (n & 1)
            res *= a;
        a *= a;
        n >>= 1;
    }
    return res;
}