50. Pow(x, n) [Leetcode][C++]

#cpp #algorithms #leetcode #programming

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Brute Force Solution:

class Solution {
public:
    double myPow(double x, int n) {
        // Brute Force Solution Time O(N) & Auxiliary Space O(N)
        if(n==0)
            return 1;
        else if(n>0) 
            return x*myPow(x,n-1); 
        else
            return (1/x)*myPow(x,n+1); 
    }
};

Efficient Solution:

class Solution {
public:
    double myPow(double x, int n) {
        // Optimal Solution Time O(logN) & Auxiliary Space O(logN)
        if(n==0) 
            return 1;
        // Using Binary Exponentiation(Time O(logN))
        // x^n=x^(n/2)*x^(n/2). So, recursive function is 
        // called logN times where y=x^(n/2) and function returns y*y
        double y = myPow(x,n/2);
        if(n%2==0)
            return y*y;
        else if(n < 0)
            return 1/x*y*y;
        else
            return x*y*y; 
    }
};