数值的整数次方
C++，实现求幂函数power。下面说下思路：
-
如果a>=0：
- 如果b是偶数：a^b = a^(b/2) x a^(b/2);
- 如果b是奇数：a^b = a^(b/2) x a^(b/2) x a;
- 边界条件：a^0 = 1, a^1 = a;
-
如果a<0：
- 如果b是偶数：a^b = a^(b/2) x a^(b/2);
- 如果b是奇数：a^b = a^(b/2) x a^(b/2) / a;
- 边界条件：a^0 = 1, a^-1 =1 / a;
代码如下：
class Solution {
public:
double Power(double base, int exponent) {
if (exponent == 0) return 1;
if (exponent == 1) return base;
if (exponent == -1) return 1 / base;
if (exponent % 2 == 0) {
double t = Power(base, exponent / 2);
return t * t;
} else {
double a = Power(base, exponent / 2);
if (exponent < 0)
return a * a / base;
else return a * a * base;
}
}
};
