61 lines
1.0 KiB
Markdown
61 lines
1.0 KiB
Markdown
---
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title: Exponentiation
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localeTitle: 幂
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---
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## 幂
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给定两个整数a和n，写一个函数来计算^ n。
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#### 码
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算法范式：分而治之。
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```C
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int power(int x, unsigned int y) {
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if (y == 0)
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return 1;
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else if (y%2 == 0)
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return power(x, y/2)*power(x, y/2);
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else
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return x*power(x, y/2)*power(x, y/2);
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}
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```
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时间复杂度：O（n）|空间复杂度：O（1）
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#### 优化的解决方案：O（logn）
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```C
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int power(int x, unsigned int y) {
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int temp;
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if( y == 0)
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return 1;
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temp = power(x, y/2);
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if (y%2 == 0)
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return temp*temp;
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else
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return x*temp*temp;
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}
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```
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## 模块化指数
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给定三个数字x，y和p，计算（x ^ y）％p
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```C
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int power(int x, unsigned int y, int p) {
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int res = 1;
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x = x % p;
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while (y > 0) {
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if (y & 1)
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res = (res*x) % p;
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// y must be even now
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y = y>>1;
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x = (x*x) % p;
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}
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return res;
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}
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```
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时间复杂度：O（Log y）。 |