1 #include <stdio.h>
2 #include <math.h>
3 //递归算法
4 int recursion(int a,int b)
5 {
6 int tem = 1;
7 if(b==0)return 1;
8 else if(b==1)return a;
9 tem = recursion(a,b>>1);
10 tem = tem*tem;
11 if(b&1) tem = tem * a;
12 return tem;
13 }
14 //循环算法
15 int loop(int a,int b)
16 {
17 int tem=1,ret=a;
18 while(b>0)
19 {
20 if(b&1) tem = tem * ret;
21 ret = ret*ret;
22 b>>=1;
23 }
24 return tem;
25 }
26 int main()
27 {
28 int a,b;
29 while(1)
30 {
31 printf("For a^b input a and b:");
32 scanf("%d%d",&a,&b);
33 printf("The recursion method:\n");
34 printf("%d\n",recursion(a,b));
35 printf("The loop method:\n");
36 printf("%d\n",loop(a,b));
37 }
38 return 0;
39 }
原理:
对应于递归算法,以下是算法依据:
直接乘要做998次乘法。但事实上可以这样做,先求出2^k次幂:
3 ^ 2 = 3 * 3
3 ^ 4 = (3 ^ 2) * (3 ^ 2)
3 ^ 8 = (3 ^ 4) * (3 ^ 4)
3 ^ 16 = (3 ^ 8) * (3 ^ 8)
3 ^ 32 = (3 ^ 16) * (3 ^ 16)
3 ^ 64 = (3 ^ 32) * (3 ^ 32)
3 ^ 128 = (3 ^ 64) * (3 ^ 64)
3 ^ 256 = (3 ^ 128) * (3 ^ 128)
3 ^ 512 = (3 ^ 256) * (3 ^ 256)
再相乘:
以下是对应非递归算法:
3 ^ 999
= 3 ^ (512 + 256 + 128 + 64 + 32 + 4 + 2 + 1)
= (3 ^ 512) * (3 ^ 256) * (3 ^ 128) * (3 ^ 64) * (3 ^ 32) * (3 ^ 4) * (3 ^ 2) * 3
原文:http://www.cnblogs.com/bendantuohai/p/4499350.html