快速阶乘算法

从网上引用，和上一篇出自同一博客。

借用上一篇的理论，可以在log2n内计算阶乘。

原理：如上图。

代码：

 1 #include <iostream>
 2 #include <iterator>
 3 #include <algorithm>
 4 
 5 using namespace std;
 6 
 7 #define MAXSIZE 100
 8 unsigned long answer[MAXSIZE];
 9 
10 unsigned long long int power(unsigned long base, unsigned long exp)
11 {
12     unsigned long long int result = 1;
13     while (exp)
14     {
15         if (exp & 0x01)
16             result *= base;
17         base *= base;
18         exp >>= 1;
19     }
20 
21     return result;
22 }
23 
24 unsigned long cn2(unsigned long n)
25 {
26     unsigned long x = (1 << n) + 1;
27     unsigned long mask = (1 << n) - 1;
28 
29     return (power(x, n) >> ((n >> 1) * n)) & mask;
30 }
31 
32 unsigned long factorial(unsigned long n)
33 {
34     unsigned long temp;
35 
36     if (n == 1)
37         return 1;
38     else if (n & 0x01 == 1)
39         return n * factorial(n - 1);
40     else
41     {
42         temp = factorial(n >> 1);
43         return cn2(n) * temp * temp;
44     }
45 }
46 
47 void main()
48 {
49     int number = 4;
50     unsigned long result = factorial(number);
51     cout << "result = " << result << endl;
52 }

还可以logn内完成，但需要把C(N,N/2),C(N/2,N/4),C(N/4，N/8).....打出来。

 1 #include <iostream>
 2 #include <iterator>
 3 #include <algorithm>
 4 
 5 using namespace std;
 6 
 7 #define MAXSIZE 100
 8 unsigned long mask;
 9 unsigned cnrs[MAXSIZE];
10 int number;
11 int p_size;
12 
13 unsigned long power(unsigned long n, unsigned long m)
14 {
15     unsigned long temp;
16 
17     if (m == 1)
18         temp = n;
19     else if (m & 0x01 != 0)
20         temp = n * power(n, m - 1);
21     else
22     {
23         temp = power(n, m >> 1);
24         temp *= temp;
25         cnrs[number++] = (temp >> ((m >> 1) * p_size)) & mask;
26     }
27 
28     return temp;
29 }
30 
31 unsigned factor(unsigned long n)
32 {
33     unsigned long temp;
34 
35     if (n == 1)
36         return 1;
37     else if (n & 0x01 == 1)
38         return n * factor(n - 1);
39     else
40     {
41         temp = factor(n >> 1);
42         return cnrs[number++] * temp * temp;
43     }
44 }
45 
46 unsigned long factorial(unsigned long n)
47 {
48     unsigned long x = (1 << n) + 1;
49 
50     number = 0;
51     mask = (1 << n) - 1;
52     p_size = n;
53     power(x, n);
54     number = 0;
55 
56     return factor(n); 
57 }
58 
59 void main()
60 {
61     int number = 6;
62     unsigned long result = factorial(number);
63     cout << "result = " << result << endl;
64     copy(cnrs, cnrs + 10, ostream_iterator<int>(cout, " "));
65 }