A * B Problem Plus HDU - 1402 (FFT)

 1 #include <iostream>
 2 #include <complex>
 3 #include <cstdio>
 4 #include <cstring>
 5 #include <cmath>
 6 #include <algorithm>
 7 using namespace std;
 8 
 9 const int maxn = 200010;
10 const double pi = acos(-1.0);
11 complex<double> omega[maxn], inverse[maxn];
12 
13 void init(int n){
14     for(int i = 0; i < n; i++){
15         omega[i] = complex<double>(cos(2 * pi / n * i), sin(2 * pi / n * i));
16         inverse[i] = conj(omega[i]);
17     }
18 }
19 void transform(complex<double> *a, int n, complex<double> *omega){
20     int k = 0;
21     while((1 << k) < n) k++;
22     for(int i = 0; i < n; i++){
23         int t = 0;
24         for(int j = 0; j < k; j++) if(i & (1 << j)) t |= (1 << (k - j - 1));
25         if(i < t) swap(a[i], a[t]);
26     }
27     for(int l = 2;  l <= n; l *= 2){
28         int m = l / 2;
29         for(complex<double> *p = a; p != a + n; p += l){
30             for(int i = 0; i < m; i++){
31                 complex<double> t = omega[n / l * i] * p[m + i];
32                 p[m + i] = p[i] - t;
33                 p[i] += t;
34             }
35         }
36     }
37 }
38 void dft(complex<double> *a, int n){
39     transform(a, n, omega);
40 }
41 void idft(complex<double> *a, int n){
42     transform(a, n, inverse);
43     for(int i = 0; i < n; i++) a[i] /= n;
44 }
45 
46 void mul(int *a, int n1, int *b, int n2, int *res){
47     int n = 1;
48     while(n < n1 + n2) n <<= 1;
49     complex<double> c1[maxn], c2[maxn];
50     for(int i = 0; i < n1; i++) c1[i].real(a[i]);
51     for(int i = 0; i < n2; i++) c2[i].real(b[i]);
52     init(n);
53     dft(c1, n); dft(c2, n);
54     for(int i = 0; i < n; i++) c1[i] *= c2[i];
55     idft(c1, n);
56     for(int i = 0; i < n1 + n2 - 1; i++) res[i] = (int)(floor(c1[i].real() + 0.5));
57 }
58 char s1[maxn], s2[maxn];
59 int a[maxn], b[maxn], res[maxn];
60 
61 void in(){
62     freopen("in.txt", "w", stdout);
63     for(int i= 0; i < 100; i++){
64         cout<<rand() % 131313 <<endl;
65     }
66 }
67 int main(){
68    // freopen("in.txt", "r", stdin);
69    // freopen("out.txt", "w", stdout);
70     while(scanf("%s %s", s1, s2) != EOF){
71         memset(res, 0, sizeof res);
72         int n1 = strlen(s1), n2 = strlen(s2);
73         for(int i = 0; i < n1; i++) a[i] = s1[n1 - i - 1] - ‘0‘;
74         for(int i = 0; i < n2; i++) b[i]  =s2[n2 - i - 1] - ‘0‘;
75         mul(a, n1, b, n2, res);
76         int m = n1 + n2 -1;
77         for(int i = 0; i < m; i++) res[i + 1] += res[i] / 10, res[i] %= 10;
78         if(res[m]) m++;
79         while(m >= 1 && !res[m - 1]) m--;
80         for(int i = m - 1; i >= 0; i--) printf("%d", res[i]);
81         if(m == 0) printf("0");
82         puts("");
83     }
84 }