dft(多项式相乘模板)
/*
Author : lifehappy
*/
#pragma GCC optimize(2)
#pragma GCC optimize(3)
#include <bits/stdc++.h>
using namespace std;
const double pi = acos(-1.0);
const int N = 3e6 + 10;
struct Complex {
double r, i;
Complex(double _r = 0, double _i = 0) : r(_r), i(_i) {}
}a[N], b[N];
Complex operator + (const Complex & a, const Complex & b) {
return Complex(a.r + b.r, a.i + b.i);
}
Complex operator - (const Complex & a, const Complex & b) {
return Complex(a.r - b.r, a.i - b.i);
}
Complex operator * (const Complex & a, const Complex & b) {
return Complex(a.r * b.r - a.i * b.i, a.r * b.i + a.i * b.r);
}
int n, m;
void dft(Complex *f, int lim, int rev) {
if(!lim) return ;
Complex a1[lim], a2[lim];
for(int i = 0; i < lim; i++) {
a1[i] = f[i << 1], a2[i] = f[i << 1 | 1];
}
dft(a1, lim >> 1, rev);
dft(a2, lim >> 1, rev);
Complex wn = Complex(cos(pi / lim), rev * sin(pi / lim)), w = Complex(1, 0);
for(int i = 0; i < lim; i++, w = w * wn) {
f[i] = a1[i] + w * a2[i];
f[i + lim] = a1[i] - w * a2[i];
}
}
int main() {
// freopen("in.txt", "r", stdin);
// freopen("out.txt", "w", stdout);
// ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
scanf("%d %d", &n, &m);
for(int i = 0; i <= n; i++) {
scanf("%lf", &a[i].r);
}
for(int i = 0; i <= m; i++) {
scanf("%lf", &b[i].r);
}
int lim = 1;
while(lim <= n + m) lim <<= 1;
dft(a, lim >> 1, 1);//dft
dft(b, lim >> 1, 1);//dft
for(int i = 0; i < lim; i++) {
a[i] = a[i] * b[i];
}
dft(a, lim >> 1, -1);//idft
for(int i = 0; i <= n + m; i++) {
printf("%d%c", int(a[i].r / lim + 0.5), i == n + m ? '\n' : ' ');
}
return 0;
}
fft(大数乘法模板)
/*
Author : lifehappy
*/
#include <bits/stdc++.h>
using namespace std;
const double pi = acos(-1.0);
const int N = 5e6 + 10;
struct Complex {
double r, i;
Complex(double _r = 0, double _i = 0) : r(_r), i(_i) {}
}a[N], b[N];
Complex operator + (const Complex & a, const Complex & b) {
return Complex(a.r + b.r, a.i + b.i);
}
Complex operator - (const Complex & a, const Complex & b) {
return Complex(a.r - b.r, a.i - b.i);
}
Complex operator * (const Complex & a, const Complex & b) {
return Complex(a.r * b.r - a.i * b.i, a.r * b.i + a.i * b.r);
}
char str1[N], str2[N];
int r[N], ans[N];
void fft(Complex * f, int lim, int rev) {
for(int i = 0; i < lim; i++) {
if(r[i] < i) {
swap(f[i], f[r[i]]);
}
}
for(int i = 1; i < lim; i <<= 1) {
Complex wn = Complex(cos(pi / i), rev * sin(pi / i));
for(int p = i << 1, j = 0; j < lim; j += p) {
Complex w = Complex(1, 0);
for(int k = 0; k < i; k++, w = w * wn) {
Complex x = f[j + k], y = w * f[i + j + k];
f[j + k] = x + y, f[i + j + k] = x - y;
}
}
}
if(rev == -1) {
for(int i = 0; i < lim; i++) {
f[i].r /= lim;
}
}
}
int main() {
// freopen("in.txt", "r", stdin);
// freopen("out.txt", "w", stdout);
// ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
int n, m, lim;
while(scanf("%s %s", str1, str2) != EOF) {
n = strlen(str1), m = strlen(str2);
for(int i = 0; i < n; i++) {
a[i] = Complex(str1[n - i - 1] - '0', 0);
}
for(int i = 0; i < m; i++) {
b[i] = Complex(str2[m - i - 1] - '0', 0);
}
lim = 1;
while(lim < (n << 1) || lim < (m << 1)) lim <<= 1;
for(int i = 0; i < lim; ++i) {
r[i] = (i & 1) * (lim >> 1) + (r[i >> 1] >> 1);
}
for(int i = n; i < lim; i++) {
a[i] = Complex(0, 0);
}
for(int i = m; i < lim; i++) {
b[i] = Complex(0, 0);
}
fft(a, lim, 1);
fft(b, lim, 1);
for(int i = 0; i < lim; i++) {
a[i] = a[i] * b[i];
}
fft(a, lim, -1);
for(int i = 0; i < lim; i++){
ans[i] = int(a[i].r + 0.5);
}
for(int i = 0; i < lim; i++){
ans[i + 1] += ans[i] / 10;
ans[i] %= 10;
}
lim = n + m - 1;
while(ans[lim] <= 0 && lim > 0) lim--;
for(int i = lim; i >= 0; i--){
printf("%d", ans[i]);
}
printf("\n");
}
return 0;
}