题目大意:FFT,给你两个多项式,请输出乘起来后的多项式。
题解:FFT
卡点:无
C++ Code:
#include <cstdio> #include <cmath> using namespace std; const double Pi = acos(-1); int n, m; struct complex { double r, i; complex (double a = 0, double b = 0) {r = a, i = b;} complex operator + (complex a) {return (complex) {r + a.r, i + a.i};} complex operator - (complex a) {return (complex) {r - a.r, i - a.i};} complex operator * (complex a) {return (complex) {r * a.r - i * a.i, r * a.i + i * a.r};} } a[500000], b[500000]; int rev[500000], dig, l; void swap(complex &a, complex &b) {complex t = a; a = b; b = t;} void FFT(complex *a, int op) { for (int i = 0; i < l; i++) if (i < rev[i]) swap(a[i], a[rev[i]]); for (int mid = 1; mid < l; mid <<= 1) { complex Wn(cos(Pi / mid), op * sin(Pi / mid)); for (int i = 0; i < l; i += (mid << 1)) { complex W(1, 0); for (int j = 0; j < mid; j++, W = W * Wn) { complex X = a[i + j], Y = W * a[i + j + mid]; a[i + j] = X + Y; a[i + j + mid] = X - Y; } } } if (op == -1) for (int i = 0; i <= l; i++) a[i].r /= l; } int main() { 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); l = 1; while (l <= (n + m)) l <<= 1, dig++; for (int i = 0; i < l; i++) rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (dig - 1)); // for (int i = 0; i < l; i++) printf("::%d\n ", rev[i]); FFT(a, 1); FFT(b, 1); // for (int i = 0; i < l; i++) printf("::%lf %lf\n", b[i].r, b[i].i); for (int i = 0; i < l; i++) a[i] = a[i] * b[i]; FFT(a, -1); for (int i = 0; i <= n + m; i++) printf("%d ", (int)(a[i].r + 0.5)); puts(""); return 0; }