洛谷 - P3803 - 【模板】多项式乘法（FFT） - FFT

https://www.luogu.org/problemnew/show/P3803

用反向学习的FFT通过这个东西。

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

const int MAXN = 3e5;
const double PI = acos(-1.0);

struct Complex {
    double x, y;
    Complex() {}
    Complex(double x, double y): x(x), y(y) {}
    friend Complex operator+(const Complex &a, const Complex &b) {
        return Complex(a.x + b.x, a.y + b.y);
    }
    friend Complex operator-(const Complex &a, const Complex &b) {
        return Complex(a.x - b.x, a.y - b.y);
    }
    friend Complex operator*(const Complex &a, const Complex &b) {
        return Complex(a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x);
    }
} A[MAXN + 5], B[MAXN + 5];

void FFT(Complex a[], int n, int op) {
    for(int i = 1, j = n >> 1; i < n - 1; ++i) {
        if(i < j)
            swap(a[i], a[j]);
        int k = n >> 1;
        while(k <= j) {
            j -= k;
            k >>= 1;
        }
        j += k;
    }
    for(int len = 2; len <= n; len <<= 1) {
        Complex wn(cos(2.0 * PI / len), sin(2.0 * PI / len)*op);
        for(int i = 0; i < n; i += len) {
            Complex w(1.0, 0.0);
            for(int j = i; j < i + (len >> 1); ++j) {
                Complex u = a[j], t = a[j + (len >> 1)] * w ;
                a[j] = u + t, a[j + (len >> 1)] = u - t;
                w = w * wn;
            }
        }
    }
    if(op == -1) {
        for(int i = 0; i < n; ++i)
            a[i].x = (int)(a[i].x / n + 0.5);
    }
}

int pow2(int x) {
    int res = 1;
    while(res < x)
        res <<= 1;
    return res;
}

void convolution(Complex A[], Complex B[], int Asize, int Bsize) {
    int n = pow2(Asize + Bsize - 1);
    for(int i = 0; i < n; ++i) {
        A[i].y = 0.0;
        B[i].y = 0.0;
    }
    for(int i = Asize; i < n; ++i)
        A[i].x = 0;
    for(int i = Bsize; i < n; ++i)
        B[i].x = 0;
    FFT(A, n, 1);
    FFT(B, n, 1);
    for(int i = 0; i < n; ++i)
        A[i] = A[i] * B[i];
    FFT(A, n, -1);
    return;
}

int C[MAXN + 5];

int carry(int n) {
    for(int i = 0; i < n; i++) {
        C[i] = A[i].x;
    }
    for(int i = 0; i < n; i++) {
        C[i + 1] += C[i] / 10;
        C[i] %= 10;
    }
    while(C[n]) {
        C[n + 1] += C[n] / 10;
        C[n] %= 10;
        n++;
    }
    while(n && !C[n - 1]) {
        n--;
    }
    return n;
}

int main() {
#ifdef Yinku
    freopen("Yinku.in", "r", stdin);
#endif // Yinku
    int n;
    scanf("%d", &n);
    for(int i = n-1; i >=0; --i) {
        int tmp;
        scanf("%1d", &tmp);
        A[i].x = tmp;
    }
    for(int i = n-1; i >=0; --i) {
        int tmp;
        scanf("%1d", &tmp);
        B[i].x = tmp;
    }
    convolution(A, B, n, n);
    n = carry(pow2(n + n - 1));
    if(n == 0) {
        printf("0\n");
    } else {
        for(int i = n - 1; i >= 0; --i) {
            printf("%d", C[i]);
        }
        printf("\n");
    }
    return 0;
}