[HDU]1402 A * B Problem Plus [FFT]

Problem Description
Calculate A * B.

Input
Each line will contain two integers A and B. Process to end of file.

Note: the length of each integer will not exceed 50000.

Output
For each case, output A * B in one line.

Sample Input
1
2
1000
2

Sample Output
2
2000

题解

这是一道FFT的入门模板题

#include<stdio.h>#include<cstring>#include<cmath>#include<complex>#include<algorithm>using namespace std;typedef complex<double> complex_t;const double PI = acos(-1.0);const int MAXN = 1 << 18;complex_t A[MAXN], B[MAXN];char str_1[MAXN], str_2[MAXN];int res[MAXN], len, len_1, len_2;void Init() {    len_1 = strlen(str_1), len_2 = strlen(str_2);    int ml = max(len_1, len_2);    for(len = 1; len < (ml << 1); len <<= 1);    for(int i = 0; i < len_1; ++i) {        A[i] = complex_t(str_1[len_1 - i - 1] - '0', 0);    }    for(int i = 0; i < len_2; ++i) {        B[i] = complex_t(str_2[len_2 - i - 1] - '0', 0);    }    for(int i = len_1; i < len; ++i) {        A[i] = complex_t(0, 0);    }    for(int i = len_2; i < len; ++i) {        B[i] = complex_t(0, 0);    }}void Rader(complex_t y[]) {    for(int i = 1, j = len >> 1, k; i < len - 1; ++ i) {        if(i < j) swap(y[i], y[j]);        k = len >> 1;        while(j >= k) {            j -= k;            k >>= 1;        }        if(j < k) j += k;    }}void FFT(complex_t y[], int op) {    Rader(y);    for(int h = 2; h <= len; h <<= 1) {        complex_t WN(cos(op * 2.0 * PI / h), sin(op * 2.0 * PI / h));        for(int i = 0; i < len; i += h) {            complex_t W(1.0, 0);            for(int j = i; j < i + h / 2; ++j) {                complex_t u = y[j];                complex_t t = W * y[j + h / 2];                y[j] = u + t;                y[j + h / 2] = u - t;                W = W * WN;            }        }    }    if(op == -1) {        for(int i = 0; i < len; ++i) {            y[i] = complex_t(y[i].real() / len, y[i].imag() / len);        }    }}void Output() {    int pos = len - 1;    while(pos && res[pos] == 0) --pos;    while(~pos) putchar(res[pos--] + '0');    putchar('\n');}void Mul(complex_t x[], complex_t y[]) {    for(int i = 0; i < len; ++i) {        x[i] = x[i] * y[i];    }}void Slove() {    FFT(A, 1);    FFT(B, 1);    Mul(A, B);    FFT(A, -1);    res[0] = 0;    for(int i = 0; i < len; ++i) {        res[i] += (int)(A[i].real() + 0.5);        res[i + 1] = res[i] / 10;        res[i] %= 10;    }    Output();}int main(){    while(scanf("%s%s", str_1, str_2) != EOF) {        Init();        Slove();    }    return 0;}