[hdu1402]大数乘法(FFT模板)

题意：大数乘法

思路：FFT模板

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/* ******************************************************************************** */
#include <iostream>                                                                 //
#include <cstdio>                                                                   //
#include <cmath>                                                                    //
#include <cstdlib>                                                                  //
#include <cstring>                                                                  //
#include <vector>                                                                   //
#include <ctime>                                                                    //
#include <deque>                                                                    //
#include <queue>                                                                    //
#include <algorithm>                                                                //
#include <map>                                                                      //
#include <cmath>                                                                    //
using namespace std;                                                                //
                                                                                    //
#define pb push_back                                                                //
#define mp make_pair                                                                //
#define X first                                                                     //
#define Y second                                                                    //
#define all(a) (a).begin(), (a).end()                                               //
#define foreach(a, i) for (typeof(a.begin()) i = a.begin(); i != a.end(); ++ i)     //
#define foreach(a, n, i) for(typeof(*a) *i = a; i < a + n; i ++)                    //
#define fillchar(a, x) memset(a, x, sizeof(a))                                      //
                                                                                    //
void RI(vector<int>&a,int n){a.resize(n);for(int i=0;i<n;i++)scanf("%d",&a[i]);}    //
void RI(){}void RI(int&X){scanf("%d",&X);}template<typename...R>                    //
void RI(int&f,R&...r){RI(f);RI(r...);}void RI(int*p,int*q){int d=p<q?1:-1;          //
while(p!=q){scanf("%d",p);p+=d;}}void print(){cout<<endl;}template<typename T>      //
void print(const T t){cout<<t<<endl;}template<typename F,typename...R>              //
void print(const F f,const R...r){cout<<f<<", ";print(r...);}template<typename T>   //
void print(T*p, T*q){int d=p<q?1:-1;while(p!=q){cout<<*p<<", ";p+=d;}cout<<endl;}   //
                                                                                    //
typedef pair<int, int> pii;                                                         //
typedef long long ll;                                                               //
typedef unsigned long long ull;                                                     //
                                                                                    //
template<typename T>bool umax(T&a, const T&b){return b>a?false:(a=b,true);}         //
template<typename T>bool umin(T&a, const T&b){return b<a?false:(a=b,true);}         //
template<typename T>                                                                //
void V2A(T a[],const vector<T>&b){for(int i=0;i<b.size();i++)a[i]=b[i];}            //
template<typename T>                                                                //
void A2V(vector<T>&a,const T b[]){for(int i=0;i<a.size();i++)a[i]=b[i];}            //
                                                                                    //
const double PI = acos(-1);                                                         //
                                                                                    //
/* -------------------------------------------------------------------------------- */
 
namespace FFT {
    const static int maxn = 5e4 + 7;
    #define L(x) (1 << (x))
    double ax[maxn << 2], ay[maxn << 2], bx[maxn << 2], by[maxn << 2];//需要四倍空间
    int revv(int x, int bits) {
        int ret = 0;
        for (int i = 0; i < bits; i++) {
            ret <<= 1;
            ret |= x & 1;
            x >>= 1;
        }
        return ret;
    }
    void fft(double * a, double * b, int n, bool rev) {
        int bits = 0;
        while (1 << bits < n) ++bits;
        for (int i = 0; i < n; i++) {
            int j = revv(i, bits);
            if (i < j)
                swap(a[i], a[j]), swap(b[i], b[j]);
        }
        for (int len = 2; len <= n; len <<= 1) {
            int half = len >> 1;
            double wmx = cos(2 * PI / len), wmy = sin(2 * PI / len);
            if (rev) wmy = -wmy;
            for (int i = 0; i < n; i += len) {
                double wx = 1, wy = 0;
                for (int j = 0; j < half; j++) {
                    double cx = a[i + j], cy = b[i + j];
                    double dx = a[i + j + half], dy = b[i + j + half];
                    double ex = dx * wx - dy * wy, ey = dx * wy + dy * wx;
                    a[i + j] = cx + ex, b[i + j] = cy + ey;
                    a[i + j + half] = cx - ex, b[i + j + half] = cy - ey;
                    double wnx = wx * wmx - wy * wmy, wny = wx * wmy + wy * wmx;
                    wx = wnx, wy = wny;
                }
            }
        }
        if (rev) {
            for (int i = 0; i < n; i++)
                a[i] /= n, b[i] /= n;
        }
    }
    int solve(int a[], int na, int b[], int nb, int ans[]) {
        int len = max(na, nb), ln;
        for(ln = 0; L(ln) < len; ++ln);
        len = L(++ln);
        for (int i = 0; i < len ; ++i) {
            if (i >= na) ax[i] = 0, ay[i] = 0;
            else ax[i] = a[i], ay[i] = 0;
        }
        fft(ax, ay, len, 0);
        for (int i = 0; i < len; ++i) {
            if (i >= nb) bx[i] = 0, by[i] = 0;
            else bx[i] = b[i], by[i] = 0;
        }
        fft(bx, by, len, 0);
        for (int i = 0; i < len; ++i) {
            double cx = ax[i] * bx[i] - ay[i] * by[i];
            double cy = ax[i] * by[i] + ay[i] * bx[i];
            ax[i] = cx, ay[i] = cy;
        }
        fft(ax, ay, len, 1);
        for (int i = 0; i < len; ++i)
            ans[i] = (int)(ax[i] + 0.5);
        return len;
    }
    #undef L(x)
}
const int maxn = 5e4 + 7;
char s1[maxn], s2[maxn];
int x[maxn], y[maxn], ans[maxn << 2];
 
int main() {
#ifndef ONLINE_JUDGE
    freopen("in.txt", "r", stdin);
#endif // ONLINE_JUDGE
    while (~scanf("%s", s1)) {
        scanf("%s", s2);
        int len1 = strlen(s1), len2 = strlen(s2);
        for (int i = 0; i < len1; i ++) x[i] = s1[len1 - i - 1] - '0';
        for (int i = 0; i < len2; i ++) y[i] = s2[len2 - i - 1] - '0';
        fillchar(ans, 0);
        int len = FFT::solve(x, len1, y, len2, ans), i;
        for (i = 0; i < len || ans[i] >= 10; i ++) {
            ans[i + 1] += ans[i] / 10;
            ans[i] %= 10;
        }
        len = i;
        while (ans[len] <= 0 && len) len --;
        for (int i = len; i >= 0; i --) putchar(ans[i] + '0');
        puts("");
    }
    return 0;
}
/* ******************************************************************************** */
posted @ 2015-07-31 19:21  jklongint  阅读(381)  评论(0)  编辑  收藏  举报