【模板】快速数论变换ntt

转自http://blog.csdn.net/zz_1215/article/details/40430041

快速数论变换模板：

#include <iostream>  
#include <string.h>  
#include <stdio.h>  
  
using namespace std;  
typedef long long LL;  
  
const int N = 1 << 18;  
const int P = (479 << 21) + 1;  
const int G = 3;  
const int NUM = 20;  
  
LL  wn[NUM];  
LL  a[N], b[N];  
char A[N], B[N];  
  
LL quick_mod(LL a, LL b, LL m)  
{  
    LL ans = 1;  
    a %= m;  
    while(b)  
    {  
        if(b & 1)  
        {  
            ans = ans * a % m;  
            b--;  
        }  
        b >>= 1;  
        a = a * a % m;  
    }  
    return ans;  
}  
  
void GetWn()  
{  
    for(int i=0; i<NUM; i++)  
    {  
        int t = 1 << i;  
        wn[i] = quick_mod(G, (P - 1) / t, P);  
    }  
}  
  
void Prepare(char A[], char B[], LL a[], LL b[], int &len)  
{  
    len = 1;  
    int len_A = strlen(A);  
    int len_B = strlen(B);  
    while(len <= 2 * len_A || len <= 2 * len_B) len <<= 1;  
    for(int i=0; i<len_A; i++)  
        A[len - 1 - i] = A[len_A - 1 - i];  
    for(int i=0; i<len - len_A; i++)  
        A[i] = '0';  
    for(int i=0; i<len_B; i++)  
        B[len - 1 - i] = B[len_B - 1 - i];  
    for(int i=0; i<len - len_B; i++)  
        B[i] = '0';  
    for(int i=0; i<len; i++)  
        a[len - 1 - i] = A[i] - '0';  
    for(int i=0; i<len; i++)  
        b[len - 1 - i] = B[i] - '0';  
}  
  
void Rader(LL a[], int len)  
{  
    int j = len >> 1;  
    for(int i=1; i<len-1; i++)  
    {  
        if(i < j) swap(a[i], a[j]);  
        int k = len >> 1;  
        while(j >= k)  
        {  
            j -= k;  
            k >>= 1;  
        }  
        if(j < k) j += k;  
    }  
}  
  
void NTT(LL a[], int len, int on)  
{  
    Rader(a, len);  
    int id = 0;  
    for(int h = 2; h <= len; h <<= 1)  
    {  
        id++;  
        for(int j = 0; j < len; j += h)  
        {  
            LL w = 1;  
            for(int k = j; k < j + h / 2; k++)  
            {  
                LL u = a[k] % P;  
                LL t = w * (a[k + h / 2] % P) % P;  
                a[k] = (u + t) % P;  
                a[k + h / 2] = ((u - t) % P + P) % P;  
                w = w * wn[id] % P;  
            }  
        }  
    }  
    if(on == -1)  
    {  
        for(int i = 1; i < len / 2; i++)  
            swap(a[i], a[len - i]);  
        LL Inv = quick_mod(len, P - 2, P);  
        for(int i = 0; i < len; i++)  
            a[i] = a[i] % P * Inv % P;  
    }  
}  
  
void Conv(LL a[], LL b[], int n)  
{  
    NTT(a, n, 1);  
    NTT(b, n, 1);  
    for(int i = 0; i < n; i++)  
        a[i] = a[i] * b[i] % P;  
    NTT(a, n, -1);  
}  
  
void Transfer(LL a[], int n)  
{  
    int t = 0;  
    for(int i = 0; i < n; i++)  
    {  
        a[i] += t;  
        if(a[i] > 9)  
        {  
            t = a[i] / 10;  
            a[i] %= 10;  
        }  
        else t = 0;  
    }  
}  
  
void Print(LL a[], int n)  
{  
    bool flag = 1;  
    for(int i = n - 1; i >= 0; i--)  
    {  
        if(a[i] != 0 && flag)  
        {  
            printf("%d", a[i]);  
            flag = 0;  
        }  
        else if(!flag)  
            printf("%d", a[i]);  
    }  
    puts("");  
}  
  
int main()  
{  
    GetWn();  
    while(scanf("%s%s", A, B)!=EOF)  
    {  
        int len;  
        Prepare(A, B, a, b, len);  
        Conv(a, b, len);  
        Transfer(a, len);  
        Print(a, len);  
    }  
    return 0;  
}