【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
, b
;
char A
, B
;

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;
}