Submission #7143619
Source Code Expand
//整数列a[i],b[i]から列c[k]=sum{a[i]*b[k-i]}を生成する.任意modに対応.O(NlogN).
//NTT_CONVOLUTION_TIME を適切に変更するのを忘れない
#include <iostream>
#include <cstring>
#include <algorithm>
#include <vector>
#include <string>
#include <math.h>
#include <iomanip>
#include <limits>
#include <list>
#include <queue>
#include <tuple>
#include <map>
#include <stack>
#include <set>
#include <complex>
using namespace std;
#define MOD (long long int)(1e9+7)
#define ll long long int
#define rep(i,n) for(int i=0; i<(int)(n); i++)
#define reps(i,n) for(int i=1; i<=(int)(n); i++)
#define REP(i,n) for(int i=n-1; i>=0; i--)
#define REPS(i,n) for(int i=n; i>0; i--)
#define INF (int)(1123456789)
#define LINF (long long int)(112345678901234567)
#define chmax(a, b) a = (((a)<(b)) ? (b) : (a))
#define chmin(a, b) a = (((a)>(b)) ? (b) : (a))
#define all(v) v.begin(), v.end()
std::vector<int> tmp;
size_t sz = 1;
inline int powMod(int n, int p, int m) {
int res = 1;
while (p) {
if (p & 1) res = (ll)res * n % m;
n = (ll)n * n % m;
p >>= 1;
}
return (int)res;
}
inline int invMod(int n, int m) {
return powMod(n, m - 2, m);
}
template <int Mod, int PrimitiveRoot>
struct NTTPart {
static std::vector<int> ntt(std::vector<int> a, bool inv = false) {
size_t mask = sz - 1;
size_t p = 0;
for (size_t i = sz >> 1; i >= 1; i >>= 1) {
auto& cur = (p & 1) ? tmp : a;
auto& nex = (p & 1) ? a : tmp;
int e = powMod(PrimitiveRoot, (Mod - 1) / sz * i, Mod);
if (inv) e = invMod(e, Mod);
int w = 1;
for (size_t j = 0; j < sz; j += i) {
for (size_t k = 0; k < i; ++k) {
nex[j + k] = (cur[((j << 1) & mask) + k] + (ll)w * cur[(((j << 1) + i) & mask) + k]) % Mod;
}
w = (ll)w * e % Mod;
}
++p;
}
if (p & 1) std::swap(a, tmp);
if (inv) {
int invSz = invMod(sz, Mod);
for (size_t i = 0; i < sz; ++i) a[i] = (ll)a[i] * invSz % Mod;
}
return a;
}
static std::vector<int> mul(std::vector<int> a, std::vector<int> b) {
a = ntt(a);
b = ntt(b);
for (size_t i = 0; i < sz; ++i) a[i] = (ll)a[i] * b[i] % Mod;
a = ntt(a, true);
return a;
}
};
constexpr int M[] = {1224736769, 469762049, 167772161};
constexpr int PR[] = {3, 3, 3};
constexpr int NTT_CONVOLUTION_TIME = 3;
/*
X := max(a)*max(b)*min(|a|, |b|) のとき,
NTT_CONVOLUTION_TIME <- 1: X < 1224736769 = 1.2*10^ 9 ~ 2^30
NTT_CONVOLUTION_TIME <- 2: X < 575334854091079681 = 5.8*10^17 ~ 2^59
NTT_CONVOLUTION_TIME <- 3: X < 2^86 (32bit * 32bit * 10^7くらいまで)
*/
inline void garner(std::vector<int> *c, int mod) {
if (NTT_CONVOLUTION_TIME == 1) {
for(auto& x : c[0]) x %= mod;
}
else if (NTT_CONVOLUTION_TIME == 2) {
const int r01 = invMod(M[0], M[1]);
for (size_t i = 0; i < sz; ++i) {
c[1][i] = (c[1][i] - c[0][i]) * (ll)r01 % M[1];
if (c[1][i] < 0) c[1][i] += M[1];
c[0][i] = (c[0][i] + (ll)c[1][i] * M[0]) % mod;
}
}
else if (NTT_CONVOLUTION_TIME == 3) {
const int R01 = invMod(M[0], M[1]);
const int R02 = invMod(M[0], M[2]);
const int R12 = invMod(M[1], M[2]);
const int M01 = (ll)M[0] * M[1] % mod;
for (size_t i = 0; i < sz; ++i) {
c[1][i] = (c[1][i] - c[0][i]) * (ll)R01 % M[1];
if (c[1][i] < 0) c[1][i] += M[1];
c[2][i] = ((c[2][i] - c[0][i]) * (ll)R02 % M[2] - c[1][i]) * R12 % M[2];
if (c[2][i] < 0) c[2][i] += M[2];
c[0][i] = (c[0][i] + (ll)c[1][i] * M[0] + (ll)c[2][i] * M01) % mod;
}
}
}
std::vector<int> mul(std::vector<int> a, std::vector<int> b, int mod) {
for (auto& x : a) x %= mod;
for (auto& x : b) x %= mod;
size_t m = a.size() + b.size() - 1;
sz = 1;
while (m > sz) sz <<= 1;
tmp.resize(sz);
a.resize(sz, 0);
b.resize(sz, 0);
std::vector<int> c[NTT_CONVOLUTION_TIME];
if (NTT_CONVOLUTION_TIME >= 1) c[0] = NTTPart<M[0], PR[0]>::mul(a, b);
if (NTT_CONVOLUTION_TIME >= 2) c[1] = NTTPart<M[1], PR[1]>::mul(a, b);
if (NTT_CONVOLUTION_TIME >= 3) c[2] = NTTPart<M[2], PR[2]>::mul(a, b);
for (auto& v : c) v.resize(m);
garner(c, mod);
return c[0];
}
int main(void){
int n; cin>>n;
vector<int> A,B,C;
A.push_back(0);
B.push_back(0);
rep(i,n){
int a,b; cin>>a>>b;
A.push_back(a);
B.push_back(b);
}
//NTT_CONVOLUTION_TIMEを変更するのを忘れない
C = mul(A,B,MOD);
reps(i,2*n){
cout<<C[i]<<endl;
}
return 0;
}
Submission Info
Submission Time |
|
Task |
C - 高速フーリエ変換 |
User |
Jirotech |
Language |
C++14 (GCC 5.4.1) |
Score |
100 |
Code Size |
4962 Byte |
Status |
AC |
Exec Time |
463 ms |
Memory |
9176 KB |
Judge Result
Set Name |
Sample |
All |
Score / Max Score |
0 / 0 |
100 / 100 |
Status |
|
|
Set Name |
Test Cases |
Sample |
00_sample_01 |
All |
00_sample_01, 01_00_01, 01_01_19, 01_02_31, 01_03_22, 01_04_31, 01_05_40, 01_06_15, 01_07_39, 01_08_28, 01_09_30, 01_10_23, 01_11_33, 01_12_11, 01_13_28, 01_14_41, 01_15_26, 01_16_49, 01_17_34, 01_18_02, 01_19_33, 01_20_29, 02_00_51254, 02_01_82431, 02_02_17056, 02_03_34866, 02_04_6779, 02_05_65534, 02_06_65535, 02_07_65536, 02_08_65537, 02_09_65538, 02_10_100000 |
Case Name |
Status |
Exec Time |
Memory |
00_sample_01 |
AC |
1 ms |
256 KB |
01_00_01 |
AC |
1 ms |
256 KB |
01_01_19 |
AC |
1 ms |
256 KB |
01_02_31 |
AC |
1 ms |
256 KB |
01_03_22 |
AC |
1 ms |
256 KB |
01_04_31 |
AC |
1 ms |
256 KB |
01_05_40 |
AC |
1 ms |
256 KB |
01_06_15 |
AC |
1 ms |
256 KB |
01_07_39 |
AC |
1 ms |
256 KB |
01_08_28 |
AC |
1 ms |
256 KB |
01_09_30 |
AC |
1 ms |
256 KB |
01_10_23 |
AC |
1 ms |
256 KB |
01_11_33 |
AC |
1 ms |
256 KB |
01_12_11 |
AC |
1 ms |
256 KB |
01_13_28 |
AC |
1 ms |
256 KB |
01_14_41 |
AC |
1 ms |
256 KB |
01_15_26 |
AC |
1 ms |
256 KB |
01_16_49 |
AC |
1 ms |
256 KB |
01_17_34 |
AC |
1 ms |
256 KB |
01_18_02 |
AC |
1 ms |
256 KB |
01_19_33 |
AC |
1 ms |
256 KB |
01_20_29 |
AC |
1 ms |
256 KB |
02_00_51254 |
AC |
234 ms |
4768 KB |
02_01_82431 |
AC |
403 ms |
9056 KB |
02_02_17056 |
AC |
87 ms |
2540 KB |
02_03_34866 |
AC |
179 ms |
4576 KB |
02_04_6779 |
AC |
31 ms |
896 KB |
02_05_65534 |
AC |
286 ms |
4840 KB |
02_06_65535 |
AC |
286 ms |
4840 KB |
02_07_65536 |
AC |
343 ms |
8936 KB |
02_08_65537 |
AC |
344 ms |
8936 KB |
02_09_65538 |
AC |
343 ms |
8936 KB |
02_10_100000 |
AC |
463 ms |
9176 KB |