Difference between revisions of "NTT & FFT"
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(Created page with "== NTT == <syntaxhighlight lang='cpp'> typedef long long LL; const int MAXN = 3e5 + 10; const int MOD = 998244353; const int G = 3; namespace NTT { int N, a[MAXN], b[MAX...") |
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Line 60: | Line 60: | ||
} | } | ||
}; | }; | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | == FFT == | ||
+ | |||
+ | <syntaxhighlight lang='cpp'> | ||
+ | #include<bits/stdc++.h> | ||
+ | using namespace std; | ||
+ | typedef complex<double> E; | ||
+ | const double pi = acos(-1.0); | ||
+ | int n, m; | ||
+ | const int N = 3e5 + 10; | ||
+ | E a[N], b[N]; | ||
+ | |||
+ | void FFT(E *x, int n, int type) { | ||
+ | if (n == 1)return; | ||
+ | E l[n >> 1], r[n >> 1]; | ||
+ | for (int i = 0; i < n; i += 2) | ||
+ | l[i >> 1] = x[i], r[i >> 1] = x[i + 1]; | ||
+ | FFT(l, n >> 1, type); | ||
+ | FFT(r, n >> 1, type); | ||
+ | E wn(cos(2 * pi / n), sin(type * 2 * pi / n)), w(1, 0); | ||
+ | for (int i = 0; i < n >> 1; i++, w *= wn) | ||
+ | x[i] = l[i] + w * r[i], x[i + (n >> 1)] = l[i] - w * r[i]; | ||
+ | } | ||
+ | |||
+ | int main() { | ||
+ | scanf("%d%d", &n, &m); | ||
+ | for (int i = 0, x; i <= n; i++) | ||
+ | scanf("%d", &x), a[i] = x; | ||
+ | for (int i = 0, x; i <= m; i++) | ||
+ | scanf("%d", &x), b[i] = x; | ||
+ | m = n + m; | ||
+ | for (n = 1; n <= m; n <<= 1); | ||
+ | FFT(a, n, 1); | ||
+ | FFT(b, n, 1); | ||
+ | for (int i = 0; i <= n; i++) | ||
+ | a[i] = a[i] * b[i]; | ||
+ | FFT(a, n, -1); | ||
+ | for (int i = 0; i <= m; i++) | ||
+ | printf("%d ", int(round(a[i].real() / n))); | ||
+ | return 0; | ||
+ | } | ||
</syntaxhighlight> | </syntaxhighlight> |
Revision as of 12:33, 22 March 2018
NTT
typedef long long LL;
const int MAXN = 3e5 + 10;
const int MOD = 998244353;
const int G = 3;
namespace NTT {
int N, a[MAXN], b[MAXN];
int pown(LL x, LL n) {
LL ret = MOD != 1; x %= MOD;
while (n) {
if (n & 1) ret = ret * x % MOD;
x = x * x % MOD;
n >>= 1;
}
return int(ret);
}
void clear() {
memset(a, 0, sizeof a);
memset(b, 0, sizeof b);
}
void ntt(int * a, int N, int f) {
int i, j = 0, t, k;
for (i = 1; i < N - 1; i++) {
for (t = N; j ^= t >>= 1, ~j & t;);
if (i < j) {
swap(a[i], a[j]);
}
}
for (i = 1; i < N; i <<= 1) {
t = i << 1;
int wn = pown(G, (MOD - 1) / t);
for (j = 0; j < N; j += t) {
int w = 1;
for (k = 0; k < i; k++, w = 1LL * w * wn % MOD) {
int x = a[j + k], y = 1LL * w * a[j + k + i] % MOD;
a[j + k] = (x + y) % MOD, a[j + k + i] = (x - y + MOD) % MOD;
}
}
}
if (f == -1) {
reverse(a + 1, a + N);
int inv = pown(N, MOD - 2);
for (i = 0; i < N; i++)
a[i] = 1LL * a[i] * inv % MOD;
}
}
void conv() {
ntt(a, N, 1);
ntt(b, N, 1);
for (int i = 0; i < N; ++i)
a[i] = 1LL * a[i] * b[i] % MOD;
ntt(a, N, -1);
}
};
FFT
#include<bits/stdc++.h>
using namespace std;
typedef complex<double> E;
const double pi = acos(-1.0);
int n, m;
const int N = 3e5 + 10;
E a[N], b[N];
void FFT(E *x, int n, int type) {
if (n == 1)return;
E l[n >> 1], r[n >> 1];
for (int i = 0; i < n; i += 2)
l[i >> 1] = x[i], r[i >> 1] = x[i + 1];
FFT(l, n >> 1, type);
FFT(r, n >> 1, type);
E wn(cos(2 * pi / n), sin(type * 2 * pi / n)), w(1, 0);
for (int i = 0; i < n >> 1; i++, w *= wn)
x[i] = l[i] + w * r[i], x[i + (n >> 1)] = l[i] - w * r[i];
}
int main() {
scanf("%d%d", &n, &m);
for (int i = 0, x; i <= n; i++)
scanf("%d", &x), a[i] = x;
for (int i = 0, x; i <= m; i++)
scanf("%d", &x), b[i] = x;
m = n + m;
for (n = 1; n <= m; n <<= 1);
FFT(a, n, 1);
FFT(b, n, 1);
for (int i = 0; i <= n; i++)
a[i] = a[i] * b[i];
FFT(a, n, -1);
for (int i = 0; i <= m; i++)
printf("%d ", int(round(a[i].real() / n)));
return 0;
}