結果

問題 No.1655 123 Swaps
ユーザー 👑 hos.lyrichos.lyric
提出日時 2021-08-21 02:25:12
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 73 ms / 2,000 ms
コード長 10,833 bytes
コンパイル時間 1,177 ms
コンパイル使用メモリ 109,696 KB
実行使用メモリ 13,516 KB
最終ジャッジ日時 2024-10-14 11:03:01
合計ジャッジ時間 3,684 ms
ジャッジサーバーID
(参考情報)
judge2 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 42
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using Int = long long;
template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
static constexpr unsigned M = M_;
unsigned x;
constexpr ModInt() : x(0U) {}
constexpr ModInt(unsigned x_) : x(x_ % M) {}
constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
ModInt pow(long long e) const {
if (e < 0) return inv().pow(-e);
ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
}
ModInt inv() const {
unsigned a = M, b = x; int y = 0, z = 1;
for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
assert(a == 1U); return ModInt(y);
}
ModInt operator+() const { return *this; }
ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
explicit operator bool() const { return x; }
bool operator==(const ModInt &a) const { return (x == a.x); }
bool operator!=(const ModInt &a) const { return (x != a.x); }
friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////
// M: prime, G: primitive root, 2^K | M - 1
template <unsigned M_, unsigned G_, int K_> struct Fft {
static_assert(2U <= M_, "Fft: 2 <= M must hold.");
static_assert(M_ < 1U << 30, "Fft: M < 2^30 must hold.");
static_assert(1 <= K_, "Fft: 1 <= K must hold.");
static_assert(K_ < 30, "Fft: K < 30 must hold.");
static_assert(!((M_ - 1U) & ((1U << K_) - 1U)), "Fft: 2^K | M - 1 must hold.");
static constexpr unsigned M = M_;
static constexpr unsigned M2 = 2U * M_;
static constexpr unsigned G = G_;
static constexpr int K = K_;
ModInt<M> FFT_ROOTS[K + 1], INV_FFT_ROOTS[K + 1];
ModInt<M> FFT_RATIOS[K], INV_FFT_RATIOS[K];
Fft() {
const ModInt<M> g(G);
for (int k = 0; k <= K; ++k) {
FFT_ROOTS[k] = g.pow((M - 1U) >> k);
INV_FFT_ROOTS[k] = FFT_ROOTS[k].inv();
}
for (int k = 0; k <= K - 2; ++k) {
FFT_RATIOS[k] = -g.pow(3U * ((M - 1U) >> (k + 2)));
INV_FFT_RATIOS[k] = FFT_RATIOS[k].inv();
}
assert(FFT_ROOTS[1] == M - 1U);
}
// as[rev(i)] <- \sum_j \zeta^(ij) as[j]
void fft(ModInt<M> *as, int n) const {
assert(!(n & (n - 1))); assert(1 <= n); assert(n <= 1 << K);
int m = n;
if (m >>= 1) {
for (int i = 0; i < m; ++i) {
const unsigned x = as[i + m].x; // < M
as[i + m].x = as[i].x + M - x; // < 2 M
as[i].x += x; // < 2 M
}
}
if (m >>= 1) {
ModInt<M> prod = 1U;
for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
for (int i = i0; i < i0 + m; ++i) {
const unsigned x = (prod * as[i + m]).x; // < M
as[i + m].x = as[i].x + M - x; // < 3 M
as[i].x += x; // < 3 M
}
prod *= FFT_RATIOS[__builtin_ctz(++h)];
}
}
for (; m; ) {
if (m >>= 1) {
ModInt<M> prod = 1U;
for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
for (int i = i0; i < i0 + m; ++i) {
const unsigned x = (prod * as[i + m]).x; // < M
as[i + m].x = as[i].x + M - x; // < 4 M
as[i].x += x; // < 4 M
}
prod *= FFT_RATIOS[__builtin_ctz(++h)];
}
}
if (m >>= 1) {
ModInt<M> prod = 1U;
for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
for (int i = i0; i < i0 + m; ++i) {
const unsigned x = (prod * as[i + m]).x; // < M
as[i].x = (as[i].x >= M2) ? (as[i].x - M2) : as[i].x; // < 2 M
as[i + m].x = as[i].x + M - x; // < 3 M
as[i].x += x; // < 3 M
}
prod *= FFT_RATIOS[__builtin_ctz(++h)];
}
}
}
for (int i = 0; i < n; ++i) {
as[i].x = (as[i].x >= M2) ? (as[i].x - M2) : as[i].x; // < 2 M
as[i].x = (as[i].x >= M) ? (as[i].x - M) : as[i].x; // < M
}
}
// as[i] <- (1/n) \sum_j \zeta^(-ij) as[rev(j)]
void invFft(ModInt<M> *as, int n) const {
assert(!(n & (n - 1))); assert(1 <= n); assert(n <= 1 << K);
int m = 1;
if (m < n >> 1) {
ModInt<M> prod = 1U;
for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
for (int i = i0; i < i0 + m; ++i) {
const unsigned long long y = as[i].x + M - as[i + m].x; // < 2 M
as[i].x += as[i + m].x; // < 2 M
as[i + m].x = (prod.x * y) % M; // < M
}
prod *= INV_FFT_RATIOS[__builtin_ctz(++h)];
}
m <<= 1;
}
for (; m < n >> 1; m <<= 1) {
ModInt<M> prod = 1U;
for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
for (int i = i0; i < i0 + (m >> 1); ++i) {
const unsigned long long y = as[i].x + M2 - as[i + m].x; // < 4 M
as[i].x += as[i + m].x; // < 4 M
as[i].x = (as[i].x >= M2) ? (as[i].x - M2) : as[i].x; // < 2 M
as[i + m].x = (prod.x * y) % M; // < M
}
for (int i = i0 + (m >> 1); i < i0 + m; ++i) {
const unsigned long long y = as[i].x + M - as[i + m].x; // < 2 M
as[i].x += as[i + m].x; // < 2 M
as[i + m].x = (prod.x * y) % M; // < M
}
prod *= INV_FFT_RATIOS[__builtin_ctz(++h)];
}
}
if (m < n) {
for (int i = 0; i < m; ++i) {
const unsigned y = as[i].x + M2 - as[i + m].x; // < 4 M
as[i].x += as[i + m].x; // < 4 M
as[i + m].x = y; // < 4 M
}
}
const ModInt<M> invN = ModInt<M>(n).inv();
for (int i = 0; i < n; ++i) {
as[i] *= invN;
}
}
void fft(vector<ModInt<M>> &as) const {
fft(as.data(), as.size());
}
void invFft(vector<ModInt<M>> &as) const {
invFft(as.data(), as.size());
}
vector<ModInt<M>> convolve(vector<ModInt<M>> as, vector<ModInt<M>> bs) const {
if (as.empty() || bs.empty()) return {};
const int len = as.size() + bs.size() - 1;
int n = 1;
for (; n < len; n <<= 1) {}
as.resize(n); fft(as);
bs.resize(n); fft(bs);
for (int i = 0; i < n; ++i) as[i] *= bs[i];
invFft(as);
as.resize(len);
return as;
}
vector<ModInt<M>> square(vector<ModInt<M>> as) const {
if (as.empty()) return {};
const int len = as.size() + as.size() - 1;
int n = 1;
for (; n < len; n <<= 1) {}
as.resize(n); fft(as);
for (int i = 0; i < n; ++i) as[i] *= as[i];
invFft(as);
as.resize(len);
return as;
}
};
const Fft<924844033U, 5U, 21> FFT;
constexpr unsigned MO = FFT.M;
using Mint = ModInt<MO>;
constexpr int LIM = 600'010;
Mint inv[LIM], fac[LIM], invFac[LIM];
void prepare() {
inv[1] = 1;
for (int i = 2; i < LIM; ++i) {
inv[i] = -((Mint::M / i) * inv[Mint::M % i]);
}
fac[0] = invFac[0] = 1;
for (int i = 1; i < LIM; ++i) {
fac[i] = fac[i - 1] * i;
invFac[i] = invFac[i - 1] * inv[i];
}
}
Mint binom(Int n, Int k) {
if (n < 0) {
if (k >= 0) {
return ((k & 1) ? -1 : +1) * binom(-n + k - 1, k);
} else if (n - k >= 0) {
return (((n - k) & 1) ? -1 : +1) * binom(-k - 1, n - k);
} else {
return 0;
}
} else {
if (0 <= k && k <= n) {
assert(n < LIM);
return fac[n] * invFac[k] * invFac[n - k];
} else {
return 0;
}
}
}
int A, B, C;
int main() {
prepare();
for (; ~scanf("%d%d%d", &A, &B, &C); ) {
Mint ans = 0;
if ((A + B + C) % 2 == 0) {
const int N = (A + B + C) / 2;
for (int rb = 0; rb < 3; ++rb) {
const int rc = (B + rb - C % 3 + 3) % 3;
vector<Mint> fs(B / 3 + 1, 0);
vector<Mint> gs(C / 3 + 1, 0);
for (int i = 0, b; (b = 3 * i + rb) <= B; ++i) fs[i] = invFac[b] * invFac[B - b];
for (int i = 0, c; (c = 3 * i + rc) <= C; ++i) gs[i] = invFac[c] * invFac[C - c];
const auto prod = FFT.convolve(fs, gs);
for (int i = 0; i < (int)prod.size(); ++i) {
const int a = N - (3 * i + rb + rc);
if (0 <= a && a <= A) {
ans += invFac[a] * invFac[A - a] * prod[i];
}
}
}
ans *= fac[N];
ans *= fac[N];
/*
Mint brt = 0;
for (int a = 0; a <= A; ++a) for (int b = 0; b <= B; ++b) for (int c = 0; c <= C; ++c) {
if (a + b + c == N && (B + b - C - c) % 3 == 0) {
Mint tmp = 1;
tmp *= fac[N] * invFac[a] * invFac[b] * invFac[c];
tmp *= fac[N] * invFac[A - a] * invFac[B - b] * invFac[C - c];
brt += tmp;
}
}
cerr<<"brt = "<<brt<<endl;
//*/
}
printf("%u\n", ans.x);
}
return 0;
}
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