結果

問題 No.2983 Christmas Color Grid (Advent Calender ver.)
ユーザー 👑 hos.lyric
提出日時 2024-12-08 17:27:50
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,313 ms / 3,340 ms
コード長 5,732 bytes
コンパイル時間 1,356 ms
コンパイル使用メモリ 118,544 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-12-08 17:28:06
合計ジャッジ時間 14,569 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 * 64
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 # 

#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 <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#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> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
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; }
#define COLOR(s) ("\x1b[" s "m")

////////////////////////////////////////////////////////////////////////////////
// Barrett
struct ModInt {
  static unsigned M;
  static unsigned long long NEG_INV_M;
  static void setM(unsigned m) { M = m; NEG_INV_M = -1ULL / M; }
  unsigned x;
  ModInt() : x(0U) {}
  ModInt(unsigned x_) : x(x_ % M) {}
  ModInt(unsigned long long x_) : x(x_ % M) {}
  ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  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) {
    const unsigned long long y = static_cast<unsigned long long>(x) * a.x;
    const unsigned long long q = static_cast<unsigned long long>((static_cast<unsigned __int128>(NEG_INV_M) * y) >> 64);
    const unsigned long long r = y - M * q;
    x = r - M * (r >= 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; }
};
unsigned ModInt::M;
unsigned long long ModInt::NEG_INV_M;
// !!!Use ModInt::setM!!!
////////////////////////////////////////////////////////////////////////////////

using Mint = ModInt;


vector<Mint> pw;

vector<int> uf;
vector<pair<int, int>> his;
Mint now;
void init(int n) {
  uf.assign(n, -1);
  his.clear();
  now = n * pw[1];
}
void update(int u, int p) {
  his.emplace_back(u, uf[u]);
  uf[u] = p;
}
int snapshot() {
  return his.size();
}
void rollback(int stamp) {
  for (; (int)his.size() > stamp; his.pop_back()) uf[his.back().first] = his.back().second;
}
int root(int u) {
  for (; ; u = uf[u]) {
    if (uf[u] < 0) {
      return u;
    }
  }
}
bool connect(int u, int v) {
  u = root(u);
  v = root(v);
  if (u == v) return false;
  if (uf[u] > uf[v]) swap(u, v);
  now -= pw[-uf[u]];
  now -= pw[-uf[v]];
  now += pw[-(uf[u] + uf[v])];
  update(u, uf[u] + uf[v]);
  update(v, u);
  return true;
}


int M, N, MO;
Int K;

int id(int x, int y) {
  return x * N + y;
}

Mint ans;
bool a[30][30];
void dfs(int x, int y, int ign) {
  if (y == N) {
    ++x;
    y = 0;
  }
  if (x == M) {
    ans += (now - ign * pw[1]);
    return;
  }
  dfs(x, y + 1, ign + 1);
  a[x][y] = true;
  const auto stamp = snapshot();
  const Mint save = now;
  
  if (x && a[x - 1][y]) connect(id(x - 1, y), id(x, y));
  if (y && a[x][y - 1]) connect(id(x, y - 1), id(x, y));
  dfs(x, y + 1, ign);
  
  a[x][y] = false;
  rollback(stamp);
  now = save;
}

int main() {
  for (; ~scanf("%d%d%lld%d", &M, &N, &K, &MO); ) {
    Mint::setM(MO);
    pw.resize(M*N + 1);
    for (int i = 0; i <= M*N; ++i) pw[i] = Mint(i).pow(K);
    
    init(M*N);
    ans = 0;
    memset(a, 0, sizeof(a));
    dfs(0, 0, 0);
    ans /= Mint(2).pow(M*N);
    
    Mint har = 0;
    for (int i = 1; i <= M*N; ++i) har += Mint(i).inv();
    ans *= har;
    printf("%u\n", ans.x);
  }
  return 0;
}
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