結果

問題 No.2983 Christmas Color Grid (Advent Calender ver.)
ユーザー 👑 Nachia
提出日時 2024-12-08 17:04:37
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 409 ms / 3,340 ms
コード長 4,842 bytes
コンパイル時間 1,232 ms
コンパイル使用メモリ 91,776 KB
最終ジャッジ日時 2025-02-26 11:35:41
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
（要ログイン）
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 #
プレゼンテーションモードにする

#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(int i=0; i<int(n); i++)
const i64 INF = 1001001001001001001;
template<typename A> void chmin(A& l, const A& r){ if(r < l) l = r; }
template<typename A> void chmax(A& l, const A& r){ if(l < r) l = r; }
using namespace std;
#include <atcoder/modint>
namespace nachia{
template<class Modint>
class Comb{
private:
    std::vector<Modint> F;
    std::vector<Modint> iF;
public:
    void extend(int newN){
        int prevN = (int)F.size() - 1;
        if(prevN >= newN) return;
        F.resize(newN+1);
        iF.resize(newN+1);
        for(int i=prevN+1; i<=newN; i++) F[i] = F[i-1] * Modint::raw(i);
        iF[newN] = F[newN].inv();
        for(int i=newN; i>prevN; i--) iF[i-1] = iF[i] * Modint::raw(i);
    }
    Comb(int n = 1){
        F.assign(2, Modint(1));
        iF.assign(2, Modint(1));
        extend(n);
    }
    Modint factorial(int n) const { return F[n]; }
    Modint invFactorial(int n) const { return iF[n]; }
    Modint invOf(int n) const { return iF[n] * F[n-1]; }
    Modint comb(int n, int r) const {
        if(n < 0 || n < r || r < 0) return Modint(0);
        return F[n] * iF[r] * iF[n-r];
    }
    Modint invComb(int n, int r) const {
        if(n < 0 || n < r || r < 0) return Modint(0);
        return iF[n] * F[r] * F[n-r];
    }
    Modint perm(int n, int r) const {
        if(n < 0 || n < r || r < 0) return Modint(0);
        return F[n] * iF[n-r];
    }
    Modint invPerm(int n, int r) const {
        if(n < 0 || n < r || r < 0) return Modint(0);
        return iF[n] * F[n-r];
    }
    Modint operator()(int n, int r) const { return comb(n,r); }
};
} // namespace nachia
namespace nachia{
int Popcount(unsigned long long c) noexcept {
#ifdef __GNUC__
    return __builtin_popcountll(c);
#else
    c = (c & (~0ull/3)) + ((c >> 1) & (~0ull/3));
    c = (c & (~0ull/5)) + ((c >> 2) & (~0ull/5));
    c = (c & (~0ull/17)) + ((c >> 4) & (~0ull/17));
    c = (c * (~0ull/257)) >> 56;
    return c;
#endif
}
// please ensure x != 0
int MsbIndex(unsigned long long x) noexcept {
#ifdef __GNUC__
    return 63 - __builtin_clzll(x);
#else
    using u64 = unsigned long long;
    int q = (x >> 32) ? 32 : 0;
    auto m = x >> q;
    constexpr u64 hi = 0x88888888;
    constexpr u64 mi = 0x11111111;
    m = (((m | ~(hi - (m & ~hi))) & hi) * mi) >> 35;
    m = (((m | ~(hi - (x & ~hi))) & hi) * mi) >> 31;
    q += (m & 0xf) << 2;
    q += 0x3333333322221100 >> (((x >> q) & 0xf) << 2) & 0xf;
    return q;
#endif
}
// please ensure x != 0
int LsbIndex(unsigned long long x) noexcept {
#ifdef __GNUC__
    return __builtin_ctzll(x);
#else
    return MsbIndex(x & -x);
#endif
}
}
using Modint = atcoder::modint;
void testcase(){
    i64 H, W; cin >> H >> W;
    i64 K, M; cin >> K >> M;
    Modint::set_mod(M);
    vector<i64> adj(H*W);
    auto Idx = [&](i64 y, i64 x) -> i64 { return y * W + x; };
    auto IdxBit = [&](i64 y, i64 x) -> i64 { return i64(1) << Idx(y,x); };
    rep(y,H) rep(x,W-1) adj[Idx(y,x)] |= IdxBit(y,x+1);
    rep(y,H) rep(x,W-1) adj[Idx(y,x+1)] |= IdxBit(y,x);
    rep(y,H-1) rep(x,W) adj[Idx(y,x)] |= IdxBit(y+1,x);
    rep(y,H-1) rep(x,W) adj[Idx(y+1,x)] |= IdxBit(y,x);
    i64 N = H*W;
    auto comb = nachia::Comb<Modint>(N+1);
    vector<Modint> ipow2(N+1, 1);
    rep(i,N) ipow2[i+1] = ipow2[i] / 2;
    vector<vector<Modint>> F(N+1, vector<Modint>(N+1));
    rep(i,N+1) rep(j,N+1) if(i+j <= N){
        Modint t1 = Modint(i).pow(K);
        //int k = N - i - j;
        //for(i64 f=0; f<=k; f++){ // 非隣接で塗る個数
        //    Modint t2 = t1 * comb(k, f);
        //    for(i64 e=0; e<=j; e++){ // 隣接で塗る個数
        //        Modint t3 = t2 * comb(j,e) * comb.invOf((k-f)+(j-e)+1);
        //        t3 *= comb.invComb(N, i+e+f) * ipow2[i+e];
        //        F[i][j] += t3;
        //    }
        //}
        F[i][j] += t1 * ipow2[i+j];
    }
    
    Modint ans = 0;
    vector<bool> vis(1<<(N));
    vector<i64> bfs;
    rep(y,H) rep(x,W) bfs.push_back(IdxBit(y,x));
    for(i64 v : bfs) vis[v] = 1;
    rep(i,bfs.size()){
        i64 v = bfs[i];
        i64 w = 0;
        rep(j,N) if((v>>j)&1) w |= adj[j];
        w -= v & w;
        int pcv = nachia::Popcount(v);
        int pcw = nachia::Popcount(w);
        //cout << "pcv = " << pcv << " , pcw = " << pcw << endl;
        ans += F[pcv][pcw];
        rep(j,N) if((w>>j)&1){
            i64 nx = v | i64(1) << j;
            if(vis[nx]) continue;
            vis[nx] = 1;
            bfs.push_back(nx);
        }
    }
    Modint t = 0;
    for(int i=1; i<=N; i++) t += comb.invOf(i);
    ans *= t;
    cout << ans.val() << '\n';
}
int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    testcase();
    return 0;
}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0