結果

問題 No.2033 Chromatic Duel
ユーザー 👑 NachiaNachia
提出日時 2022-08-05 22:40:47
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 8 ms / 2,000 ms
コード長 2,969 bytes
コンパイル時間 2,446 ms
コンパイル使用メモリ 115,812 KB
最終ジャッジ日時 2025-01-30 18:28:43
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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 * 4
other AC * 37
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 # 

#line 1 "Main.cpp"
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <atcoder/modint>

#line 2 "nachia\\math\\combination.hpp"

#line 4 "nachia\\math\\combination.hpp"


namespace nachia{

template<class Modint>
class Comb{
private:
    ::std::vector<Modint> F;
    ::std::vector<Modint> iF;
public:
    Comb(int n){
        F.assign(n+1, Modint(1));
        for(int i=1; i<=n; i++) F[i] = F[i-1] * Modint(i);
        iF.assign(n+1, Modint(1));
        iF[n] = F[n].inv();
        for(int i=n; i>=1; i--) iF[i-1] = iF[i] * Modint(i);
    }
    Modint factorial(int n) const { return F[n]; }
    Modint inv_factorial(int n) const { return iF[n]; }
    Modint inv_of(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 inv_comb(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 inv_perm(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
#line 8 "Main.cpp"
//#include "nachia/fps/formal-power-series-struct.hpp"

using namespace std;
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
#define rep(i,n) for(int i=0; i<(int)(n); i++)


const i64 INF = 1001001001001001001;
//using FPS = nachia::FormalPowerSeriesNTT<998244353>;
using modint = atcoder::static_modint<998244353>;
//using modint = FPS::Elem;

auto comb = nachia::Comb<modint>(300000);

modint solve(int N, int B, int W){
    //cout << "solve(" << N << ", " << B << ", " << W << ")" << endl;
    N -= B;
    B++;
    //cout << "N = " << N << " , B = " << B << " , W = " << W << endl;
    modint ans = 0;
    for(int a=0; a<=B; a++){
        int b = W - (N-2*(B-a));
        int c = B - a - b;
        if(b < 0 || c < 0 || b + 2*c + W != N) continue;
        //cout << "   a = " << a << " , b = " << b << " , c = " << c << endl;
        if(c != 0) ans += comb(B, a) * comb(B-a, b) * comb(W+c-1, c-1);
        else if(W == 0) ans += comb(B, a) * comb(B-a, b);
    }
    //cout << "ans = " << ans.val() << '\n';
    return ans;
}

int main(){
    int N, B, W; cin >> N >> B >> W;
    if(B == 1){
        if(W == N - 2){ cout << 2 << '\n'; }
        else if(W == N - 3){ cout << (N-2) << '\n'; }
        else{ cout << 0 << '\n'; }
    }
    else{
        modint ans = solve(N+2, B, W) - solve(N+1, B-1, W) * 2 + solve(N, B-2, W);
        cout << ans.val() << '\n';
    }
    return 0;
}


struct ios_do_not_sync{
    ios_do_not_sync(){
        std::ios::sync_with_stdio(false);
        std::cin.tie(nullptr);
    }
} ios_do_not_sync_instance;
0