#1191350 (C++17) No.3753 Certainly a Cretan

• 問題: No.3753 Certainly a Cretan
• ユーザー: GOTKAKO
• 提出日時: 2026-10-03 18:00:33
• 言語: C++17 (gcc 15.3.0 + boost 1.92.0 + ACL)
• 結果: AC
• 実行時間: 304 ms / 2,500 ms
• コード長: 7,311 bytes
• コンパイル時間: 4,002 ms
• コンパイル使用メモリ: 233,400 KB
• 実行使用メモリ: 97,948 KB
• 最終ジャッジ日時: 2026-10-03 18:01:33
• 合計ジャッジ時間: 8,159 ms
• ジャッジサーバーID （参考情報）: judge1_0 / judge4_0

ファイルパターン	結果
sample	AC * 2
other	AC * 46

ソースコード

#include <bits/stdc++.h>
using namespace std;

//入力が必ず-mod<=a<modの時.
template<const int mod> //mod<2^30.
struct modint{ //mod変更が不可能.
    public:
    long long v;
    static void setmod(int m){} //飾り.
    static constexpr long long getmod(){return mod;}
    modint():v(0){}
    template<typename T>
    modint(T a):v(a){if(v < 0) v += mod;}
    long long val()const{return v;}
 
    modint &operator=(const modint &b) = default;
    modint &operator+()const{return (*this);}
    modint operator-()const{return modint(0)-(*this);}
    modint operator+(const modint b)const{return modint(v)+=b;}
    modint operator-(const modint b)const{return modint(v)-=b;}
    modint operator*(const modint b)const{return modint(v)*=b;}
    modint operator/(const modint b)const{return modint(v)/=b;}
    modint &operator+=(const modint b){
        v += b.v; if(v >= mod) v -= mod;
        return *this;
    }
    modint &operator-=(const modint b){
        v -= b.v; if(v < 0) v += mod; 
        return *this;
    }   
    modint &operator*=(const modint b){v = v*b.v%mod; return *this;}
    modint &operator/=(modint b){ //b!=0 mod素数が必須.
        assert(b.v != 0);
        (*this) *= b.pow(mod-2);
        return *this;
    }
    modint pow(long long n)const{
        modint ret = 1,p = v;
        if(n < 0) p = p.inv(),n = -n;
        while(n){
            if(n&1) ret *= p;
            p *= p; n >>= 1;
        }
        return ret;
    }
    modint inv()const{return pow(mod-2);} //素数mod必須.
 
    modint &operator++(){*this += 1; return *this;}
    modint &operator--(){*this -= 1; return *this;}
    modint operator++(int){modint ret = *this; *this += 1; return ret;}
    modint operator--(int){modint ret = *this; *this -= 1; return ret;}
    friend bool operator==(const modint a,const modint b){return a.v==b.v;}
    friend bool operator!=(const modint a,const modint b){return a.v!=b.v;}
    friend bool operator<(const modint a,const modint b){return a.v<b.v;}
    friend bool operator<=(const modint a,const modint b){return a.v<=b.v;}
    friend bool operator>=(const modint a,const modint b){return a.v>=b.v;}
    friend bool operator>(const modint a,const modint b){return a.v>b.v;}
    friend ostream &operator<<(ostream &os,const modint a){return os<<a.v;}
    friend istream &operator>>(istream &is,modint &a){ //入力はmodをとってくれる.
        long long x; is >> x; x %= mod;
        a = modint(x); return is;
    }
};
using mint = modint<998244353>; const long long mod = 998244353;

template<typename T>
vector<pair<T,long long>> RLE(vector<T> &A){
    if(A.size() == 0) return {};
    vector<pair<T,long long>> ret;
    T back = A.at(0);
    long long streak = 1;
    for(int i=1; i<A.size(); i++){
        if(back == A.at(i)) streak++;
        else{
            ret.push_back({back,streak});
            back = A.at(i); streak = 1;
        }
    }
    ret.push_back({back,streak});
    return ret;
}
vector<pair<char,long long>> RLE(string &s){
    if(s.size() == 0) return {};
    vector<pair<char,long long>> ret;
    char back = s.at(0);
    long long streak = 1;
    for(int i=1; i<s.size(); i++){
        if(back == s.at(i)) streak++;
        else{
            ret.push_back({back,streak});
            back = s.at(i); streak = 1;
        }
    }
    ret.push_back({back,streak});
    return ret;
}

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int N,Q; cin >> N >> Q;
    int Limit = 2*N+1; //Limit->必要なサイズ fac->x! facinv->1/x! inv->1/x.
    vector<mint> fac(Limit+1,1),facinv(Limit+1);
    {
        int mod = mint::getmod(),invstart = min(mod-1,Limit); 
        for(int i=1; i<=Limit; i++) fac.at(i) = fac.at(i-1)*i;
        facinv.at(invstart) = fac.at(invstart).inv();
        for(int i=invstart-1; i>=0; i--) facinv.at(i) = facinv.at(i+1)*(i+1);
    }
    vector<mint> inv(Limit+1); for(int i=1; i<=Limit; i++) inv.at(i) = fac.at(i-1)*facinv.at(i); //必要なら解放.
    auto nCr = [&](int n,int r) -> mint {
        if(n < r || r < 0 || n < 0) return 0;
        return fac.at(n)*facinv.at(r)*facinv.at(n-r);
    };
    vector<mint> C(N+1),C2(N+1);
    for(int i=0; i<=N; i++) C.at(i) = nCr(2*i,i)*inv.at(i+1);
    for(int i=0; i<=N; i++) C2.at(i) = C.at(i).inv();

    string s; cin >> s;
    mint answer = 1;
    int odd = 0,idx = 0;
    set<pair<int,int>> S;
    for(auto [c,len] : RLE(s)) S.insert({idx,len}),idx += len;
    for(auto [pos,len] : S){
        if(len%2) odd++;
        else answer *= C.at(len/2);
    }
    auto add = [&](int l,int len) -> void {
        if(len%2) odd++;
        else answer *= C.at(len/2);
        S.insert({l,len});
    };
    auto era = [&](int l,int len) -> void {
        if(len%2) odd--;
        else answer *= C2.at(len/2);
        S.erase({l,len});
    };

    while(Q--){
        int t,v; cin >> t >> v;
        if(t == 1){
            v--;
            s.at(v) ^= 'Y'^'N';
            auto itr = S.lower_bound({v+1,-1});
            itr--;
            auto [l,len] = *itr;
            int r = l+len-1;
            era(l,len);
            if(l < v && v < r) add(l,v-l),add(v,1),add(v+1,r-v);
            else if(len == 1){
                int L = 1;
                if(r < N-1){
                    itr = S.lower_bound({l,-1});
                    auto [l2,len2] = *itr;
                    era(l2,len2),L += len2;
                }
                if(l){
                    itr = S.lower_bound({l,-1});
                    itr--;
                    auto [l2,len2] = *itr;
                    era(l2,len2),L += len2,l = l2;
                }
                add(l,L);
            }
            else if(l == v){
                add(v+1,r-v);
                if(l){
                    itr = S.lower_bound({v+1,-1});
                    itr--;
                    auto [l2,len2] = *itr;
                    era(l2,len2),add(l2,len2+1); 
                }
                else add(0,1);
            }
            else{
                add(l,len-1);
                if(r < N-1){
                    itr = S.lower_bound({l+1,-1});
                    auto [l2,len2] = *itr;
                    era(l2,len2),add(l2-1,len2+1);
                }
                else add(r,1);
            }
        }
        else{
            {
                auto [ign,len] = *S.rbegin();
                if(len%2) odd--;
                else answer *= C2.at(len/2);
            }
            if(odd) cout << "0\n";
            else{
                auto [ign,len] = *S.rbegin();
                int n = N-len;
                if(n/2 > v) cout << "0\n";
                else{
                    v -= n/2;
                    if(s.back() == 'Y'){
                        int y = len-v,n = v;
                        if(y < n) cout << "0\n";
                        else cout << answer*(nCr(y+n,n)-nCr(y+n,n-1)) << "\n";
                    }
                    else{
                        int y = len-v,n = v;
                        if(y > n) cout << "0\n";
                        else cout << answer*(nCr(y+n,y)-nCr(y+n,y-1)) << "\n";
                    }
                }
            }
            {
                auto [ign,len] = *S.rbegin();
                if(len%2) odd++;
                else answer *= C.at(len/2);
            }

        }
    }
}