結果

問題 No.1321 塗るめた
ユーザー carrot46carrot46
提出日時 2020-12-18 00:38:54
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 505 ms / 2,000 ms
コード長 14,988 bytes
コンパイル時間 2,204 ms
コンパイル使用メモリ 183,828 KB
実行使用メモリ 30,732 KB
最終ジャッジ日時 2023-10-21 07:42:12
合計ジャッジ時間 13,421 ms
ジャッジサーバーID
(参考情報)
judge10 / judge12
このコードへのチャレンジ(β)

テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 12 ms
12,444 KB
testcase_01 AC 23 ms
13,288 KB
testcase_02 AC 12 ms
12,444 KB
testcase_03 AC 12 ms
12,444 KB
testcase_04 AC 12 ms
12,444 KB
testcase_05 AC 12 ms
12,444 KB
testcase_06 AC 12 ms
12,444 KB
testcase_07 AC 12 ms
12,444 KB
testcase_08 AC 13 ms
12,444 KB
testcase_09 AC 13 ms
12,444 KB
testcase_10 AC 12 ms
12,444 KB
testcase_11 AC 13 ms
12,444 KB
testcase_12 AC 240 ms
21,252 KB
testcase_13 AC 62 ms
14,684 KB
testcase_14 AC 118 ms
17,004 KB
testcase_15 AC 240 ms
21,548 KB
testcase_16 AC 243 ms
22,092 KB
testcase_17 AC 17 ms
13,072 KB
testcase_18 AC 499 ms
30,264 KB
testcase_19 AC 120 ms
17,320 KB
testcase_20 AC 239 ms
21,192 KB
testcase_21 AC 242 ms
21,996 KB
testcase_22 AC 497 ms
30,152 KB
testcase_23 AC 497 ms
30,116 KB
testcase_24 AC 497 ms
29,880 KB
testcase_25 AC 505 ms
30,684 KB
testcase_26 AC 501 ms
30,328 KB
testcase_27 AC 494 ms
29,388 KB
testcase_28 AC 490 ms
29,220 KB
testcase_29 AC 499 ms
29,528 KB
testcase_30 AC 500 ms
30,732 KB
testcase_31 AC 242 ms
21,564 KB
testcase_32 AC 237 ms
21,092 KB
testcase_33 AC 238 ms
21,316 KB
testcase_34 AC 244 ms
22,028 KB
testcase_35 AC 240 ms
21,156 KB
testcase_36 AC 12 ms
12,444 KB
testcase_37 AC 241 ms
21,788 KB
testcase_38 AC 241 ms
21,788 KB
testcase_39 AC 243 ms
21,788 KB
testcase_40 AC 246 ms
21,788 KB
testcase_41 AC 246 ms
21,788 KB
testcase_42 AC 12 ms
12,444 KB
testcase_43 AC 239 ms
21,092 KB
testcase_44 AC 238 ms
21,316 KB
testcase_45 AC 244 ms
22,028 KB
testcase_46 AC 62 ms
14,876 KB
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 <bits/stdc++.h>
//#include <chrono>
//#pragma GCC optimize("O3")
using namespace std;
#define reps(i,s,n) for(int i = s; i < n; i++)
#define rep(i,n) reps(i,0,n)
#define Rreps(i,n,e) for(int i = n - 1; i >= e; --i)
#define Rrep(i,n) Rreps(i,n,0)
#define ALL(a) a.begin(), a.end()

using ll = long long;
using vec = vector<ll>;
using mat = vector<vec>;

ll N,M,H,W,Q,K,A,B;
string S;
using P = pair<ll, ll>;
const ll INF = (1LL<<60);

template<class T> bool chmin(T &a, const T &b){
    if(a > b) {a = b; return true;}
    else return false;
}
template<class T> bool chmax(T &a, const T &b){
    if(a < b) {a = b; return true;}
    else return false;
}
template<class T> void my_printv(std::vector<T> v,bool endline = true){
    if(!v.empty()){
        for(std::size_t i{}; i<v.size()-1; ++i) std::cout<<v[i]<<" ";
        std::cout<<v.back();
    }
    if(endline) std::cout<<std::endl;
}

struct edge{
        int to, cost;
        edge(int a, int b) : to(a), cost(b){}
    };
using ve = vector<edge>;

template <unsigned long long mod > class modint{
public:
    ll x;
    constexpr modint(){x = 0;}
    constexpr modint(ll _x) : x((_x < 0 ? ((_x += (LLONG_MAX / mod) * mod) < 0 ? _x + (LLONG_MAX / mod) * mod : _x) : _x)%mod){}
    constexpr modint set_raw(ll _x){
        //_x in [0, mod)
        x = _x;
        return *this;
    }
    constexpr modint operator-(){
        return x == 0 ? 0 : mod - x;
    }
    constexpr modint& operator+=(const modint& a){
        if((x += a.x) >= mod) x -= mod;
        return *this;
    }
    constexpr modint operator+(const modint& a) const{
        return modint(*this) += a;
    }
    constexpr modint& operator-=(const modint& a){
        if((x -= a.x) < 0) x += mod;
        return *this;
    }
    constexpr modint operator-(const modint& a) const{
        return modint(*this) -= a;
    }
    constexpr modint& operator*=(const modint& a){
        (x *= a.x)%=mod;
        return *this;
    }
    constexpr modint operator*(const modint& a) const{
        return modint(*this) *= a;
    }
    constexpr modint pow(unsigned long long pw) const{
        modint res(1), comp(*this);
        while(pw){
            if(pw&1) res *= comp;
            comp *= comp;
            pw >>= 1;
        }
        return res;
    }
    //以下、modが素数のときのみ
    constexpr modint inv() const{
        if(x == 2) return (mod + 1) >> 1;
        return modint(*this).pow(mod - 2);
    }
    constexpr modint& operator/=(const modint &a){
        (x *= a.inv().x)%=mod;
        return *this;
    }
    constexpr modint operator/(const modint &a) const{
        return modint(*this) /= a;
    }
    constexpr bool sqrt(bool find_mini = false) {
        if(x == 0) return true;
        modint jge = this->pow((mod - 1)>>1);
        if(jge.x + 1 == mod) return false;
        if((mod&3) == 3){
            *this = this->pow((mod + 1)>>2);
        }else{
            int m = 0;
            modint c, t;
            if(mod == 998244353){
                m = 23; c = 15311432; t = this->pow(119);
                *this = this->pow(60);
            }else{
                ll q = mod - 1;
                modint z = 2;
                while(!(q&1)){q>>=1; ++m;}
                while(z.pow((mod-1)>>1).x == 1) z += 1;
                c = z.pow(q); t = this->pow(q);
                *this = this->pow((q+1)>>1);
            }
            while(t.x != 1){
                modint cpy_t = t;
                int pw = m;
                while(cpy_t.x != 1){--pw; cpy_t *= cpy_t;}
                rep(i, pw-1) c *= c;
                (*this) *= c;
                c *= c;
                t *= c;
                m -= pw;
            }
        }
        if(find_mini) this->x = min(this->x, (ll)mod - this->x);
        return true;
    }
};
#define mod1 998244353
using mint = modint<mod1>;

ostream& operator<<(ostream& os, const mint& a){
    os << a.x;
    return os;
}
using vm = vector<mint>;

class NTT{
    static int root;
    static vector<int> id;

    static void make_bit_reverse(int n){
        //n must be 2^k
        int sz = id.size(), _chk = n;
        while(_chk > 1){assert(!(_chk&1)); _chk>>=1;}
        if(n > sz) {
            id.resize(n);
            while (sz < n) {
                rep(i, sz) {
                    id[i] <<= 1;
                    id[i | sz] = id[i] | 1;
                }
                sz <<= 1;
            }
        }
        if(n < sz){
            int k = 1;
            while(n * k < sz) k <<= 1;
            for(int i = 1, cpy = k; cpy < sz; ++i, cpy += k) id[i] = id[cpy];
            id.resize(n);
        }
    }
    static void dft(vm &f, bool inv, int n = INT_MAX){
        if(n > (int)f.size()) n = f.size();
        make_bit_reverse(n);
        rep(i, n) if (i > id[i]) swap(f[i], f[id[i]]);
        int l{1};
        for (int len = 1; len < n; ++l, len <<= 1) {
            mint root_diff = mint(root).pow(inv ? (mod1 - 1) - ((mod1 - 1)>>l) : ((mod1 - 1)>>l));
            int len2 = len << 1;
            for (int i = 0; i < n; i += len2) {
                mint z = 1;
                reps(j, i, i + len) {
                    mint z_f = z * f[j + len];
                    f[j + len] = f[j] - z_f;
                    f[j] += z_f;
                    z *= root_diff;
                }
            }
        }
        if(inv) {
            mint n_inv = mint(n).inv();
            rep(i, n) f[i] *= n_inv;
        }
    }
public:
    static void dft_2D(int n, int m, vector<vm> &a, bool inv){
        //簡単に、書き換える形で
        //aがn×mサイズであることや、n,mが2冪であることは仮定
        rep(i, n) dft(a[i], inv);
        rep(j, m){
            vm temp(n);
            rep(i, n) temp[i] = a[i][j];
            dft(temp, inv);
            rep(i, n) a[i][j] = temp[i];
        }
    }
    static vm convolution(vm g, vm h){
        int sz = g.size() + h.size() - 1, n = 1;
        while(sz > n) n *= 2;
        g.resize(n); h.resize(n);
        dft(g, false); dft(h, false);
        rep(i, n) g[i] *= h[i];
        dft(g, true);
        g.resize(sz);
        return g;
    }
    static vm simple_pow(vm &a, ll pw){
        int sz = a.size(), n = 1;
        while(sz > n) n <<= 1;
        n <<= 1;
        vm res(n, 0), cpy(n, 0);
        res[0] = 1;
        copy(ALL(a), cpy.begin());
        while(pw){
            dft(cpy, false);
            if(pw&1){
                dft(res, false);
                rep(i, n) res[i] *= cpy[i];
                dft(res, true);
                reps(i, n / 2, n) res[i] = 0;
            }
            rep(i, n) cpy[i] *= cpy[i];
            dft(cpy, true);
            reps(i, n / 2, n) cpy[i] = 0;
            pw >>= 1;
        }
        res.resize(sz);
        return res;
    }
    static vm inversion(vm f){
        assert(f[0].x != 0);
        int n = 1, sz = 1, first_sz = f.size();
        while(first_sz > n) n <<= 1;
        f.resize(n);
        vm g(n), cpy_f(n<<1), cpy_g(n<<1);
        g[0] = f[0].inv();
        while(sz < n){
            sz <<= 1;
            copy(f.begin(), f.begin() + sz, cpy_f.begin());
            copy(g.begin(), g.begin() + sz, cpy_g.begin());

            dft(cpy_f, false, sz<<1);
            dft(cpy_g, false, sz<<1);
            rep(i, sz<<1) cpy_f[i] *= cpy_g[i] * cpy_g[i];
            dft(cpy_f, true, sz<<1);

            rep(i, sz) (g[i] += g[i])-= cpy_f[i];
        }
        g.resize(first_sz);
        return g;
    }
    static void differential(vm &f){
        int n = f.size();
        rep(i, n - 1) f[i] = f[i + 1] * (i + 1);
        f[n-1] = 0;
    }
    static void integral(vm &f){
        int n = f.size();
        Rreps(i, n, 1) f[i] = f[i - 1];
        f[0] = 0;
        mint fct(1);
        reps(i, 1, n){f[i] *= fct; fct*=i;}
        fct = fct.inv();
        Rreps(i, n, 1){f[i] *= fct; fct*=i;}
    }
    static vm log(vm f){
        assert(f[0].x == 1);
        vm res = inversion(f);
        differential(f);
        res = convolution(f, res);
        res.resize((int)f.size());
        integral(res);
        return res;
    }
    static vm exp(vm f){
        assert(f[0].x == 0);
        int n = 1, sz = 1, first_sz = f.size();
        while(first_sz > n) n <<= 1;
        f.resize(n);
        vm g(1, 1), log_g;
        while(sz < n){
            sz <<= 1;
            g.resize(sz);
            reps(i, sz>>1, sz) g[i] = 0;
            log_g = log(g);
            rep(i, sz) log_g[i] = f[i] - log_g[i];
            log_g[0] += 1;
            g = convolution(g, log_g);
        }
        g.resize(first_sz);
        return g;
    }
    static vm pow(vm f, ll pw_int){
        int n = f.size(), non_zero_id{0};
        mint pw(pw_int);
        vm res(n, 0);
        if(pw_int == 0){
            res[0] = 1;
            return res;
        }
        while(non_zero_id < n && f[non_zero_id].x == 0) ++non_zero_id;
        if((n + pw_int - 1) / pw_int <= non_zero_id) return res;

        mint d = f[non_zero_id], d_inv = d.inv();
        rep(i, n - non_zero_id) f[i] = f[i + non_zero_id] * d.inv();

        non_zero_id *= pw_int;
        d = d.pow(pw_int%(mod1 - 1));
        f.resize(n - non_zero_id);

        res = log(f);
        for(auto &e : res) e *= pw;
        res = exp(res);
        res.resize(n);
        Rrep(i, n) res[i] = (i >= non_zero_id ? res[i - non_zero_id] * d : 0);
        return res;
    }
    static vm geometric_series(vm f){
        assert(f[0].x == 0);
        f[0] = 1;
        reps(i, 1, (int)f.size()) if(f[i].x) f[i].set_raw(mod1 - f[i].x);
        return inversion(f);
    }
    static vm sqrt(vm f, bool &suc){
        suc = true;
        int n = 1, sz = 1, first_sz = f.size(), non_zero_id{0};
        vm g(1, 1);
        while(non_zero_id < first_sz && f[non_zero_id].x == 0){
            ++non_zero_id;
            if(non_zero_id == first_sz) return vm(first_sz, 0);
            if(f[non_zero_id].x != 0){suc = false; return g;}
            ++non_zero_id;
        }
        if(non_zero_id >= first_sz)return vm(first_sz, 0);
        mint sq = f[non_zero_id], div = sq.inv();
        if(!sq.sqrt(true)){suc = false; return g;}
        rep(i, first_sz - non_zero_id) f[i] = f[i+non_zero_id] * div;
        reps(i, first_sz - non_zero_id, first_sz) f[i] = 0;
        non_zero_id >>= 1;
        while(first_sz > n) n <<= 1;
        f.resize(n);
        vm cpy_f, g_inv;
        while(sz < n){
            sz<<=1;
            g.resize(sz); cpy_f.resize(sz);
            g_inv = inversion(g);
            copy(f.begin(), f.begin() + sz, cpy_f.begin());
            g_inv = convolution(cpy_f, g_inv);
            rep(i, sz) {
                g[i] += g_inv[i];
                if(g[i].x&1) g[i].set_raw((g[i].x + mod1)>>1);
                else g[i].set_raw(g[i].x>>1);
            }
        }
        g.resize(first_sz);
        Rreps(i, first_sz, non_zero_id) g[i] = g[i - non_zero_id] * sq;
        rep(i, non_zero_id) g[i] = 0;
        return g;
    }
    /* 未完成
    static vm composition(vm f, vm g){
        assert(g[0].x == 0);
        int first_sz = min(f.size(), g.size()), n = 1, k = 0;
        while(first_sz > n) {n <<= 1; ++k;}
        {
            int lb = (1 << (k >> 1)) / k, ub = (1 << ((k + 1) >> 1)) + 1;
            while (ub - lb > 1) {int cen = (ub + lb) >> 1; (cen * cen * k <= n ? lb : ub) = cen;}
            rep(i, n){
                chmax(lb, i + 1);
                if(g[i].x != 0) break;
                if(i == n - 1){
                    vm res(first_sz, 0);
                    res[0] = f[0];
                    return res;
                }
            }
            k = 1;
            while(k < lb) k <<= 1;
            if(k > n) k = n;
        }
        vm p(n<<1), p_prime_inv(k), q(n<<1), qpow, res, temp(n<<1);
        vector<vm> dp(n);
        f.resize(n); g.resize(n);
        reps(i, first_sz, n) f[i] = g[i] = 0;
        copy(g.begin(), g.begin() + min(k, (int)g.size()), p.begin());
        copy(g.begin(), g.begin() + min(k, (int)g.size()), p_prime_inv.begin());
        copy(g.begin() + k, g.end(), q.begin());
        dft(q, false);
        qpow = q;
        dft(p, false, k<<1);
        rep(i, n) dp[i].push_back(f[i]);

        auto calc = [&](vm &s, vm &t){
            assert((int)t.size() <= k && (int)s.size() <= k);
            t.resize(k<<1);
            dft(t, false);
            rep(j, k<<1) t[j] *= p[j];
            dft(t, true);
            rep(j, (int)s.size()) t[j] += s[j];
            if(t.size() > n) t.resize(n);
            return t;
        };
        for(int cmp = 1; cmp < n; cmp <<= 1){
            for(int i = 0; i < n; i += (cmp<<1)){
                dp[i] = calc(dp[i], dp[i + cmp]);
                dp[i + cmp].clear();
            }
            if((cmp<<1) != n){
                rep(i, k<<1) p[i] *= p[i];
                dft(p, true, k<<1);
                if(k < n) k <<= 1;
                else {reps(i, n, n<<1) p[i] = 0;}
                dft(p, false, k<<1);
            }
        }

        res = dp[0]; res.resize(first_sz);
        k = p_prime_inv.size();
        dp[0].resize(n<<1);
        dft(dp[0], false);
        differential(p_prime_inv);
        p_prime_inv = inversion(p_prime_inv);
        p_prime_inv.resize(n<<1);
        dft(p_prime_inv, false);
        for(int i = k; i < n; i += k){
            rep(j, n<<1) dp[0][j] *= p_prime_inv[j];
            dft(dp[0], true);
            mint i_inv = mint(i / k).inv();
            rep(j, n) dp[0][j] *= i_inv;
            reps(j, n, n<<1) dp[0][j] = 0;
            differential(dp[0]);
            dft(dp[0], false);
            copy(dp[0].begin(), dp[0].end(), temp.begin());
            rep(j, n<<1) {
                temp[j] *= qpow[j];
                qpow[j] *= q[j];
            }
            dft(temp, true);
            reps(j, i, first_sz) res[j] += temp[j-i];
            dft(qpow, true);
            reps(j, n, n<<1) qpow[j] = 0;
            dft(qpow, false);
        }
        return res;
    }
     */
};
int NTT::root = 3;
vector<int> NTT::id(1, 0);

const ll MAX_N = ll(4e+5) + 10;
vm fact(MAX_N, mint(1)), fact_inv(MAX_N, mint(1)), n_inv(MAX_N, mint(1));
void makefact(){
    mint tmp;
    reps(i,2,MAX_N) fact[i] = fact[i-1] * tmp.set_raw(i);
    fact_inv[MAX_N - 1] = fact[MAX_N - 1].inv();
    Rreps(i, MAX_N - 1, 1){
        fact_inv[i] = fact_inv[i + 1] * tmp.set_raw(i + 1);
        n_inv[i + 1] = fact[i] * fact_inv[i + 1];
    }
}
mint nCm(ll n, ll m){
    return fact[n] * fact_inv[n-m] * fact_inv[m];
}
mint nCm_inv(ll n, ll m){
    return fact[n-m] * fact[m] * fact_inv[n];
}

int main(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    makefact();
    cin>>N>>M>>K;
    vm Kcolor_in_i(N - K + 1);
    mint res(0), mpow(1), M_C_K = nCm(M, K);
    rep(i, N - K + 1) Kcolor_in_i[i] = fact_inv[i + 1];
    Kcolor_in_i = NTT::pow(Kcolor_in_i, K);
    rep(i, N - K + 1) Kcolor_in_i[i] *= fact[i + K];
    Rreps(i, N + 1, K){
        res += nCm(N, i) * mpow * Kcolor_in_i[i - K] * M_C_K;
        mpow *= M;
    }
    cout<<res<<endl;
}
0