#983868 (C++17) No.1561 connect x connect

提出ソース

結果

問題	No.1561 connect x connect
ユーザー	👑 Nachia
提出日時	2024-05-28 03:35:13
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	301 ms / 2,000 ms
コード長	11,041 bytes
コンパイル時間	5,173 ms
コンパイル使用メモリ	183,596 KB
実行使用メモリ	6,820 KB
最終ジャッジ日時	2024-12-20 20:38:42
合計ジャッジ時間	9,237 ms
ジャッジサーバーID （参考情報）	judge3 / judge1

このコードへのチャレンジ
（要ログイン）

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	3 ms 6,820 KB
testcase_01	AC	5 ms 6,816 KB
testcase_02	AC	26 ms 6,820 KB
testcase_03	AC	2 ms 6,816 KB
testcase_04	AC	3 ms 6,816 KB
testcase_05	AC	3 ms 6,820 KB
testcase_06	AC	2 ms 6,816 KB
testcase_07	AC	2 ms 6,816 KB
testcase_08	AC	3 ms 6,820 KB
testcase_09	AC	3 ms 6,816 KB
testcase_10	AC	4 ms 6,816 KB
testcase_11	AC	5 ms 6,820 KB
testcase_12	AC	10 ms 6,820 KB
testcase_13	AC	28 ms 6,820 KB
testcase_14	AC	69 ms 6,816 KB
testcase_15	AC	73 ms 6,816 KB
testcase_16	AC	37 ms 6,820 KB
testcase_17	AC	7 ms 6,816 KB
testcase_18	AC	4 ms 6,820 KB
testcase_19	AC	93 ms 6,816 KB
testcase_20	AC	15 ms 6,816 KB
testcase_21	AC	3 ms 6,820 KB
testcase_22	AC	15 ms 6,816 KB
testcase_23	AC	2 ms 6,816 KB
testcase_24	AC	93 ms 6,816 KB
testcase_25	AC	3 ms 6,820 KB
testcase_26	AC	293 ms 6,816 KB
testcase_27	AC	296 ms 6,816 KB
testcase_28	AC	289 ms 6,820 KB
testcase_29	AC	292 ms 6,820 KB
testcase_30	AC	301 ms 6,816 KB
testcase_31	AC	11 ms 6,816 KB
testcase_32	AC	26 ms 6,820 KB
testcase_33	AC	72 ms 6,820 KB
testcase_34	AC	96 ms 6,820 KB
testcase_35	AC	198 ms 6,820 KB
testcase_36	AC	213 ms 6,816 KB
testcase_37	AC	291 ms 6,820 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

raw source code

#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <utility>
#include <atcoder/modint>

// (edited) Nyaan's library

namespace nachia{

// output : denominator of rational gf
template <typename Modint>
std::vector<Modint> BerlekampMassey(const std::vector<Modint> &s){
    const int N = (int)s.size();
    std::vector<Modint> b, c;
    b.reserve(N+1);
    c.reserve(N+1);
    const Modint Zero = Modint(0);
    const Modint One = Modint(1);
    b.push_back(One);
    c.push_back(One);
    Modint y = One;
    for(int ed=1; ed<=N; ed++){
        int l = int(c.size());
        int m = int(b.size());
        Modint x = Zero;
        for(int i=0; i<l; i++) x += c[i] * s[ed-l+i];
        b.push_back(Zero);
        m++;
        if(x.val() == 0) continue;
        Modint freq = x / y;
        if(l < m){
            auto tmp = c;
            c.insert(c.begin(), m-l, Zero);
            for(int i=0; i<m; i++) c[i] -= freq * b[i];
            std::swap(b, tmp); y = x;
        } else {
            for(int i=0; i<m; i++) c[l-m+i] -= freq * b[i];
        }
    }
    std::reverse(c.begin(), c.end());
    return c;
}

} // namespace nachia
#include <atcoder/convolution>
#include <cassert>

namespace nachia{

// ax + by = gcd(a,b)
// return ( x, - )
std::pair<long long, long long> ExtGcd(long long a, long long b){
    long long x = 1, y = 0;
    while(b){
        long long u = a / b;
        std::swap(a-=b*u, b);
        std::swap(x-=y*u, y);
    }
    return std::make_pair(x, a);
}

} // namespace nachia

namespace nachia{

class DynamicModSupplier{
    using u64 = unsigned long long;
    using Int = unsigned int;
private:
    u64 imod;
    Int mod;
    // atcoder library
    u64 reduce2(u64 z) const noexcept {
        // atcoder library
#ifdef _MSC_VER
        u64 x; _umul128(z, im, &x);
#else
        using u128 = unsigned __int128;
        u64 x = (u64)(((u128)(z)*imod) >> 64);
#endif
        return z - x * mod;
    }
    Int reduce(u64 z) const noexcept {
        Int v = reduce2(z);
        if(mod <= v) v += mod;
        return v;
    }
public:
    DynamicModSupplier(unsigned int MOD = 998244353) : mod(MOD) {
        assert(2 <= MOD);
        assert(MOD < (1u << 31));
        imod = (u64)(-1) / mod + 1;
    }
    Int add(Int a, Int b) const { a += b; if(a >= mod){ a -= mod; } return a; }
    Int sub(Int a, Int b) const { a -= b; if(a >= mod){ a += mod; } return a; }
    Int mul(Int a, Int b) const { return reduce((u64)a * b); }
    Int muladd(Int a, Int b, Int c) const { return reduce((u64)a * b + c); }
    Int inv(Int a) const {
        Int v = ExtGcd(a, mod).first;
        return (v < mod) ? v : (v + mod);
    }
    Int pow(Int a, u64 i) const {
        Int r = a, ans = 1;
        while(i){
            if(i & 1) ans = mul(ans, r);
            i /= 2;
            r = mul(r, r);
        }
        return ans;
    }
    Int getMod() const { return mod; }
};

} // namespace nachia

namespace nachia{

template<class FinishType>
struct GarnerMod{
    using Int = unsigned int;
    using IntLong = unsigned long long;
    std::vector<Int> mods;
    std::vector<DynamicModSupplier> dynmods;
    std::vector<std::vector<Int>> table_coeff;
    std::vector<Int> table_coeffinv;

    void precalc(std::vector<Int> new_mods){
        mods = std::move(new_mods);
        dynmods.resize(mods.size());
        for(size_t i=0; i<mods.size(); i++) dynmods[i] = DynamicModSupplier(mods[i]);
        int nmods = mods.size();
        table_coeff.assign(nmods+1, std::vector<Int>(nmods, 1));
        for(int j=0; j<nmods; j++){
            for(int k=0; k<nmods; k++) table_coeff[j+1][k] = table_coeff[j][k];
            for(int k=j+1; k<nmods; k++) table_coeff[j+1][k] = dynmods[k].mul(table_coeff[j+1][k], mods[j] % mods[k]);
        }
        table_coeffinv.resize(nmods);
        for(int i=0; i<nmods; i++) table_coeffinv[i] = dynmods[i].inv(table_coeff[i][i]);
    }

    FinishType calc(const std::vector<Int>& x){
        int nmods = mods.size();
        std::vector<Int> table_const(nmods);
        FinishType res = 0;
        FinishType res_coeff = 1;
        for(int j=0; j<nmods; j++){
            Int t = dynmods[j].mul(dynmods[j].sub(x[j], table_const[j]), table_coeffinv[j]);
            for(int k=j+1; k<nmods; k++){
                table_const[k] = dynmods[k].muladd(t, table_coeff[j][k], table_const[k]);
            }
            res += res_coeff * FinishType(t);
            res_coeff *= mods[j];
        }
        return res;
    }

    std::vector<FinishType> calc(std::vector<std::vector<Int>> x){
        int n = x[0].size(), m = x.size();
        std::vector<FinishType> res(n);
        std::vector<Int> buf(m);
        for(int i=0; i<n; i++){
            for(int j=0; j<m; j++) buf[j] = x[j][i];
            res[i] = calc(buf);
        }
        return res;
    }
};

} // namespace nachia

namespace nachia{

template<class Modint, unsigned int nttmod> std::vector<unsigned int>
    PartConvolution(std::vector<Modint> A, std::vector<Modint> B)
{
    std::vector<atcoder::static_modint<nttmod>> AA(A.size());
    for(std::size_t i=0; i<A.size(); i++) AA[i] = A[i].val();
    std::vector<atcoder::static_modint<nttmod>> BB(B.size());
    for(std::size_t i=0; i<B.size(); i++) BB[i] = B[i].val();
    auto AB = atcoder::convolution(AA, BB);
    std::vector<unsigned int> res(AB.size());
    for(std::size_t i=0; i<AB.size(); i++) res[i] = AB[i].val();
    return res;
}

template<class Modint>
std::vector<Modint> Convolution(std::vector<Modint> A, std::vector<Modint> B){
    auto Q1 = PartConvolution<Modint, 998244353>(A, B);
    auto Q2 = PartConvolution<Modint, 897581057>(A, B);
    auto Q3 = PartConvolution<Modint, 880803841>(A, B);
    GarnerMod<Modint> garner;
    garner.precalc({ 998244353, 897581057, 880803841 });
    return garner.calc({ Q1, Q2, Q3 });
}

} // namespace nachia

namespace nachia{

template<class Modint>
Modint KthTermOfRationalGF(
    std::vector<Modint> denom,
    std::vector<Modint> numer,
    unsigned long long K
){
    assert(denom.size() != 0);
    assert(denom.size() == numer.size());
    assert(denom[0].val() != 0);
    int n = (int)denom.size();
    while(K != 0){
        auto Qn = denom;
        Qn.push_back(Modint(0));
        for(int i=1; i<n; i+=2) Qn[i] = -Qn[i];
        int f = K % 2;
        denom = Convolution(denom, Qn);
        for(int i=0; i<n; i++) denom[i] = denom[i*2];
        denom.resize(n);
        numer = Convolution(numer, Qn);
        for(int i=0; i<n; i++) numer[i] = numer[i*2+f];
        numer.resize(n);
        K /= 2;
    }
    return numer[0] / denom[0];
}

// divisor of fractional representation
//   and first terms
template<class Modint>
Modint KthTermOfLinearRecurrence(
    std::vector<Modint> denom,
    std::vector<Modint> firstTerms,
    unsigned long long K
){
    assert(denom.size() <= firstTerms.size());
    firstTerms.resize(denom.size());
    auto numer = Convolution(firstTerms, denom);
    numer.resize(denom.size());
    return KthTermOfRationalGF(std::move(denom), std::move(numer), K);
}

} // namespace nachia
using Modint = atcoder::modint1000000007;
using i64 = long long;
#define rep(i,n) for(int i=0; i<int(n); i++)
const i64 INF = 1001001001001001001;
using namespace std;

vector<vector<int>> enumBaseState(int N){
    vector<int> st;
    vector<int> arr(N, -1);
    vector<vector<int>> res;
    auto dfs = [&](auto& rec, int p, int nx){
        if(p == N){
            res.push_back(arr);
            return;
        }
        arr[p] = -1;
        rec(rec, p+1, nx);
        if(p != 0 && arr[p-1] != -1){
            arr[p] = arr[p-1];
            rec(rec, p+1, nx);
        }
        else {
            vector<int> stbuf = st;

            arr[p] = nx;
            st.push_back(nx);
            rec(rec, p+1, nx+1);
            st.pop_back();

            for(int x=0; x<int(stbuf.size()); x++){
                st = vector(stbuf.begin(), stbuf.begin() + (x+1));
                arr[p] = st.back();
                rec(rec, p+1, nx);
            }
            
            st = stbuf;
        }
    };
    dfs(dfs, 0, 0);
    return res;
}

void refine(vector<int>& Q){
    vector<int> occ;
    for(int& q : Q) if(q != -1){
        int res = -1;
        rep(i,occ.size()) if(occ[i] == q) res = i;
        if(res == -1){ res = int(occ.size()); occ.push_back(q); }
        q = res;
    }
}

vector<vector<int>> enumNextState(vector<int> cur, int at){
    int n = int(cur.size());
    int q = cur[at];
    auto t0 = cur; t0[at] = -1;
    auto t1 = cur;
    vector<vector<int>> res;
    if(q == -1){
        t1[at] = 1001001001;
        if(at != 0 && t1[at-1] != -1) t1[at] = t1[at-1];
    } else {
        int qocc = 0;
        rep(i,n) if(cur[i] == q) qocc++;
        if(qocc == 1) t0 = vector<int>(0);
        int p = -1;
        if(at != 0 && cur[at-1] != -1) p = cur[at-1];
        if(p != -1) rep(i,n) if(t1[i] == p) t1[i] = q;
    }
    if(!t0.empty()){
        refine(t0);
        res.push_back(move(t0));
    }
    if(!t1.empty()){
        refine(t1);
        res.push_back(move(t1));
    }
    return res;
}

int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    int N; cin >> N;
    i64 L; cin >> L;
    auto baseState = enumBaseState(N);
    sort(baseState.begin(), baseState.end());
    vector<vector<vector<int>>> stateList(N+1);
    vector<vector<pair<int,int>>> transList(N);
    auto lbi = [&](const vector<vector<int>>& l, const vector<int>& tg) -> int {
        return int(lower_bound(l.begin(), l.end(), tg) - l.begin());
    };
    stateList[0] = baseState;
    rep(i,N){
        auto& dest = stateList[i+1];
        for(auto q : stateList[i]) for(auto r : enumNextState(q, i)){
            dest.push_back(r);
        }
        sort(dest.begin(), dest.end());
        dest.erase(unique(dest.begin(), dest.end()), dest.end());
        rep(j,stateList[i].size()){
            for(auto r : enumNextState(stateList[i][j], i)){
                int k = lbi(dest, r);
                transList[i].push_back({ j, k });
            }
        }
    }
    
    vector<int> sz(N+1);
    rep(i,N+1) sz[i] = int(stateList[i].size());

    rep(i,N){
        vector<int> F(N, -1);
        F[i] = 0;
        int j = lbi(stateList[i], F);
        transList[i].push_back({ j, sz[i+1] });
        transList[i].push_back({ sz[i], sz[i+1] });
    }
    rep(i,N+1) sz[i]++;

    vector<Modint> firstTerms;
    vector<Modint> dp(sz[0]);
    dp.back() = 1;
    dp[0] = 1;
    firstTerms.push_back(1);
    //int Z = sz[0] * 2 + 5;
    int Z = 1143 * 2 + 5; // according to the editorial https://yukicoder.me/problems/no/1561/editorial
    rep(l,Z){
        rep(y,N){
            vector<Modint> nx(sz[y+1]);
            for(auto [u,v] : transList[y]) nx[v] += dp[u];
            swap(dp, nx);
        }
        firstTerms.push_back(dp.back());
    }
    auto bm = nachia::BerlekampMassey(firstTerms);
    firstTerms.resize(bm.size());
    Modint ans = nachia::KthTermOfLinearRecurrence(bm, firstTerms, L+1) - 1;
    cout << ans.val() << endl;
    return 0;
}