#677473 (C++17) No.1621 Sequence Inversions

提出ソース
結果

問題	No.1621 Sequence Inversions
ユーザー	yuto1115
提出日時	2021-07-11 12:58:44
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	380 ms / 3,000 ms
コード長	15,609 bytes
コンパイル時間	2,679 ms
コンパイル使用メモリ	219,872 KB
実行使用メモリ	243,316 KB
最終ジャッジ日時	2024-07-17 15:53:40
合計ジャッジ時間	8,317 ms
ジャッジサーバーID （参考情報）	judge1 / judge3
このコードへのチャレンジ
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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	2 ms 5,248 KB
testcase_01	AC	2 ms 5,376 KB
testcase_02	AC	5 ms 5,632 KB
testcase_03	AC	10 ms 10,496 KB
testcase_04	AC	230 ms 194,944 KB
testcase_05	AC	2 ms 5,376 KB
testcase_06	AC	5 ms 5,376 KB
testcase_07	AC	15 ms 12,416 KB
testcase_08	AC	293 ms 243,200 KB
testcase_09	AC	289 ms 243,200 KB
testcase_10	AC	312 ms 243,220 KB
testcase_11	AC	305 ms 243,200 KB
testcase_12	AC	320 ms 243,296 KB
testcase_13	AC	328 ms 243,300 KB
testcase_14	AC	302 ms 243,200 KB
testcase_15	AC	303 ms 243,072 KB
testcase_16	AC	254 ms 180,736 KB
testcase_17	AC	369 ms 234,752 KB
testcase_18	AC	243 ms 174,080 KB
testcase_19	AC	7 ms 6,528 KB
testcase_20	AC	96 ms 62,336 KB
testcase_21	AC	376 ms 243,308 KB
testcase_22	AC	312 ms 243,200 KB
testcase_23	AC	380 ms 243,316 KB
testcase_24	AC	3 ms 5,376 KB
testcase_25	AC	3 ms 5,376 KB
testcase_26	AC	2 ms 5,376 KB
testcase_27	AC	2 ms 5,376 KB
testcase_28	AC	3 ms 5,376 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<bits/stdc++.h>
#define overload4(_1, _2, _3, _4, name, ...) name
#define rep1(i, n) for (ll i = 0; i < ll(n); ++i)
#define rep2(i, s, n) for (ll i = ll(s); i < ll(n); ++i)
#define rep3(i, s, n, d) for(ll i = ll(s); i < ll(n); i+=d)
#define rep(...) overload4(__VA_ARGS__,rep3,rep2,rep1)(__VA_ARGS__)
#define rrep1(i, n) for (ll i = ll(n)-1; i >= 0; i--)
#define rrep2(i, n, t) for (ll i = ll(n)-1; i >= (ll)t; i--)
#define rrep3(i, n, t, d) for (ll i = ll(n)-1; i >= (ll)t; i-=d)
#define rrep(...) overload4(__VA_ARGS__,rrep3,rrep2,rrep1)(__VA_ARGS__)
#define all(a) a.begin(),a.end()
#define rall(a) a.rbegin(),a.rend()
#define SUM(a) accumulate(all(a),0LL)
#define MIN(a) *min_element(all(a))
#define MAX(a) *max_element(all(a))
#define popcount(x) __builtin_popcountll(x)
#define pb push_back
#define eb emplace_back
#ifdef __LOCAL
#define debug(...) { cout << #__VA_ARGS__; cout << ": "; print(__VA_ARGS__); cout << flush; }
#else
#define debug(...) void(0)
#endif
#define INT(...) int __VA_ARGS__;scan(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;scan(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;scan(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;scan(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;scan(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;scan(__VA_ARGS__)
using namespace std;
using ll = long long;
using ld = long double;
using P = pair<int, int>;
using LP = pair<ll, ll>;
using vi = vector<int>;
using vvi = vector<vi>;
using vl = vector<ll>;
using vvl = vector<vl>;
using vd = vector<double>;
using vvd = vector<vd>;
using vs = vector<string>;
using vc = vector<char>;
using vvc = vector<vc>;
using vb = vector<bool>;
using vvb = vector<vb>;
using vp = vector<P>;
using vvp = vector<vp>;

template<class S, class T>
istream &operator>>(istream &is, pair<S, T> &p) { return is >> p.first >> p.second; }

template<class S, class T>
ostream &operator<<(ostream &os, const pair<S, T> &p) { return os << '{' << p.first << ", " << p.second << '}'; }

template<class S, class T, class U>
istream &operator>>(istream &is, tuple<S, T, U> &t) { return is >> get<0>(t) >> get<1>(t) >> get<2>(t); }

template<class S, class T, class U>
ostream &operator<<(ostream &os, const tuple<S, T, U> &t) {
    return os << '{' << get<0>(t) << ", " << get<1>(t) << ", " << get<2>(t) << '}';
}

template<class T>
istream &operator>>(istream &is, vector<T> &v) {
    for (T &t:v) { is >> t; }
    return is;
}

template<class T>
ostream &operator<<(ostream &os, const vector<T> &v) {
    os << '[';
    rep(i, v.size())os << v[i] << (i == int(v.size() - 1) ? "" : ", ");
    return os << ']';
}

template<class T>
void vecout(const vector<T> &v, char div = '\n') {
    rep(i, v.size()) cout << v[i] << (i == int(v.size() - 1) ? '\n' : div);
}

template<class T>
bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}

template<class T>
bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

void scan() {}

template<class Head, class... Tail>
void scan(Head &head, Tail &... tail) {
    cin >> head;
    scan(tail...);
}

template<class T>
void print(const T &t) { cout << t << '\n'; }

template<class Head, class... Tail>
void print(const Head &head, const Tail &... tail) {
    cout << head << ' ';
    print(tail...);
}

template<class... T>
void fin(const T &... a) {
    print(a...);
    exit(0);
}

struct Init_io {
    Init_io() {
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
        cout.tie(nullptr);
        cout << boolalpha << fixed << setprecision(15);
        cerr << boolalpha << fixed << setprecision(15);
    }
} init_io;

const string yes[] = {"no", "yes"};
const string Yes[] = {"No", "Yes"};
const string YES[] = {"NO", "YES"};
const int inf = 1001001001;
const ll linf = 1001001001001001001;

template<class T, class S>
vector<T> cumsum(const vector<S> &v, bool shift_one = true) {
    int n = v.size();
    vector<T> res;
    if (shift_one) {
        res.resize(n + 1);
        rep(i, n) res[i + 1] = res[i] + v[i];
    } else {
        res.resize(n);
        if (n) {
            res[0] = v[0];
            rep(i, 1, n) res[i] = res[i - 1] + v[i];
        }
    }
    return res;
}

vvi graph(int n, int m, bool directed = false, int origin = 1) {
    vvi G(n);
    rep(_, m) {
        INT(u, v);
        u -= origin, v -= origin;
        G[u].pb(v);
        if (!directed) G[v].pb(u);
    }
    return G;
}

template<class T>
vector<vector<pair<int, T>>> weighted_graph(int n, int m, bool directed = false, int origin = 1) {
    vector<vector<pair<int, T>>> G(n);
    rep(_, m) {
        int u, v;
        T w;
        scan(u, v, w);
        u -= origin, v -= origin;
        G[u].eb(v, w);
        if (!directed) G[v].eb(u, w);
    }
    return G;
}

template<class T>
void resemble(vector<T> &v) {}

template<class T, class... Tail>
void resemble(vector<T> &v, vector<T> &head, Tail &...tail) {
    for (T &e : head) v.pb(e);
    resemble(v, tail...);
}

template<class T>
void renumber(vector<T> &v) {}

template<class T, class... Tail>
void renumber(vector<T> &v, vector<T> &head, Tail &...tail) {
    for (T &e : head) e = lower_bound(all(v), e) - v.begin();
    renumber(v, tail...);
}

template<class T, class... Tail>
vector<T> zip(vector<T> &head, Tail &... tail) {
    vector<T> v;
    resemble(v, head, tail...);
    sort(all(v));
    v.erase(unique(all(v)), v.end());
    renumber(v, head, tail...);
    return v;
}

template<int mod>
class modint {
    ll x;
public:
    constexpr modint(ll x = 0) : x((x % mod + mod) % mod) {}
    
    static constexpr int get_mod() { return mod; }
    
    constexpr int val() const { return x; }
    
    constexpr modint operator-() const { return modint(-x); }
    
    constexpr modint &operator+=(const modint &a) {
        if ((x += a.val()) >= mod) x -= mod;
        return *this;
    }
    
    constexpr modint &operator++() { return *this += 1; }
    
    constexpr modint &operator-=(const modint &a) {
        if ((x += mod - a.val()) >= mod) x -= mod;
        return *this;
    }
    
    constexpr modint &operator--() { return *this -= 1; }
    
    constexpr modint &operator*=(const modint &a) {
        (x *= a.val()) %= mod;
        return *this;
    }
    
    constexpr modint operator+(const modint &a) const {
        modint res(*this);
        return res += a;
    }
    
    constexpr modint operator-(const modint &a) const {
        modint res(*this);
        return res -= a;
    }
    
    constexpr modint operator*(const modint &a) const {
        modint res(*this);
        return res *= a;
    }
    
    constexpr modint pow(ll t) const {
        modint res = 1, a(*this);
        while (t > 0) {
            if (t & 1) res *= a;
            t >>= 1;
            a *= a;
        }
        return res;
    }
    
    template<int m>
    friend istream &operator>>(istream &, modint<m> &);
    
    // for prime mod
    constexpr modint inv() const { return pow(mod - 2); }
    
    constexpr modint &operator/=(const modint &a) { return *this *= a.inv(); }
    
    constexpr modint operator/(const modint &a) const {
        modint res(*this);
        return res /= a;
    }
};

using modint998244353 = modint<998244353>;
using modint1000000007 = modint<1000000007>;

template<int mod>
istream &operator>>(istream &is, modint<mod> &a) { return is >> a.x; }

template<int mod>
constexpr ostream &operator<<(ostream &os, const modint<mod> &a) { return os << a.val(); }

template<int mod>
constexpr bool operator==(const modint<mod> &a, const modint<mod> &b) { return a.val() == b.val(); }

template<int mod>
constexpr bool operator!=(const modint<mod> &a, const modint<mod> &b) { return a.val() != b.val(); }

template<int mod>
constexpr modint<mod> &operator++(modint<mod> &a) { return a += 1; }

template<int mod>
constexpr modint<mod> &operator--(modint<mod> &a) { return a -= 1; }

using mint = modint998244353;

using vm = vector<mint>;
using vvm = vector<vm>;

class NTT {
    int pr;
    
    constexpr ll pow_mod(ll x, ll n, int m) {
        if (m == 1) return 0;
        ll res = 1;
        ll now = x % m;
        while (n > 0) {
            if (n & 1) res = (res * now) % m;
            now = (now * now) % m;
            n >>= 1;
        }
        return res;
    }
    
    constexpr int primitive_root(int mod) {
        if (mod == 2) return 1;
        if (mod == 167772161) return 3;
        if (mod == 469762049) return 3;
        if (mod == 754974721) return 11;
        if (mod == 998244353) return 3;
        int divs[20] = {};
        divs[0] = 2;
        int cnt = 1;
        int x = (mod - 1) / 2;
        while (x % 2 == 0) x /= 2;
        for (int i = 3; (ll) i * i <= x; i += 2) {
            if (x % i == 0) {
                divs[cnt++] = i;
                while (x % i == 0) {
                    x /= i;
                }
            }
        }
        if (x > 1) divs[cnt++] = x;
        for (int g = 2;; g++) {
            bool ok = true;
            for (int i = 0; i < cnt; i++) {
                if (pow_mod(g, (mod - 1) / divs[i], mod) == 1) {
                    ok = false;
                    break;
                }
            }
            if (ok) return g;
        }
    }

public:
    bool first = true;
    mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
    mint sum_ie[30];  // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
    
    void init(int mod) {
        first = false;
        pr = primitive_root(mod);
        mint es[30], ies[30];  // es[i]^(2^(2+i)) == 1
        int cnt2 = __builtin_ctz(mint::get_mod() - 1);
        mint e = mint(pr).pow((mint::get_mod() - 1) >> cnt2), ie = e.inv();
        for (int i = cnt2; i >= 2; i--) {
            // e^(2^i) == 1
            es[i - 2] = e;
            ies[i - 2] = ie;
            e *= e;
            ie *= ie;
        }
        mint now = 1;
        for (int i = 0; i <= cnt2 - 2; i++) {
            sum_e[i] = es[i] * now;
            now *= ies[i];
        }
        now = 1;
        for (int i = 0; i <= cnt2 - 2; i++) {
            sum_ie[i] = ies[i] * now;
            now *= es[i];
        }
    }
    
    void operator()(vector<mint> &a, bool inverse = false) {
        int n = a.size();
        int h = __builtin_ctz(n);
        if (inverse) {
            rrep(ph, h + 1, 1) {
                int w = 1 << (ph - 1), p = 1 << (h - ph);
                mint now = 1;
                rep(s, w) {
                    int offset = s << (h - ph + 1);
                    rep(i, p) {
                        auto l = a[i + offset];
                        auto r = a[i + offset + p];
                        a[i + offset] = l + r;
                        a[i + offset + p] = (l - r) * now;
                    }
                    now *= sum_ie[__builtin_ctz(~(unsigned int) (s))];
                }
            }
        } else {
            rep(ph, 1, h + 1) {
                int w = 1 << (ph - 1), p = 1 << (h - ph);
                mint now = 1;
                rep(s, w) {
                    int offset = s << (h - ph + 1);
                    rep(i, p) {
                        auto l = a[i + offset];
                        auto r = a[i + offset + p] * now;
                        a[i + offset] = l + r;
                        a[i + offset + p] = l - r;
                    }
                    now *= sum_e[__builtin_ctz(~(unsigned int) (s))];
                }
            }
        }
    }
} ntt;

vm convolution(const vm &a, const vm &b) {
    if (a.empty()) return {};
    if (b.empty()) return {};
    int s = a.size() + b.size() - 1;
    if (min(a.size(), b.size()) <= 50) {
        vm res(s);
        if (a.size() >= b.size()) {
            rep(i, a.size()) rep(j, b.size()) res[i + j] += a[i] * b[j];
        } else {
            rep(j, b.size()) rep(i, a.size()) res[i + j] += a[i] * b[j];
        }
        return res;
    }
    int t = 1;
    while (t < s) t *= 2;
    vm A(t), B(t);
    rep(i, a.size()) A[i] = a[i];
    rep(i, b.size()) B[i] = b[i];
    if (ntt.first) ntt.init(mint::get_mod());
    ntt(A);
    ntt(B);
    rep(i, t) A[i] *= B[i];
    ntt(A, true);
    vm res(s);
    mint it = mint(t).inv();
    rep(i, s) res[i] = A[i] * it;
    return res;
}

template<class T>
class polynomial : public vector<T> {
public:
    using vector<T>::vector;
    
    constexpr T eval(T x) const {
        T res = 0;
        T now = 1;
        rep(i, this->size()) {
            res += (*this)[i] * now;
            now *= x;
        }
        return res;
    }
    
    // return f'(x)
    constexpr polynomial differ() const {
        vector<T> res;
        rep2(i, 1, this->size()) res.pb((*this)[i] * i);
        return polynomial(all(res));
    }
    
    // return ∫ f(x)dx
    constexpr polynomial integral() const {
        int n = this->size();
        if (n == 0) return vector<T>();
        vector<T> res = {0};
        rep(i, n) res.pb((*this)[i] / (i + 1));
        return polynomial(all(res));
    };
    
    constexpr polynomial operator+(const polynomial &a) const {
        vector<T> res(max(this->size(), a.size()));
        rep(i, this->size()) res[i] += (*this)[i];
        rep(i, a.size()) res[i] += a[i];
        return polynomial(all(res));
    }
    
    constexpr polynomial operator-(const polynomial &a) const {
        vector<T> res(max(this->size(), a.size()));
        rep(i, this->size()) res[i] += (*this)[i];
        rep(i, a.size()) res[i] -= a[i];
        return polynomial(all(res));
    }
    
    constexpr polynomial operator*(const polynomial &a) const {
        vector<T> res = convolution(*this, a);
        return polynomial(all(res));
    }
    
    constexpr polynomial operator*(T k) const {
        polynomial res(*this);
        rep(i, res.size()) res[i] *= k;
        return res;
    }
    
    constexpr polynomial &operator+=(const polynomial &a) {
        return *this = *this + a;
    }
    
    constexpr polynomial &operator-=(const polynomial &a) {
        return *this = *this - a;
    }
    
    constexpr polynomial &operator*=(const polynomial &a) {
        return *this = *this * a;
    }
    
    // P *= (ax + b)
    constexpr void multiply(T a = 0, T b = 1) {
        int n = this->size();
        this->push_back(T(0));
        rrep(i, n) {
            (*this)[i + 1] += (*this)[i] * a;
            (*this)[i] *= b;
        }
    }
    
    // P /= (ax + b)
    constexpr void divide(T a = 0, T b = 1) {
        int n = this->size();
        assert(n >= 2);
        assert(a != 0 or b != 0);
        if (b == T(0)) {
            assert((*this)[0] == T(0));
            T inv = T(1) / a;
            rep(i, n - 1) (*this)[i] = (*this)[i + 1] * inv;
            this->back() = T(0);
        } else {
            T inv = T(1) / b;
            rep(i, n - 1) {
                (*this)[i] *= inv;
                (*this)[i + 1] -= (*this)[i] * a;
            }
            assert(this->back() == T(0));
        }
    }
};

using poly = polynomial<mint>;

mint dp[101][101][10001];

int main() {
    INT(n, k);
    vi a(n);
    cin >> a;
    int sz = zip(a).size();
    vi cnt(sz);
    rep(i, n) cnt[a[i]]++;
    dp[0][0][0] = 1;
    dp[0][1][1] = -1;
    rep(i, n) rep(j, n) rep(s, i * j + 1) {
                dp[i + 1][j][s + j] += dp[i][j][s];
                dp[i][j + 1][s + 1] += dp[i][j][s];
            }
    poly ans(k + 1);
    ans[0] = 1;
    int sum = 0;
    rep(i, sz) {
        poly now(k + 1);
        rep(j, sum + 1) rep(l, k + 1) now[l] += dp[cnt[i]][j][l];
        ans *= now;
        ans.resize(k + 1);
        sum += cnt[i];
    }
    print(ans[k]);
}
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結果

テストケース

ソースコード
