結果

問題 No.1001 注文の多い順列
コンテスト
ユーザー kcvlex
提出日時 2020-02-28 23:13:39
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 126 ms / 2,000 ms
コード長 5,802 bytes
コンパイル時間 1,889 ms
コンパイル使用メモリ 174,252 KB
実行使用メモリ 50,944 KB
最終ジャッジ日時 2024-10-13 19:05:22
合計ジャッジ時間 3,621 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 31
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 # 

// #define DEBUGGING
#include <bits/stdc++.h>
#define endl '\n'
#define ALL(v) std::begin(v), std::end(v)
#define ALLR(v) std::rbegin(v), std::rend(v)
using ll = std::int64_t;
using ull = std::uint64_t;
using pll = std::pair<ll, ll>;
using tll = std::tuple<ll, ll, ll>;
template <typename T> using vec = std::vector<T>;
template <typename T> using vvec = vec<vec<T>>;
template <typename T> const T& var_min(const T &t) { return t; }
template <typename T> const T& var_max(const T &t) { return t; }
template <typename T, typename... Tail> const T& var_min(const T &t, const Tail&... tail) { return std::min(t, var_min(tail...)); }
template <typename T, typename... Tail> const T& var_max(const T &t, const Tail&... tail) { return std::max(t, var_max(tail...)); }
template <typename T, typename... Tail> void chmin(T &t, const Tail&... tail) { t = var_min(t, tail...); }
template <typename T, typename... Tail> void chmax(T &t, const Tail&... tail) { t = var_max(t, tail...); }
template <typename T> const T& clamp(const T &t, const T &low, const T &high) { return std::max(low, std::min(high, t)); }
template <typename T> void chclamp(T &t, const T &low, const T &high) { return t = clamp(t, low, high); }
namespace init__ { struct InitIO { InitIO() { std::cin.tie(nullptr); std::ios_base::sync_with_stdio(false); std::cout << std::fixed << std::setprecision(30); } } init_io; }
#define mv_rec make_v(init, tail...)
template <typename T> T make_v(T init) { return init; }
template <typename T, typename... Tail> auto make_v(T init, size_t s, Tail... tail) { return vec<decltype(mv_rec)>(s, mv_rec); }
#undef mv_rec

#ifdef DEBUGGING
#else
#define DEBUG(...) 0
#define DEBUG_SEPARATOR_LINE 0
#endif

namespace math {

template <typename T>
constexpr T pow(const T &n, ll k) {
    T ret = n.mul_id_ele();
    T cur = n;
    while (k) {
        if (k & 1) ret *= cur;
        cur *= cur;
        k /= 2;
    }
    return ret;
}

}

namespace math {

template <ll Mod>
struct Modint {

    constexpr Modint(ll x) : x(x % Mod) { }
    
    constexpr Modint() : Modint(0) { }
    
    constexpr Modint<Mod> add_id_ele() const { 
        return Modint<Mod>(0); 
    }
    
    constexpr Modint<Mod> mul_id_ele() const {
        return Modint<Mod>(1); 
    }
    
    constexpr ll& value() { 
        return x; 
    }
    
    constexpr ll value() const {
        return x; 
    }

    constexpr Modint& operator +=(const Modint &oth) {
        x += oth.value();
        if (Mod <= x) x -= Mod;
        return *this;
    }

    constexpr Modint& operator -=(const Modint &oth) {
        x += Mod - oth.value();
        if (Mod <= x) x -= Mod;
        return *this;
    }

    constexpr Modint& operator *=(const Modint &oth) {
        x *= oth.value();
        x %= Mod;
        return *this;
    }

    constexpr Modint& operator /=(const Modint &oth) {
        x *= oth.inv();
        x %= Mod;
        return *this;
    }

    constexpr Modint operator +(const Modint &oth) const {
        return Modint(x) += oth;
    }

    constexpr Modint operator -(const Modint &oth) const {
        return Modint(x) -= oth;
    }

    constexpr Modint operator *(const Modint &oth) const {
        return Modint(x) *= oth;
    }

    constexpr Modint operator /(const Modint &oth) const {
        return Modint(x) /= oth;
    }

    constexpr Modint operator -() const {
        return Modint((x != 0) * (Mod - x)); 
    }

    template <typename T>
    constexpr typename std::enable_if<std::is_integral<T>::value, const Modint&>::type
    operator =(T t) {
        (*this) = Modint(std::forward<T>(t)); 
        return *this;
    }

    constexpr Modint inv() const {
        return ::math::pow(*this, Mod - 2);
    }

    constexpr ll mod() const {
        return Mod;
    }

private:
    ll x;
};

}

namespace math {

template <ll Mod>
class Combination {
    using mint = Modint<Mod>;

    ssize_t maxv;
    vec<mint> factv, ifactv;

public:
    Combination(ssize_t maxv) : maxv(maxv), factv(maxv + 1), ifactv(maxv + 1) {
        factv[0] = mint(1);
        for (ll i = 1; i <= maxv; i++) factv[i] = factv[i - 1] * i;
        ifactv.back() = factv.back().inv();
        for (ll i = maxv - 1; 0 <= i; i--) ifactv[i] = ifactv[i + 1] * (i + 1);
    }

    mint fact(ll n) const {
        return factv[n]; 
    }

    mint ifact(ll n) const {
        return ifactv[n];
    }

    mint perm(ll n, ll k) const {
        return factv[n] * ifactv[n - k];
    }

    mint comb(ll n, ll k) const {
        return perm(n, k) * ifactv[k];
    }
};

}

constexpr ll mod = 1e9 + 7;
using mint = math::Modint<mod>;
using namespace std;
const size_t SIZE = 3010;
mint dp[2 * SIZE][2 * SIZE];  // not used down arrow 

int main() {
    math::Combination<mod> C(SIZE * 10);
    ll n;
    cin >> n;
    vec<pll> tx(n);
    for (auto &&e : tx) {
        ll t, x;
        cin >> t >> x;
        e = pll(t, x);
    }

    vec<pll> cnts(n + 1);
    for (ll i = 0; i < n; i++) {
        ll t, x;
        tie(t, x) = tx[i];
        x--;
        (t == 0 ? cnts[x].first : cnts[x].second)++;
    }

    dp[0][0] = 1;
    ll up_sum = 0, down_sum = 0;
    for (ll i = 0; i < n; i++) {
        ll a, b;
        tie(a, b) = cnts[i];
        DEBUG(a, b);
        for (ll j = 0; j <= down_sum; j++) {
            ll rest = (i + 1) - up_sum - (down_sum - j);
            DEBUG(rest);
            if (j + b && a <= rest - 1) {
                mint c(j + b);
                c *= C.perm(rest - 1, a);
                DEBUG(j + b, rest, C.comb(rest - 1, a));
                dp[i + 1][j + b - 1] += dp[i][j] * c;
            }
            if (a <= rest) {
                dp[i + 1][j + b] += dp[i][j] * C.perm(rest, a);
            }
        }
        up_sum += a;
        down_sum += b;
    }

    cout << dp[n][0].value() << endl;
    return 0;
}
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