Submission #404889

#	Time	Username	Problem	Language	Result	Execution time	Memory
404889		Forested	Boat (APIO16_boat)	C++17	9 / 100	707 ms	13184 KiB

boat

// Template
#include <iostream>
#include <vector>
#include <algorithm>
#include <numeric>
#include <iomanip>
#include <tuple>
#include <utility>
#include <queue>
#include <set>
#include <map>
#include <array>
#include <cassert>
#include <cmath>
#define rep_override(x, y, z, name, ...) name
#define rep2(i, n) for (int i = 0; i < (int)(n); ++i)
#define rep3(i, l, r) for (int i = (int)(l); i < (int)(r); ++i)
#define rep(...) rep_override(__VA_ARGS__, rep3, rep2)(__VA_ARGS__)
#define all(x) (x).begin(), (x).end()
using namespace std;
using ll = long long;
constexpr int inf = 1001001001;
constexpr ll infll = 3003003003003003003LL;
template <typename T>
inline bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T> 
inline bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &vec) {
    for (T &element : vec) is >> element;
    return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &vec) {
    for (int i = 0, vec_len = (int)vec.size(); i < vec_len; ++i) {
        os << vec[i] << (i + 1 == vec_len ? "" : " ");
    }
    return os;
}
struct IOSET {
    IOSET() {
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(10);
    }
} ioset;

// Mod-Int
#include <iostream>

template <unsigned int mod>
struct ModInt {
    static_assert(mod >= 1 && mod < (1u << 31));
    
    unsigned int val;
    
    ModInt() : val(0) {}
    
    ModInt(long long x) : val(x < 0 ? x % mod + mod : (unsigned long long)x % mod) {}
    
    ModInt<mod> &operator+=(const ModInt<mod> &x) {
        val += x.val;
        if (val >= mod) val -= mod;
        return *this;
    }
    
    ModInt<mod> &operator-=(const ModInt<mod> &x) {
        if (val < x.val) val += mod;
        val -= x.val;
        return *this;
    }
    
    ModInt<mod> &operator*=(const ModInt<mod> &x) {
        unsigned long long s = (unsigned long long)val * x.val;
        val = (unsigned int)(s % mod);
        return *this;
    }
    
    ModInt<mod> operator+() const {
        return *this;
    }
    
    ModInt<mod> operator-() const {
        return ModInt<mod>(0u) - *this;
    }
    
    friend ModInt<mod> operator+(const ModInt<mod> &x, const ModInt<mod> &y) {
        return ModInt<mod>(x) += y;
    }
    
    friend ModInt<mod> operator-(const ModInt<mod> &x, const ModInt<mod> &y) {
        return ModInt<mod>(x) -= y;
    }
    
    friend ModInt<mod> operator*(const ModInt<mod> &x, const ModInt<mod> &y) {
        return ModInt<mod>(x) *= y;
    }
    
    friend std::istream &operator>>(std::istream &is, ModInt<mod> &x) {
        is >> x.val;
        // x.value %= mod;
        return is;
    }
    
    friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &x) {
        os << x.val;
        return os;
    }
    
    ModInt<mod> pow(unsigned long long x) const {
        ModInt<mod> res(1), s(*this);
        while (x) {
            if (x & 1) res *= s;
            s *= s;
            x >>= 1;
        }
        return res;
    }
    
    // --- prime number ---
    ModInt<mod> &operator/=(const ModInt<mod> &x) {
        *this *= x.pow(mod - 2);
        return *this;
    }
    
    friend ModInt<mod> operator/(const ModInt<mod> &x, const ModInt<mod> &y) {
        return ModInt<mod>(x) /= y;
    }
};

// Main
int main() {
    constexpr unsigned mod = 1000000007;
    using Mint = ModInt<mod>;
    
    int n;
    cin >> n;
    vector<int> a(n), b(n);
    rep(i, n) {
        cin >> a[i] >> b[i];
        ++b[i];
    }
    
    vector<int> ps;
    ps.reserve(2 * n);
    rep(i, n) {
        ps.push_back(a[i]);
        ps.push_back(b[i]);
    }
    sort(all(ps));
    ps.erase(unique(all(ps)), ps.end());
    rep(i, n) {
        a[i] = lower_bound(all(ps), a[i]) - ps.begin();
        b[i] = lower_bound(all(ps), b[i]) - ps.begin();
    }
    
    int k = ps.size() - 1;
    
    vector<vector<Mint>> comb(k, vector<Mint>(n + 1));
    rep(i, k) {
        int d = ps[i + 1] - ps[i];
        Mint p(1);
        comb[i][0] = Mint(1);
        rep(j, 1, min(d, n) + 1) {
            p *= Mint(d - j + 1);
            p /= Mint(j);
            comb[i][j] = p;
        }
    }
    vector<vector<Mint>> comb1(k, vector<Mint>(n + 1));
    rep(i, k) {
        int d = ps[i + 1] - ps[i] - 1;
        Mint p(1);
        comb1[i][0] = Mint(1);
        rep(j, 1, min(d, n) + 1) {
            p *= Mint(d - j + 1);
            p /= Mint(j);
            comb1[i][j] = p;
        }
    }
    vector<vector<Mint>> comb2(k, vector<Mint>(n + 1));
    rep(i, k) {
        int d = ps[i + 1] - ps[i] - 2;
        if (d == -1) continue;
        Mint p(1);
        comb2[i][0] = Mint(1);
        rep(j, 1, min(d, n) + 1) {
            p *= Mint(d - j + 1);
            p /= Mint(j);
            comb2[i][j] = p;
        }
    }
    vector<vector<Mint>> combn(n + 1, vector<Mint>(n + 1));
    combn[0][0] = Mint(1);
    rep(i, 1, n + 1) rep(j, i + 1) {
        combn[i][j] += combn[i - 1][j];
        if (j != 0) combn[i][j] += combn[i - 1][j - 1];
    }
    vector<vector<Mint>> _sum(k, vector<Mint>(n + 1));
    rep(i, k) {
        int d = ps[i + 1] - ps[i];
        _sum[i][1] = Mint(d);
        rep(j, 2, min(d, n) + 1) {
            rep(l, 2, j + 1) {
                _sum[i][j] += comb[i][l] * combn[j][l] - Mint(2) * comb1[i][l] * combn[j][l] + comb2[i][l] * combn[j][l];
            }
        }
    }
    
    vector<vector<Mint>> dp(n + 1, vector<Mint>(k + 1)), sum(n + 1, vector<Mint>(k + 1));
    dp[0][0] = Mint(1);
    sum[0] = vector<Mint>(k + 1, Mint(1));
    rep(i, n) {
        dp[i + 1] = dp[i];
        sum[i + 1][0] = dp[i + 1][0];
        rep(j, 1, k + 1) {
            int d = ps[j] - ps[j - 1];
            int cnt = 0;
            for (int l = i; l >= 0; --l) {
                if (b[l] <= j - 1 || a[l] >= j) {
                    if (l == i) break;
                    continue;
                }
                if (++cnt > d) break;
                dp[i + 1][j] += _sum[j - 1][cnt] * sum[l][j - 1];
            }
            sum[i + 1][j] = sum[i + 1][j - 1] + dp[i + 1][j];
        }
    }
    
    cout << sum[n][k] - Mint(1) << '\n';
}

• Subtask 1: 9 / 9
• Subtask 2: 0 / 22
• Subtask 3: 0 / 27
• Subtask 4: 0 / 42