oj.uz

Submission #720102

# Submission time Handle Problem Language Result Execution time Memory
720102 2023-04-07T12:11:22 Z Forested Boat (APIO16_boat) C++17
58 / 100
 2000 ms 4304 KB 
#ifndef LOCAL
#define FAST_IO
#endif

// ============
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER(i, n) for (i32 i = (i32)(n) - 1; i >= 0; --i)
#define ALL(x) begin(x), end(x)

using namespace std;

using u32 = unsigned int;
using u64 = unsigned long long;
using i32 = signed int;
using i64 = signed long long;
using f64 = double;
using f80 = long double;

template <typename T>
using Vec = vector<T>;

template <typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}

template <typename T>
Vec<tuple<i32, i32, T>> runlength(const Vec<T> &a) {
    if (a.empty()) {
        return Vec<tuple<i32, i32, T>>();
    }
    Vec<tuple<i32, i32, T>> ret;
    i32 prv = 0;
    REP(i, 1, a.size()) {
        if (a[i - 1] != a[i]) {
            ret.emplace_back(prv, i, a[i - 1]);
            prv = i;
        }
    }
    ret.emplace_back(prv, (i32)a.size(), a.back());
    return ret;
}

#ifdef INT128

using u128 = __uint128_t;
using i128 = __int128_t;

istream &operator>>(istream &is, i128 &x) {
    i64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, i128 x) {
    os << (i64)x;
    return os;
}
istream &operator>>(istream &is, u128 &x) {
    u64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, u128 x) {
    os << (u64)x;
    return os;
}

#endif

[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
    SetUpIO() {
#ifdef FAST_IO
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
#endif
        cout << fixed << setprecision(15);
    }
} set_up_io;
// ============

#ifdef DEBUGF
#else
#define DBG(x) (void)0
#endif

// ============

#include <cassert>
#include <iostream>
#include <type_traits>

// ============

constexpr bool is_prime(unsigned n) {
    if (n == 0 || n == 1) {
        return false;
    }
    for (unsigned i = 2; i * i <= n; ++i) {
        if (n % i == 0) {
            return false;
        }
    }
    return true;
}

constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {
    unsigned ret = 1, self = x;
    while (y != 0) {
        if (y & 1) {
            ret = (unsigned) ((unsigned long long) ret * self % mod);
        }
        self = (unsigned) ((unsigned long long) self * self % mod);
        y /= 2;
    }
    return ret;
}

template <unsigned mod>
constexpr unsigned primitive_root() {
    static_assert(is_prime(mod), "`mod` must be a prime number.");
    if (mod == 2) {
        return 1;
    }

    unsigned primes[32] = {};
    int it = 0;
    {
        unsigned m = mod - 1;
        for (unsigned i = 2; i * i <= m; ++i) {
            if (m % i == 0) {
                primes[it++] = i;
                while (m % i == 0) {
                    m /= i;
                }
            }
        }
        if (m != 1) {
            primes[it++] = m;
        }
    }
    for (unsigned i = 2; i < mod; ++i) {
        bool ok = true;
        for (int j = 0; j < it; ++j) {
            if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
                ok = false;
                break;
            }
        }
        if (ok)
            return i;
    }
    return 0;
}

// y >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
    x %= y;
    if (x < 0) {
        x += y;
    }
    return x;
}

// y != 0
template <typename T>
constexpr T floor_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return x / y;
    } else {
        return -((-x + y - 1) / y);
    }
}

// y != 0
template <typename T>
constexpr T ceil_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return (x + y - 1) / y;
    } else {
        return -(-x / y);
    }
}
// ============

template <unsigned mod>
class ModInt {
    static_assert(mod != 0, "`mod` must not be equal to 0.");
    static_assert(
        mod < (1u << 31),
        "`mod` must be less than (1u << 31) = 2147483648.");

    unsigned val;

public:
    static constexpr unsigned get_mod() {
        return mod;
    }
    
    constexpr ModInt() : val(0) {}
    template <typename T, std::enable_if_t<std::is_signed_v<T>> * = nullptr>
    constexpr ModInt(T x) : val((unsigned) ((long long) x % (long long) mod + (x < 0 ? mod : 0))) {}
    template <typename T, std::enable_if_t<std::is_unsigned_v<T>> * = nullptr>
    constexpr ModInt(T x) : val((unsigned) (x % mod)) {}

    static constexpr ModInt raw(unsigned x) {
        ModInt<mod> ret;
        ret.val = x;
        return ret;
    }

    constexpr unsigned get_val() const {
        return val;
    }

    constexpr ModInt operator+() const {
        return *this;
    }
    constexpr ModInt operator-() const {
        return ModInt<mod>(0u) - *this;
    }

    constexpr ModInt &operator+=(const ModInt &rhs) {
        val += rhs.val;
        if (val >= mod)
            val -= mod;
        return *this;
    }
    constexpr ModInt &operator-=(const ModInt &rhs) {
        if (val < rhs.val)
            val += mod;
        val -= rhs.val;
        return *this;
    }
    constexpr ModInt &operator*=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.val % mod;
        return *this;
    }
    constexpr ModInt &operator/=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.inv().val % mod;
        return *this;
    }

    friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) += rhs;
    }
    friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) -= rhs;
    }
    friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) *= rhs;
    }
    friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) /= rhs;
    }

    constexpr ModInt pow(unsigned long long x) const {
        ModInt<mod> ret = ModInt<mod>::raw(1);
        ModInt<mod> self = *this;
        while (x != 0) {
            if (x & 1)
                ret *= self;
            self *= self;
            x >>= 1;
        }
        return ret;
    }
    constexpr ModInt inv() const {
        static_assert(is_prime(mod), "`mod` must be a prime number.");
        assert(val != 0);
        return this->pow(mod - 2);
    }

    friend std::istream &operator>>(std::istream &is, ModInt<mod> &x) {
        long long val;
        is >> val;
        x.val = val % mod + (val < 0 ? mod : 0);
        return is;
    }

    friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &x) {
        os << x.val;
        return os;
    }

    friend bool operator==(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val == rhs.val;
    }
    
    friend bool operator!=(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val != rhs.val;
    }
};

[[maybe_unused]] constexpr unsigned mod998244353 = 998244353;
[[maybe_unused]] constexpr unsigned mod1000000007 = 1000000007;

// ============
using Mint = ModInt<mod1000000007>;

int main() {
    i32 n;
    cin >> n;
    Vec<i32> a(n), b(n);
    REP(i, n) {
        cin >> a[i] >> b[i];
        ++b[i];
    }
    
    Vec<i32> c;
    c.reserve(2 * n);
    REP(i, n) {
        c.push_back(a[i]);
        c.push_back(b[i]);
    }
    sort(ALL(c));
    c.erase(unique(ALL(c)), c.end());
    REP(i, n) {
        a[i] = (i32)(lower_bound(ALL(c), a[i]) - c.begin());
        b[i] = (i32)(lower_bound(ALL(c), b[i]) - c.begin());
    }
    Vec<i32> lens(c.size() - 1);
    REP(i, c.size() - 1) {
        lens[i] = c[i + 1] - c[i];
    }
    
    Vec<Mint> inv(n + 1);
    REP(i, 1, n + 1) {
        inv[i] = Mint(i).inv();
    }
    
    Vec<Vec<Mint>> pre(lens.size(), Vec<Mint>(n + 1));
    REP(i, lens.size()) {
        i32 l = lens[i];
        REP(j, 1, n + 1) {
            Mint p(l);
            REP(k, 1, min(l, j) + 1) {
                if (k >= 2) {
                    p *= Mint::raw(l - k + 1);
                    p *= inv[k];
                    p *= Mint::raw(j - k + 1);
                    p *= inv[k - 1];
                }
                pre[i][j] += p;
            }
        }
    }
    
    Vec<Vec<Mint>> dp(n + 1, Vec<Mint>(c.size()));
    REP(i, c.size()) {
        dp[0][i] = Mint(1);
    }
    REP(i, n) {
        Vec<Mint> raw(lens.size());
        REP(j, a[i], b[i]) {
            i32 cnt = 0;
            PER(k, i + 1) {
                if (a[k] <= j && j < b[k]) {
                    ++cnt;
                }
                raw[j] += pre[j][cnt] * dp[k][j];
            }
        }
        REP(j, lens.size()) {
            dp[i + 1][j + 1] = dp[i + 1][j] + raw[j];
        }
    }
    Mint ans;
    REP(i, 1, n + 1) {
        ans += dp[i][lens.size()];
    }
    cout << ans << '\n';
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 961 ms 4240 KB Output is correct
2 Correct 966 ms 4240 KB Output is correct
3 Correct 960 ms 4232 KB Output is correct
4 Correct 964 ms 4228 KB Output is correct
5 Correct 980 ms 4304 KB Output is correct
6 Correct 966 ms 4236 KB Output is correct
7 Correct 972 ms 4228 KB Output is correct
8 Correct 960 ms 4240 KB Output is correct
9 Correct 964 ms 4172 KB Output is correct
10 Correct 962 ms 4228 KB Output is correct
11 Correct 967 ms 4228 KB Output is correct
12 Correct 981 ms 4224 KB Output is correct
13 Correct 974 ms 4228 KB Output is correct
14 Correct 976 ms 4228 KB Output is correct
15 Correct 960 ms 4232 KB Output is correct
16 Correct 170 ms 932 KB Output is correct
17 Correct 184 ms 1072 KB Output is correct
18 Correct 180 ms 936 KB Output is correct
19 Correct 190 ms 1072 KB Output is correct
20 Correct 175 ms 972 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 961 ms 4240 KB Output is correct
2 Correct 966 ms 4240 KB Output is correct
3 Correct 960 ms 4232 KB Output is correct
4 Correct 964 ms 4228 KB Output is correct
5 Correct 980 ms 4304 KB Output is correct
6 Correct 966 ms 4236 KB Output is correct
7 Correct 972 ms 4228 KB Output is correct
8 Correct 960 ms 4240 KB Output is correct
9 Correct 964 ms 4172 KB Output is correct
10 Correct 962 ms 4228 KB Output is correct
11 Correct 967 ms 4228 KB Output is correct
12 Correct 981 ms 4224 KB Output is correct
13 Correct 974 ms 4228 KB Output is correct
14 Correct 976 ms 4228 KB Output is correct
15 Correct 960 ms 4232 KB Output is correct
16 Correct 170 ms 932 KB Output is correct
17 Correct 184 ms 1072 KB Output is correct
18 Correct 180 ms 936 KB Output is correct
19 Correct 190 ms 1072 KB Output is correct
20 Correct 175 ms 972 KB Output is correct
21 Correct 179 ms 4068 KB Output is correct
22 Correct 177 ms 3992 KB Output is correct
23 Correct 165 ms 3916 KB Output is correct
24 Correct 181 ms 3892 KB Output is correct
25 Correct 178 ms 3920 KB Output is correct
26 Correct 218 ms 3736 KB Output is correct
27 Correct 220 ms 3872 KB Output is correct
28 Correct 219 ms 3792 KB Output is correct
29 Correct 217 ms 3796 KB Output is correct
30 Correct 906 ms 4224 KB Output is correct
31 Correct 967 ms 4228 KB Output is correct
32 Correct 952 ms 4240 KB Output is correct
33 Correct 981 ms 4228 KB Output is correct
34 Correct 990 ms 4220 KB Output is correct
35 Correct 943 ms 4224 KB Output is correct
36 Correct 912 ms 4236 KB Output is correct
37 Correct 937 ms 4224 KB Output is correct
38 Correct 913 ms 4220 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 17 ms 468 KB Output is correct
2 Correct 17 ms 408 KB Output is correct
3 Correct 17 ms 408 KB Output is correct
4 Correct 17 ms 404 KB Output is correct
5 Correct 18 ms 468 KB Output is correct
6 Correct 18 ms 468 KB Output is correct
7 Correct 18 ms 412 KB Output is correct
8 Correct 18 ms 404 KB Output is correct
9 Correct 17 ms 468 KB Output is correct
10 Correct 18 ms 404 KB Output is correct
11 Correct 17 ms 468 KB Output is correct
12 Correct 17 ms 408 KB Output is correct
13 Correct 18 ms 492 KB Output is correct
14 Correct 17 ms 408 KB Output is correct
15 Correct 17 ms 468 KB Output is correct
16 Correct 8 ms 340 KB Output is correct
17 Correct 8 ms 340 KB Output is correct
18 Correct 8 ms 340 KB Output is correct
19 Correct 8 ms 340 KB Output is correct
20 Correct 9 ms 376 KB Output is correct

Subtask #4
0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 961 ms 4240 KB Output is correct
2 Correct 966 ms 4240 KB Output is correct
3 Correct 960 ms 4232 KB Output is correct
4 Correct 964 ms 4228 KB Output is correct
5 Correct 980 ms 4304 KB Output is correct
6 Correct 966 ms 4236 KB Output is correct
7 Correct 972 ms 4228 KB Output is correct
8 Correct 960 ms 4240 KB Output is correct
9 Correct 964 ms 4172 KB Output is correct
10 Correct 962 ms 4228 KB Output is correct
11 Correct 967 ms 4228 KB Output is correct
12 Correct 981 ms 4224 KB Output is correct
13 Correct 974 ms 4228 KB Output is correct
14 Correct 976 ms 4228 KB Output is correct
15 Correct 960 ms 4232 KB Output is correct
16 Correct 170 ms 932 KB Output is correct
17 Correct 184 ms 1072 KB Output is correct
18 Correct 180 ms 936 KB Output is correct
19 Correct 190 ms 1072 KB Output is correct
20 Correct 175 ms 972 KB Output is correct
21 Correct 179 ms 4068 KB Output is correct
22 Correct 177 ms 3992 KB Output is correct
23 Correct 165 ms 3916 KB Output is correct
24 Correct 181 ms 3892 KB Output is correct
25 Correct 178 ms 3920 KB Output is correct
26 Correct 218 ms 3736 KB Output is correct
27 Correct 220 ms 3872 KB Output is correct
28 Correct 219 ms 3792 KB Output is correct
29 Correct 217 ms 3796 KB Output is correct
30 Correct 906 ms 4224 KB Output is correct
31 Correct 967 ms 4228 KB Output is correct
32 Correct 952 ms 4240 KB Output is correct
33 Correct 981 ms 4228 KB Output is correct
34 Correct 990 ms 4220 KB Output is correct
35 Correct 943 ms 4224 KB Output is correct
36 Correct 912 ms 4236 KB Output is correct
37 Correct 937 ms 4224 KB Output is correct
38 Correct 913 ms 4220 KB Output is correct
39 Correct 17 ms 468 KB Output is correct
40 Correct 17 ms 408 KB Output is correct
41 Correct 17 ms 408 KB Output is correct
42 Correct 17 ms 404 KB Output is correct
43 Correct 18 ms 468 KB Output is correct
44 Correct 18 ms 468 KB Output is correct
45 Correct 18 ms 412 KB Output is correct
46 Correct 18 ms 404 KB Output is correct
47 Correct 17 ms 468 KB Output is correct
48 Correct 18 ms 404 KB Output is correct
49 Correct 17 ms 468 KB Output is correct
50 Correct 17 ms 408 KB Output is correct
51 Correct 18 ms 492 KB Output is correct
52 Correct 17 ms 408 KB Output is correct
53 Correct 17 ms 468 KB Output is correct
54 Correct 8 ms 340 KB Output is correct
55 Correct 8 ms 340 KB Output is correct
56 Correct 8 ms 340 KB Output is correct
57 Correct 8 ms 340 KB Output is correct
58 Correct 9 ms 376 KB Output is correct
59 Execution timed out 2077 ms 4224 KB Time limit exceeded
60 Halted 0 ms 0 KB -