oj.uz

Submission #720095

# Submission time Handle Problem Language Result Execution time Memory
720095 2023-04-07T12:05:09 Z Forested Boat (APIO16_boat) C++17
58 / 100
 2000 ms 4428 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(l - k + 1);
                    p *= inv[k];
                    p *= Mint(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 1018 ms 4244 KB Output is correct
2 Correct 985 ms 4240 KB Output is correct
3 Correct 989 ms 4240 KB Output is correct
4 Correct 981 ms 4244 KB Output is correct
5 Correct 995 ms 4240 KB Output is correct
6 Correct 968 ms 4240 KB Output is correct
7 Correct 972 ms 4252 KB Output is correct
8 Correct 983 ms 4240 KB Output is correct
9 Correct 968 ms 4236 KB Output is correct
10 Correct 981 ms 4236 KB Output is correct
11 Correct 969 ms 4240 KB Output is correct
12 Correct 967 ms 4244 KB Output is correct
13 Correct 976 ms 4300 KB Output is correct
14 Correct 987 ms 4236 KB Output is correct
15 Correct 970 ms 4240 KB Output is correct
16 Correct 171 ms 972 KB Output is correct
17 Correct 186 ms 1084 KB Output is correct
18 Correct 175 ms 940 KB Output is correct
19 Correct 189 ms 1084 KB Output is correct
20 Correct 186 ms 964 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 1018 ms 4244 KB Output is correct
2 Correct 985 ms 4240 KB Output is correct
3 Correct 989 ms 4240 KB Output is correct
4 Correct 981 ms 4244 KB Output is correct
5 Correct 995 ms 4240 KB Output is correct
6 Correct 968 ms 4240 KB Output is correct
7 Correct 972 ms 4252 KB Output is correct
8 Correct 983 ms 4240 KB Output is correct
9 Correct 968 ms 4236 KB Output is correct
10 Correct 981 ms 4236 KB Output is correct
11 Correct 969 ms 4240 KB Output is correct
12 Correct 967 ms 4244 KB Output is correct
13 Correct 976 ms 4300 KB Output is correct
14 Correct 987 ms 4236 KB Output is correct
15 Correct 970 ms 4240 KB Output is correct
16 Correct 171 ms 972 KB Output is correct
17 Correct 186 ms 1084 KB Output is correct
18 Correct 175 ms 940 KB Output is correct
19 Correct 189 ms 1084 KB Output is correct
20 Correct 186 ms 964 KB Output is correct
21 Correct 185 ms 3952 KB Output is correct
22 Correct 182 ms 3996 KB Output is correct
23 Correct 170 ms 3936 KB Output is correct
24 Correct 181 ms 3908 KB Output is correct
25 Correct 169 ms 3804 KB Output is correct
26 Correct 213 ms 3752 KB Output is correct
27 Correct 230 ms 3896 KB Output is correct
28 Correct 219 ms 3788 KB Output is correct
29 Correct 221 ms 3804 KB Output is correct
30 Correct 929 ms 4428 KB Output is correct
31 Correct 924 ms 4300 KB Output is correct
32 Correct 940 ms 4300 KB Output is correct
33 Correct 939 ms 4252 KB Output is correct
34 Correct 931 ms 4232 KB Output is correct
35 Correct 922 ms 4240 KB Output is correct
36 Correct 921 ms 4232 KB Output is correct
37 Correct 936 ms 4232 KB Output is correct
38 Correct 914 ms 4236 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 18 ms 408 KB Output is correct
3 Correct 18 ms 416 KB Output is correct
4 Correct 18 ms 408 KB Output is correct
5 Correct 18 ms 468 KB Output is correct
6 Correct 18 ms 444 KB Output is correct
7 Correct 18 ms 412 KB Output is correct
8 Correct 19 ms 408 KB Output is correct
9 Correct 18 ms 404 KB Output is correct
10 Correct 18 ms 444 KB Output is correct
11 Correct 18 ms 404 KB Output is correct
12 Correct 17 ms 416 KB Output is correct
13 Correct 18 ms 408 KB Output is correct
14 Correct 18 ms 412 KB Output is correct
15 Correct 18 ms 408 KB Output is correct
16 Correct 8 ms 340 KB Output is correct
17 Correct 9 ms 372 KB Output is correct
18 Correct 8 ms 320 KB Output is correct
19 Correct 8 ms 340 KB Output is correct
20 Correct 9 ms 368 KB Output is correct

Subtask #4
0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 1018 ms 4244 KB Output is correct
2 Correct 985 ms 4240 KB Output is correct
3 Correct 989 ms 4240 KB Output is correct
4 Correct 981 ms 4244 KB Output is correct
5 Correct 995 ms 4240 KB Output is correct
6 Correct 968 ms 4240 KB Output is correct
7 Correct 972 ms 4252 KB Output is correct
8 Correct 983 ms 4240 KB Output is correct
9 Correct 968 ms 4236 KB Output is correct
10 Correct 981 ms 4236 KB Output is correct
11 Correct 969 ms 4240 KB Output is correct
12 Correct 967 ms 4244 KB Output is correct
13 Correct 976 ms 4300 KB Output is correct
14 Correct 987 ms 4236 KB Output is correct
15 Correct 970 ms 4240 KB Output is correct
16 Correct 171 ms 972 KB Output is correct
17 Correct 186 ms 1084 KB Output is correct
18 Correct 175 ms 940 KB Output is correct
19 Correct 189 ms 1084 KB Output is correct
20 Correct 186 ms 964 KB Output is correct
21 Correct 185 ms 3952 KB Output is correct
22 Correct 182 ms 3996 KB Output is correct
23 Correct 170 ms 3936 KB Output is correct
24 Correct 181 ms 3908 KB Output is correct
25 Correct 169 ms 3804 KB Output is correct
26 Correct 213 ms 3752 KB Output is correct
27 Correct 230 ms 3896 KB Output is correct
28 Correct 219 ms 3788 KB Output is correct
29 Correct 221 ms 3804 KB Output is correct
30 Correct 929 ms 4428 KB Output is correct
31 Correct 924 ms 4300 KB Output is correct
32 Correct 940 ms 4300 KB Output is correct
33 Correct 939 ms 4252 KB Output is correct
34 Correct 931 ms 4232 KB Output is correct
35 Correct 922 ms 4240 KB Output is correct
36 Correct 921 ms 4232 KB Output is correct
37 Correct 936 ms 4232 KB Output is correct
38 Correct 914 ms 4236 KB Output is correct
39 Correct 17 ms 468 KB Output is correct
40 Correct 18 ms 408 KB Output is correct
41 Correct 18 ms 416 KB Output is correct
42 Correct 18 ms 408 KB Output is correct
43 Correct 18 ms 468 KB Output is correct
44 Correct 18 ms 444 KB Output is correct
45 Correct 18 ms 412 KB Output is correct
46 Correct 19 ms 408 KB Output is correct
47 Correct 18 ms 404 KB Output is correct
48 Correct 18 ms 444 KB Output is correct
49 Correct 18 ms 404 KB Output is correct
50 Correct 17 ms 416 KB Output is correct
51 Correct 18 ms 408 KB Output is correct
52 Correct 18 ms 412 KB Output is correct
53 Correct 18 ms 408 KB Output is correct
54 Correct 8 ms 340 KB Output is correct
55 Correct 9 ms 372 KB Output is correct
56 Correct 8 ms 320 KB Output is correct
57 Correct 8 ms 340 KB Output is correct
58 Correct 9 ms 368 KB Output is correct
59 Execution timed out 2084 ms 4236 KB Time limit exceeded
60 Halted 0 ms 0 KB -