oj.uz

Submission #720108

# Submission time Handle Problem Language Result Execution time Memory
720108 2023-04-07T12:18:03 Z Forested Boat (APIO16_boat) C++17
100 / 100
 870 ms 4368 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<i32> nd(lens.size(), 0);
    REP(i, n) {
        REP(j, a[i], b[i]) {
            ++nd[j];
        }
    }
    
    Vec<Vec<Mint>> pre(lens.size(), Vec<Mint>(n + 1));
    REP(i, lens.size()) {
        i32 l = lens[i];
        REP(j, 1, nd[i] + 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 4 ms 4308 KB Output is correct
2 Correct 4 ms 4308 KB Output is correct
3 Correct 6 ms 4308 KB Output is correct
4 Correct 4 ms 4308 KB Output is correct
5 Correct 5 ms 4308 KB Output is correct
6 Correct 4 ms 4308 KB Output is correct
7 Correct 4 ms 4308 KB Output is correct
8 Correct 4 ms 4308 KB Output is correct
9 Correct 4 ms 4308 KB Output is correct
10 Correct 4 ms 4308 KB Output is correct
11 Correct 4 ms 4320 KB Output is correct
12 Correct 5 ms 4308 KB Output is correct
13 Correct 6 ms 4308 KB Output is correct
14 Correct 4 ms 4308 KB Output is correct
15 Correct 5 ms 4308 KB Output is correct
16 Correct 3 ms 980 KB Output is correct
17 Correct 2 ms 980 KB Output is correct
18 Correct 2 ms 980 KB Output is correct
19 Correct 2 ms 980 KB Output is correct
20 Correct 2 ms 980 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 4308 KB Output is correct
2 Correct 4 ms 4308 KB Output is correct
3 Correct 6 ms 4308 KB Output is correct
4 Correct 4 ms 4308 KB Output is correct
5 Correct 5 ms 4308 KB Output is correct
6 Correct 4 ms 4308 KB Output is correct
7 Correct 4 ms 4308 KB Output is correct
8 Correct 4 ms 4308 KB Output is correct
9 Correct 4 ms 4308 KB Output is correct
10 Correct 4 ms 4308 KB Output is correct
11 Correct 4 ms 4320 KB Output is correct
12 Correct 5 ms 4308 KB Output is correct
13 Correct 6 ms 4308 KB Output is correct
14 Correct 4 ms 4308 KB Output is correct
15 Correct 5 ms 4308 KB Output is correct
16 Correct 3 ms 980 KB Output is correct
17 Correct 2 ms 980 KB Output is correct
18 Correct 2 ms 980 KB Output is correct
19 Correct 2 ms 980 KB Output is correct
20 Correct 2 ms 980 KB Output is correct
21 Correct 166 ms 3952 KB Output is correct
22 Correct 163 ms 3996 KB Output is correct
23 Correct 147 ms 3924 KB Output is correct
24 Correct 166 ms 3900 KB Output is correct
25 Correct 158 ms 3928 KB Output is correct
26 Correct 205 ms 3824 KB Output is correct
27 Correct 209 ms 3880 KB Output is correct
28 Correct 205 ms 3796 KB Output is correct
29 Correct 210 ms 3804 KB Output is correct
30 Correct 5 ms 4180 KB Output is correct
31 Correct 6 ms 4308 KB Output is correct
32 Correct 5 ms 4180 KB Output is correct
33 Correct 5 ms 4308 KB Output is correct
34 Correct 6 ms 4180 KB Output is correct
35 Correct 6 ms 4180 KB Output is correct
36 Correct 6 ms 4180 KB Output is correct
37 Correct 8 ms 4180 KB Output is correct
38 Correct 5 ms 4180 KB Output is correct

Subtask #3
27.0 / 27.0

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

Subtask #4
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 4308 KB Output is correct
2 Correct 4 ms 4308 KB Output is correct
3 Correct 6 ms 4308 KB Output is correct
4 Correct 4 ms 4308 KB Output is correct
5 Correct 5 ms 4308 KB Output is correct
6 Correct 4 ms 4308 KB Output is correct
7 Correct 4 ms 4308 KB Output is correct
8 Correct 4 ms 4308 KB Output is correct
9 Correct 4 ms 4308 KB Output is correct
10 Correct 4 ms 4308 KB Output is correct
11 Correct 4 ms 4320 KB Output is correct
12 Correct 5 ms 4308 KB Output is correct
13 Correct 6 ms 4308 KB Output is correct
14 Correct 4 ms 4308 KB Output is correct
15 Correct 5 ms 4308 KB Output is correct
16 Correct 3 ms 980 KB Output is correct
17 Correct 2 ms 980 KB Output is correct
18 Correct 2 ms 980 KB Output is correct
19 Correct 2 ms 980 KB Output is correct
20 Correct 2 ms 980 KB Output is correct
21 Correct 166 ms 3952 KB Output is correct
22 Correct 163 ms 3996 KB Output is correct
23 Correct 147 ms 3924 KB Output is correct
24 Correct 166 ms 3900 KB Output is correct
25 Correct 158 ms 3928 KB Output is correct
26 Correct 205 ms 3824 KB Output is correct
27 Correct 209 ms 3880 KB Output is correct
28 Correct 205 ms 3796 KB Output is correct
29 Correct 210 ms 3804 KB Output is correct
30 Correct 5 ms 4180 KB Output is correct
31 Correct 6 ms 4308 KB Output is correct
32 Correct 5 ms 4180 KB Output is correct
33 Correct 5 ms 4308 KB Output is correct
34 Correct 6 ms 4180 KB Output is correct
35 Correct 6 ms 4180 KB Output is correct
36 Correct 6 ms 4180 KB Output is correct
37 Correct 8 ms 4180 KB Output is correct
38 Correct 5 ms 4180 KB Output is correct
39 Correct 4 ms 468 KB Output is correct
40 Correct 3 ms 468 KB Output is correct
41 Correct 4 ms 468 KB Output is correct
42 Correct 4 ms 468 KB Output is correct
43 Correct 5 ms 468 KB Output is correct
44 Correct 9 ms 468 KB Output is correct
45 Correct 7 ms 468 KB Output is correct
46 Correct 8 ms 468 KB Output is correct
47 Correct 8 ms 404 KB Output is correct
48 Correct 7 ms 468 KB Output is correct
49 Correct 4 ms 468 KB Output is correct
50 Correct 3 ms 468 KB Output is correct
51 Correct 3 ms 468 KB Output is correct
52 Correct 3 ms 468 KB Output is correct
53 Correct 4 ms 468 KB Output is correct
54 Correct 3 ms 340 KB Output is correct
55 Correct 2 ms 340 KB Output is correct
56 Correct 2 ms 340 KB Output is correct
57 Correct 2 ms 340 KB Output is correct
58 Correct 3 ms 340 KB Output is correct
59 Correct 441 ms 4232 KB Output is correct
60 Correct 402 ms 4352 KB Output is correct
61 Correct 381 ms 4356 KB Output is correct
62 Correct 437 ms 4244 KB Output is correct
63 Correct 414 ms 4368 KB Output is correct
64 Correct 859 ms 4312 KB Output is correct
65 Correct 862 ms 4320 KB Output is correct
66 Correct 870 ms 4312 KB Output is correct
67 Correct 862 ms 4312 KB Output is correct
68 Correct 868 ms 4312 KB Output is correct
69 Correct 359 ms 4312 KB Output is correct
70 Correct 359 ms 4368 KB Output is correct
71 Correct 358 ms 4312 KB Output is correct
72 Correct 383 ms 4312 KB Output is correct
73 Correct 385 ms 4300 KB Output is correct
74 Correct 62 ms 948 KB Output is correct
75 Correct 57 ms 972 KB Output is correct
76 Correct 62 ms 960 KB Output is correct
77 Correct 62 ms 1076 KB Output is correct
78 Correct 63 ms 960 KB Output is correct