oj.uz

Submission #1084831

# Submission time Handle Problem Language Result Execution time Memory
1084831 2024-09-07T04:45:20 Z kilkuwu Trains (BOI24_trains) C++17
100 / 100
 350 ms 132220 KB 
#include <bits/stdc++.h>

#ifdef LOCAL
#include "template/debug.hpp"
#else
#define dbg(...) ;
#define timer(...) ;
#endif

#define nl '\n'

template <int md>
struct Modular {
    int v;
    constexpr Modular() : v(0) {}
    template <typename T>
    static inline int normalize(const T& x) {
        int res = -mod() <= x && x < mod() ? static_cast<int>(x) : static_cast<int>(x % mod());
        return res + (res < 0) * mod();
    }
    static constexpr int mod() {
        return md;
    }
    template <typename U>
    Modular(const U& x) : v(normalize(x)) {}
    const int& operator()() const {
        return v;
    }
    template <typename U>
    explicit operator U() const {
        return static_cast<U>(v);
    }
    using M = Modular;
    template <typename U>
    friend std::enable_if_t<std::is_integral_v<U>, M> power(M b, U e) {
        assert(e >= 0);
        M ans = 1;
        while (e) {
            if (e & 1) ans *= b;
            b *= b;
            e >>= 1;
        }
        return ans;
    }
    M inv() const {
        M res = power(*this, mod() - 2);
        return res;
    }
    M& operator+=(const M& y) {
        return v += y.v, v -= (v >= mod()) * mod(), *this;
    }
    M& operator-=(const M& y) {
        return v -= y.v, v += (v < 0) * mod(), *this;
    }
    M& operator*=(const M& y) {
        return v = (int)((int64_t)v * y.v % mod()), *this;
    }
    M& operator/=(const M& y) {
        return *this *= y.inv();
    }
    M& operator++() {
        return v++, v = (v == mod()) ? 0 : v, *this;
    }
    M& operator--() {
        return v = (v == 0) ? mod() : v, v--, *this;
    }
    M operator++(int) {
        M res(*this);
        return ++(*this), res;
    }
    M operator--(int) {
        M res(*this);
        return --(*this), res;
    }
    M operator+() const {
        return M(v);
    }
    M operator-() const {
        return M(-v);
    }
    friend bool operator==(const M& x, const M& y) {
        return x.v == y.v;
    }
    friend bool operator<(const M& x, const M& y) {
        return x.v < y.v;
    }
    friend bool operator>(const M& x, const M& y) {
        return x.v > y.v;
    }
    friend bool operator<=(const M& x, const M& y) {
        return x.v <= y.v;
    }
    friend bool operator>=(const M& x, const M& y) {
        return x.v >= y.v;
    }
    friend bool operator!=(const M& x, const M& y) {
        return x.v != y.v;
    }
    template <typename Istream>
    friend Istream& operator>>(Istream& is, M& y) {
        int64_t x;
        is >> x;
        y.v = y.normalize(x);
        return is;
    }
    template <typename Ostream>
    friend Ostream& operator<<(Ostream& os, const M& y) {
        return os << y.v;
    }
    friend M operator+(const M& x, const M& y) {
        return M(x) += y;
    }
    friend M operator-(const M& x, const M& y) {
        return M(x) -= y;
    }
    friend M operator*(const M& x, const M& y) {
        return M(x) *= y;
    }
    friend M operator/(const M& x, const M& y) {
        return M(x) /= y;
    }
};

constexpr int md = 1e9 + 7;
using Mint = Modular<md>;


signed main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    int N;
    std::cin >> N;
    std::vector<int> d(N), x(N);
    for (int i = 0; i < N; i++) {
        std::cin >> d[i] >> x[i];
    }

    std::vector<std::pair<int, int>> compressed;

    for (int i = 0; i < N; i++) {
        if (d[i] != 0) {
            compressed.emplace_back(i % d[i], d[i]);
        }
    }

    std::sort(compressed.begin(), compressed.end());
    compressed.erase(std::unique(compressed.begin(), compressed.end()), compressed.end());

    auto get_id = [&](std::pair<int, int> key) -> int {
        return std::lower_bound(compressed.begin(), compressed.end(), key) - compressed.begin();
    };

    int sz = compressed.size();


    std::vector<int> belong(N, -1);

    for (int i = 0; i < N; i++) {
        if (d[i] != 0) {
            belong[i] = get_id({i % d[i], d[i]});
        }
    }


    int B = std::sqrt(N);
    //dbg(B);
    int num_block = (N - 1) / B + 1;
    std::vector<std::vector<Mint>> add(sz, std::vector<Mint>(num_block));

    std::vector<int> has_update(num_block, 0);

    std::vector<Mint> dp(N);

    auto collapse_block = [&](int b) -> void { // O(N)

        if (!has_update[b]) return;
        has_update[b] = 0;
        int lb = b * B;
        int rb = std::min((b + 1) * B, N);
        for (int i = 0; i < sz; i++) {
            // moi thang nay co 1 delta
            auto [from, delta] = compressed[i];
            // from + x * delta >= lb
            if (from < lb) {
                int t = (lb - from + delta - 1) / delta;
                from += t * delta;
            }
            if (from >= rb) continue;

            for (int j = from; j < rb; j += delta) {
                dp[j] += add[i][b];
            }
        }
    };

    // 1,  x[i] = 3
    // 1 + 1 * 1 -> 1 + 3 * 1
    // 2 -> 4

    auto update = [&](int index) -> void {
        int id = belong[index];
        auto val = dp[index];
        int l = index + d[index];
        int max_t = (N - 1 - index) / d[index];
        int r = index + std::min(max_t, x[index]) * d[index];
        if (l > r) return;
        int bl = l / B;
        int br = r / B;



        if (bl == br) {
            for (int i = l; i <= r; i += d[index]) {

                dp[i] += val;
            }
            return;
        }
        for (int i = l; i < B * (bl + 1); i += d[index]) {
            dp[i] += val;
        }

        for (int b = bl + 1; b < br; b++) {
            has_update[b] = 1;
            add[id][b] += val;
        }

        for (int i = r; i >= br * B; i -= d[index]) {
            dp[i] += val;
        }
    };


   // dbg("got here");
    dp[0] = 1;
    Mint res = 0;
//
// bought already we can go there if bought lmao
//
    for (int i = 0; i < N; i++) {
        collapse_block(i / B);
        res += dp[i];
       // dbg(i, dp[i]);
        if (d[i] == 0) continue;
        update(i);
    }

    std::cout << res << nl;


}

Subtask #1
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 0 ms 424 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 416 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct

Subtask #2
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 0 ms 424 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 416 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 3 ms 604 KB Output is correct
21 Correct 1 ms 860 KB Output is correct
22 Correct 13 ms 4696 KB Output is correct
23 Correct 2 ms 604 KB Output is correct
24 Correct 4 ms 1628 KB Output is correct
25 Correct 6 ms 2136 KB Output is correct
26 Correct 1 ms 600 KB Output is correct
27 Correct 3 ms 604 KB Output is correct
28 Correct 2 ms 860 KB Output is correct
29 Correct 4 ms 1112 KB Output is correct
30 Correct 6 ms 4956 KB Output is correct
31 Correct 3 ms 604 KB Output is correct
32 Correct 3 ms 860 KB Output is correct
33 Correct 8 ms 2396 KB Output is correct
34 Correct 9 ms 4956 KB Output is correct
35 Correct 7 ms 4872 KB Output is correct
36 Correct 7 ms 2396 KB Output is correct

Subtask #3
16.0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 2 ms 472 KB Output is correct
3 Correct 1 ms 604 KB Output is correct
4 Correct 3 ms 724 KB Output is correct
5 Correct 10 ms 2524 KB Output is correct
6 Correct 50 ms 3528 KB Output is correct
7 Correct 49 ms 3540 KB Output is correct
8 Correct 1 ms 344 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 3 ms 860 KB Output is correct
12 Correct 53 ms 4056 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 4 ms 860 KB Output is correct
15 Correct 51 ms 3800 KB Output is correct

Subtask #4
34.0 / 34.0

# Verdict Execution time Memory Grader output
1 Correct 18 ms 2264 KB Output is correct
2 Correct 18 ms 1776 KB Output is correct
3 Correct 39 ms 3952 KB Output is correct
4 Correct 26 ms 3036 KB Output is correct
5 Correct 1 ms 600 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 3 ms 860 KB Output is correct
8 Correct 51 ms 3928 KB Output is correct

Subtask #5
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 0 ms 424 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 416 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 3 ms 604 KB Output is correct
21 Correct 1 ms 860 KB Output is correct
22 Correct 13 ms 4696 KB Output is correct
23 Correct 2 ms 604 KB Output is correct
24 Correct 4 ms 1628 KB Output is correct
25 Correct 6 ms 2136 KB Output is correct
26 Correct 1 ms 600 KB Output is correct
27 Correct 3 ms 604 KB Output is correct
28 Correct 2 ms 860 KB Output is correct
29 Correct 4 ms 1112 KB Output is correct
30 Correct 6 ms 4956 KB Output is correct
31 Correct 3 ms 604 KB Output is correct
32 Correct 3 ms 860 KB Output is correct
33 Correct 8 ms 2396 KB Output is correct
34 Correct 9 ms 4956 KB Output is correct
35 Correct 7 ms 4872 KB Output is correct
36 Correct 7 ms 2396 KB Output is correct
37 Correct 0 ms 348 KB Output is correct
38 Correct 2 ms 472 KB Output is correct
39 Correct 1 ms 604 KB Output is correct
40 Correct 3 ms 724 KB Output is correct
41 Correct 10 ms 2524 KB Output is correct
42 Correct 50 ms 3528 KB Output is correct
43 Correct 49 ms 3540 KB Output is correct
44 Correct 1 ms 344 KB Output is correct
45 Correct 0 ms 348 KB Output is correct
46 Correct 0 ms 348 KB Output is correct
47 Correct 3 ms 860 KB Output is correct
48 Correct 53 ms 4056 KB Output is correct
49 Correct 0 ms 348 KB Output is correct
50 Correct 4 ms 860 KB Output is correct
51 Correct 51 ms 3800 KB Output is correct
52 Correct 18 ms 2264 KB Output is correct
53 Correct 18 ms 1776 KB Output is correct
54 Correct 39 ms 3952 KB Output is correct
55 Correct 26 ms 3036 KB Output is correct
56 Correct 1 ms 600 KB Output is correct
57 Correct 0 ms 348 KB Output is correct
58 Correct 3 ms 860 KB Output is correct
59 Correct 51 ms 3928 KB Output is correct
60 Correct 36 ms 4312 KB Output is correct
61 Correct 39 ms 3628 KB Output is correct
62 Correct 29 ms 3288 KB Output is correct
63 Correct 38 ms 3544 KB Output is correct
64 Correct 120 ms 132220 KB Output is correct
65 Correct 350 ms 110880 KB Output is correct
66 Correct 33 ms 3796 KB Output is correct
67 Correct 130 ms 131808 KB Output is correct
68 Correct 32 ms 3548 KB Output is correct
69 Correct 161 ms 52872 KB Output is correct
70 Correct 183 ms 131312 KB Output is correct
71 Correct 198 ms 131104 KB Output is correct
72 Correct 164 ms 53520 KB Output is correct