Submission #548341

#	Time	Username	Problem	Language	Result	Execution time	Memory
548341		gimabd30	Boat (APIO16_boat)	C++17	100 / 100	581 ms	4432 KiB

boat

//#define _GLIBCXX_DEBUG

//#pragma GCC optimize("Ofast")
//#pragma GCC optimize("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")

#include <bits/stdc++.h>

using namespace std;

#include <ext/pb_ds/assoc_container.hpp>

using namespace __gnu_pbds;

template<typename T>
using ordered_set = tree<T, null_type, less < T>, rb_tree_tag, tree_order_statistics_node_update>;

template<typename T>
using normal_queue = priority_queue <T, vector<T>, greater<>>;

mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());

#define ll long long
#define trace(x) cout << #x << ": " << (x) << endl;
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define uniq(x) x.resize(unique(all(x)) - begin(x))
#define ld long double
#define sz(s) ((int) size(s))
#define pii pair<int, int>
#define mp(x, y) make_pair(x, y)
#define int128 __int128
#define pb push_back
#define eb emplace_back


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

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

int bit(int x, int b) {
    return (x >> b) & 1;
}

int rand(int l, int r) { return (int) ((ll) rnd() % (r - l + 1)) + l; }

//soryan za musor sverhu

const ll infL = 3e18;
const int infI = 1'000'000'000 + 7;
const int N = 1001;
const ll mod = 1e9 + 7;
const ld eps = 1e-9;

ll fastp(ll a, ll p) {
    ll ans = 1;
    a %= mod;
    while (p) {
        if (p & 1)
            ans = ans * a % mod;
        a = a * a % mod;
        p >>= 1;
    }
    return ans;
}

ll fac[N];
ll invfac[N];
ll invnum[N];

void init() {
    int n = N - 1;
    fac[0] = invnum[0] = invfac[0] = 1;
    for (int i = 1; i <= n; ++i) {
        fac[i] = fac[i - 1] * i % mod;
    }
    invfac[n] = fastp(fac[n], mod - 2);
    invnum[n] = invfac[n] * fac[n - 1] % mod;
    for (int i = n - 1; i > 0; --i) {
        invfac[i] = invfac[i + 1] * (i + 1) % mod;
        invnum[i] = invfac[i] * fac[i - 1] % mod;
    }
}

ll inv(ll a) {
    if (a < N) return invnum[a];
    return fastp(a, mod - 2);
}

ll cnk(int n, int k) {
    if (k < 0 || k > n) return 0;
    return fac[n] * invfac[n - k] % mod * invfac[k] % mod;
}

ll dp[N][N];
int A[N], B[N], cord[N];

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    init();
    int n;
    cin >> n;
    for (int i = 1; i <= n; ++i) {
        cin >> A[i] >> B[i];
        ++B[i];
        cord[(i - 1) * 2] = A[i];
        cord[(i - 1) * 2 + 1] = B[i];
    }
    sort(cord, cord + n * 2);
    int m = unique(cord, cord + 2 * n) - cord;
    for (int i = 1; i <= n; ++i) {
        A[i] = lower_bound(cord, cord + m, A[i]) - cord + 1;
        B[i] = lower_bound(cord, cord + m, B[i]) - cord + 1;
    }
    for (int i = 0; i < m; ++i) dp[0][i] = 1;
    for (int i = 1; i <= n; ++i) {
        for (int j = A[i]; j < B[i]; ++j) {
            ll len = cord[j] - cord[j - 1];
            ll x = len;
            int cnt = 1;
            //this number is C(len + cnt - 1, cnt - 1)
            //so when we increase cnt, x = x * (len + cnt - 1) / cnt
            //because the last one is 100% not zero
            for (int k = i - 1; k >= 0; --k) {
                dp[i][j] = (dp[i][j] + x * dp[k][j - 1]) % mod;
                if (A[k] <= j && j < B[k]) {
                    ++cnt;
                    x = x * (len + cnt - 1) % mod * inv(cnt) % mod;
                }
            }
        }
        for (int j = 1; j < N; ++j) {
            dp[i][j] = (dp[i][j] + dp[i][j - 1]) % mod;
        }
    }
    ll ans = 0;
    for (int i = 1; i <= n; ++i) {
        ans = (ans + dp[i][N - 1]) % mod;
    }
    cout << ans;
    return 0;

}

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