Submission #849182

#	Time	Username	Problem	Language	Result	Execution time	Memory
849182		hngwlog	Boat (APIO16_boat)	C++14	100 / 100	535 ms	6072 KiB

boat

#include <bits/stdc++.h>
using namespace std;

const int maxn = 505;
const long long mod = 1e9 + 7;

int n;
int a[maxn], b[maxn], has[maxn];
long long sum[maxn], g[maxn], p[maxn], dp[maxn], ivp[maxn];
long long f[2 * maxn][maxn]; // segment i, last boat: j
vector<int> c;
vector<vector<int>> adj(2 * maxn);

long long pow_(long long o, long long q) {
    
    if (!q) return 1;
    long long t = pow_(o, q / 2);
    t = (t * t) % mod;
    if (q % 2) t = (t * o) % mod;
    return t;
}

void load() {
    
    p[0] = 1;
    for (int i = 1; i <= n; i++) p[i] = (p[i - 1] * i) % mod;
    for (int i = 0; i <= n; i++) ivp[i] = pow_(p[i], mod - 2);
    for (int i = 1; i <= n; i++) {
        int l = lower_bound(c.begin(), c.end(), a[i] - 1) - c.begin();
        int r = lower_bound(c.begin(), c.end(), b[i]) - c.begin();
        for (int j = l; j < r; j++) adj[j].push_back(i);
    }
}

long long C(int k, int n_) {
    
    if (!k || k == n_) return 1;
    if (k > n) return 0;
    return p[n_] * (ivp[k] * ivp[n_ - k] % mod) % mod;
}

void solve() {
    
    sum[0] = 1;
    for (int i = 0; i < (int)c.size(); i++) {
        int sz = (int)adj[i].size();
        int value = c[i + 1] - c[i];
        for (int j = 1; j <= sz; j++) {
            dp[j] = 0;
            long long res = 1;
            for (int z = 0; z < j; z++) {
                res = (res * (value - z)) % mod;
                if (z < j - 1) dp[j] = (dp[j] + C(z, j - 1) * g[z + 1]) % mod;
            }
            g[j] = (res * ivp[j]) % mod;
            if (j > value) g[j] = 0;
            dp[j] = (dp[j] + g[j]) % mod;
        }
        for (int j = 1; j <= sz; j++) g[j] = 0;
        for (auto j: adj[i]) {
            has[j]++;
            int cnt = 1;
            for (int z = j - 1; z >= 0; z--) {
                f[i][j] = (f[i][j] + sum[z] * dp[cnt]) % mod;
                if (has[z]) cnt++;
            }
        }
        for (auto j: adj[i]) sum[j] = (sum[j] + f[i][j]) % mod, has[j]--;
    }
    long long ans = 0;
    for (int i = 1; i <= n; i++) ans = (ans + sum[i]) % mod;
    cout << ans << '\n';
}

int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
    
    cin >> n;
    for (int i = 1; i <= n; i++) {
        cin >> a[i] >> b[i];
        c.push_back(a[i] - 1);
        c.push_back(b[i]);
    }
    sort(c.begin(), c.end());
    c.resize(unique(c.begin(), c.end()) - c.begin());
    load();
    solve();
    return 0;
}

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