Submission #969349

#	Time	Username	Problem	Language	Result	Execution time	Memory
969349		MinaRagy06	Boat (APIO16_boat)	C++17	100 / 100	640 ms	6548 KiB

boat

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define SZ(x) (int) x.size()

const int mod = 1e9 + 7;
struct mint {
	int v;
	mint(long long x) {
		if (x >= mod) x %= mod;
		v = x;
	}
	mint() {v = 0;}
	mint& operator+=(mint b) {
		if ((v += b.v) >= mod) {
			v -= mod;
		}
		return *this;
	}
	mint& operator-=(mint b) {
		if ((v -= b.v) < 0) {
			v += mod;
		}
		return *this;
	}
	mint& operator*=(mint b) {
		v = 1ll * v * b.v % mod;
		return *this;
	}
	mint power(mint a, int b) {
		mint ans = 1;
		while (b) {
			if (b & 1) {
				ans *= a;
			}
			a *= a, b >>= 1;
		}
		return ans;
	}
	mint& operator/=(mint b) {
		v = 1ll * v * power(b, mod - 2).v % mod;
		return *this;
	}
	friend mint operator+(mint a, mint b) {
		return a += b;
	}
	friend mint operator-(mint a, mint b) {
		return a -= b;
	}
	friend mint operator*(mint a, mint b) {
		return a *= b;
	}
	friend mint operator/(mint a, mint b) {
		return a /= b;
	}
	friend istream& operator>>(istream &is, mint &a) {
		return is >> a.v;
	}
	friend ostream& operator<<(ostream &os, mint a) {
		return os << a.v;
	}
};
const int N = 505;
mint inv[N];
int main() {
	ios_base::sync_with_stdio(0), cin.tie(0);
	for (int i = 1; i < N; i++) {
		inv[i] = mint(1) / i;
	}
	int n;
	cin >> n;
	array<int, 2> a[n];
	vector<int> v;
	for (int i = 0; i < n; i++) {
		cin >> a[i][0] >> a[i][1];
		v.push_back(a[i][0]);
		v.push_back(a[i][1]);
		v.push_back(a[i][1] + 1);
	}
	sort(v.begin(), v.end());
	v.resize(unique(v.begin(), v.end()) - v.begin());
	auto get = [&] (int x) {
		return lower_bound(v.begin(), v.end(), x) - v.begin();
	};
	int m = v.size();
	vector<int> gud[m];
	for (int i = 0; i < n; i++) {
		int l = get(a[i][0]), r = get(a[i][1]);
		for (int j = l; j <= r; j++) {
			gud[j].push_back(i + 1);
		}
	}
	mint dp[m + 1][n + 1];
	for (int j = 1; j <= n; j++) {
		dp[m][j] = 1;
	}
	for (int i = m - 1; i >= 0; i--) {
		int sz = gud[i].size();
		mint dp2[sz + 1][sz + 1];
		for (int j = sz - 1; j >= 0; j--) {
			for (int k = 1; k <= sz; k++) {
				dp2[j][k] += dp2[j + 1][k];
				if (k == 1) {
					dp2[j][k] += dp[i + 1][gud[i][j]];
				} else {
					dp2[j][k] += dp2[j + 1][k - 1];
				}
			}
		}
		for (int j = 0; j <= n; j++) {
			int pos = SZ(gud[i]);
			for (int k = 0; k < SZ(gud[i]); k++) {
				if (j < gud[i][k]) {
					pos = k;
					break;
				}
			}
			dp[i][j] = dp[i + 1][j];
			int slots = v[i + 1] - v[i];
			mint C = 1;
			for (int k = 1; k <= min(SZ(gud[i]) - pos, slots); k++) {
				C *= (slots - k + 1) * inv[k];
				dp[i][j] += dp2[pos][k] * C;
			}
		}
	}
//	for (int i = 0; i < m; i++) {
//		for (int j = 0; j <= n; j++) {
//			cout << dp[i][j] << ' ';
//		}
//		cout << '\n';
//	}
	cout << dp[0][0] << '\n';
	return 0;
}

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