제출 #545853

#제출 시각아이디문제언어결과실행 시간메모리
545853Sohsoh84Boat (APIO16_boat)C++17
27 / 100
727 ms7228 KiB
#include <bits/stdc++.h>

using namespace std;


typedef long long ll;
typedef pair<ll, ll> pll;

#define all(x)			(x).begin(),(x).end()
#define X			first
#define Y			second
#define sep			' '
#define endl			'\n'
#define debug(x)		cerr << #x << ": " <<  x << endl;

const ll MAXN = 500 + 10;
const ll MOD = 1e9 + 7;

void mkey(int& a) {
	if (a >= MOD) a -= MOD;
}

inline ll poww(ll a, ll b) {
	ll ans = 1;
	while (b) {
		if (b & 1) ans = ans * a % MOD;
		b >>= 1;
		a = a * a % MOD;
	}

	return ans;
}

int n, L[MAXN], R[MAXN], C[MAXN][MAXN], PC[MAXN << 1][MAXN], dp[MAXN][MAXN << 1], 
    ps[MAXN << 1][MAXN], inv[MAXN << 1];
vector<int> vec;

inline int ind(int x) {
	return lower_bound(all(vec), x) - vec.begin();
}

int main() {
	ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);	
	C[0][0] = 1;
	for (int i = 1; i < MAXN; i++) {
		C[i][0] = 1;
		for (int j = 1; j <= i; j++)
			mkey(C[i][j] = C[i - 1][j - 1] + C[i - 1][j]);
	}

	cin >> n;
	for (int i = 1; i <= n; i++) {
		cin >> L[i] >> R[i];
		vec.push_back(L[i] - 1);
		vec.push_back(R[i]);
		inv[i] = poww(i, MOD - 2);
	}

	vec.push_back(-1);
	sort(all(vec));
	vec.resize(unique(all(vec)) - vec.begin());

	for (int j = 1; j < int(vec.size()); j++) {
		for (int i = 1; i <= n; i++) {
			ps[j][i] = ps[j][i - 1] + (vec[j - 1] + 1 >= L[i] && vec[j] <= R[i]);
		}

		int sz = vec[j] - vec[j - 1];
		for (int k = 1; k <= n; k++) {	
			ll f = 1;
			for (int i = 1; i <= min(sz, k); i++) {
				f = f * (sz - i + 1) % MOD * inv[i] % MOD;
				mkey(PC[j][k] += f * C[k - 1][i - 1] % MOD);
			}
		}
	}


	fill(dp[0], dp[0] + MAXN, 1);
	int ans = 0;
	for (int i = 1; i <= n; i++) {
		int l = ind(L[i] - 1), r = ind(R[i]);
		for (int j = 1; j < int(vec.size()); j++) {
			dp[i][j] = dp[i][j - 1];
			
			if (j > l && j <= r) {
				for (int k = 0; k < i; k++) {
					dp[i][j] = (dp[i][j] + 1ll * PC[j][ps[j][i] - ps[j][k]] * dp[k][j - 1]) % MOD;	
				}
			}
		}

		mkey(ans += dp[i][int(vec.size()) - 1]);
	}

	cout << ans << endl;
	return 0;
}
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