Submission #447811

#	Time	Username	Problem	Language	Result	Execution time	Memory
447811		dutch	Boat (APIO16_boat)	C++17	9 / 100	2090 ms	4412 KiB

boat

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

const int MOD = 1e9+7, LIM = 501;

int modInverse(int x){
	int r = 1, p = (MOD - 2) * 2;
	for(int y=x; p/=2; y=(y*y) % MOD)
		if(p & 1) r = (r*y) % MOD;
	return r;
}

int n, a[LIM], b[LIM], dp[LIM][LIM*2], F[LIM], invF[LIM], C[LIM];
bool valid[LIM];
vector<int> pts;

int nCr(int x, int y){
	return (((F[x] * invF[y]) % MOD) * invF[x-y]) % MOD;
}

void add(int &x, int y){
	x += y;
	while(x >= MOD) x -= MOD;
	while(x <=-MOD) x += MOD;
}

signed main(){
	cin.tie(0)->sync_with_stdio(0);

	cin >> n;
	for(int i=0; i<n; ++i){
		cin >> a[i] >> b[i];
		pts.push_back(a[i]);
		pts.push_back(b[i]+1);
	}
	sort(pts.begin(), pts.end());
	pts.resize(unique(pts.begin(), pts.end()) - pts.begin());

	int m = size(pts) - 1, ans = 0;

	F[0] = invF[0] = 1;
	for(int i=1; i<=n; ++i){
		F[i] = (F[i-1] * i) % MOD;
		invF[i] = modInverse(F[i]);
	}
	for(int k=0; k<m; ++k){
		for(int i=1; i<=n; ++i){
			int p = 1; C[i] = 0;
			for(int j=1; j<=i; ++j){
				(p *= pts[k+1] - pts[k] - j + 1) %= MOD;
				(C[i] += ((p * invF[j]) % MOD) * nCr(i-1, j-1)) %= MOD;
			}
		}
		for(int i=0; i<n; ++i){
			valid[i] = a[i] <= pts[k] && pts[k+1] <= b[i]+1;
		}
		for(int i=0; i<n; ++i){
			if(valid[i]){
				int cnt = 1;
				for(int j=i; --j>=0; ){
					if(k) add(dp[i][k], dp[j][k-1] * C[cnt]);
					cnt += valid[j];
				}
				add(dp[i][k], C[cnt]);
				add(ans, dp[i][k]);
			}
			if(k){
				add(dp[i][k], dp[i][k-1]);
			}
		}
	}
	cout << (ans % MOD + MOD) % MOD;
}

• Subtask 1: 9 / 9
• Subtask 2: 0 / 22
• Subtask 3: 0 / 27
• Subtask 4: 0 / 42