Submission #970750

#	Time	Username	Problem	Language	Result	Execution time	Memory
970750		starchan	Boat (APIO16_boat)	C++17	0 / 100	2052 ms	53328 KiB

boat

#include<bits/stdc++.h>
using namespace std;
#define int long long
#define in array<int, 2>
#define pb push_back
#define pob pop_back
#define INF (int)1e17
#define fast() ios_base::sync_with_stdio(false); cin.tie(NULL)

const int mod = 1e9+7; 
const int MX = 5e3+5;


int inv[MX];
int dp[MX][2*MX];
int ans[2*MX];
int R[MX][2*MX];
int C[MX][2*MX];

void pre()
{
	inv[1] = 1;
	for(int i = 2; i < MX; i++)
	{
		inv[i] = (-(mod/i)*inv[mod%i])%mod; inv[i]+=mod;
		inv[i]%=mod;
	}
}

int solve(int a, int b, int c, int d)
{
	int cnt = b+d-a-c;
	for(int i = a; i < b; i++)
	{
		for(int j = c; j < d; j++)
		{
			if(i < j)
				cnt++;
		}
	}
	return cnt;
}

signed main()
{
	fast();
	pre();
	vector<int> v;
	int n;
	cin >> n;
	n++;
	vector<in> a(n+1);
	for(int i = 1; i < n; i++)
	{
		cin >> a[i][0] >> a[i][1]; 
		v.pb(a[i][0]); v.pb(++a[i][1]);
	}
	cout << "EXPECTED ANS = " << solve(a[1][0], a[1][1], a[2][0], a[2][1]) << endl;
	a[n][0] = 1e9+1; a[n][1] = 1e9+2;
	v.pb(a[n][0]); v.pb(a[n][1]);
	sort(v.begin(), v.end());
	vector<int> CC; CC.pb(v[0]);
	for(auto x: v)
	{
		if(x != CC.back())
			CC.pb(x);
	}
	int M = CC.size();
	for(int i = 0; i < M-1; i++)
	{
		C[0][i] = 1; int tm = CC[i+1]-CC[i];
		for(int j = 1; j <= n; j++)
		{
			if(j > tm)
				break;
			C[j][i] = C[j-1][i]*(tm-j+1); C[j][i]%=mod;
			C[j][i]*=inv[j]; C[j][i]%=mod;
		}
		//for(int j = 0; j <= n; j++)
		//	cout << C[j][i] << " ";
		//cout << "\n";
	}
	for(int i = 1; i <= n; i++)
	{
		a[i][0] = lower_bound(CC.begin(), CC.end(), a[i][0])-CC.begin();
		a[i][1] = lower_bound(CC.begin(), CC.end(), a[i][1])-CC.begin();
	}
	for(int i = 0; i < M; i++)
		R[0][i] = ans[i] = 1;
	//cout << endl;
	for(int i = 1; i <= n; i++)
	{
		//cout << "Currently processing i = " << i << endl;
		for(int j = a[i][0]; j < a[i][1]; j++)
		{
			//R[L][j] = number of ways to do stuff if picking L things from jth bracket.
			//cout << "Bracket range = [" << CC[j] << ", " << CC[j+1] << ")" << endl;
			for(int L = 0; L < i; L++)
			{
				//cout << "If we pick L = " << L << " things in the current (" << j << ") bracket, we have: " << endl;
				//cout << R[L][j] << endl;
				dp[i][j]+=((R[L][j]*C[L+1][j])%mod);
			}
			dp[i][j]%=mod;
			for(int T = j; T < M-1; T++)
			{
				ans[T]+=dp[i][j];
				ans[T]%=mod;
			}
			//cout << "For j, computed: " << dp[i][j] << endl;
			//Currently working in intervl [CC[j], CC[j+1])
		}
		for(int j = a[i][0]; j < a[i][1]; j++)
		{
			//how does R[L][j] change?
			for(int L = i; L >= 1; L--)
			{
				R[L][j]+=R[L-1][j];
				R[L][j]%=mod;
			}
		}
		for(int j = 1; j < M-1; j++)
			R[0][j] = ans[j-1];
	}
	dp[n][M-2]+=(mod-1); dp[n][M-2]%=mod;
	cout << dp[n][M-2] << "\n";
	return 0;
}

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