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Submission #763656

# Submission time Handle Problem Language Result Execution time Memory
763656 2023-06-22T15:08:44 Z parsadox2 Ruins 3 (JOI20_ruins3) C++14
100 / 100
 458 ms 3216 KB 
#include <bits/stdc++.h>
#define pb 		push_back
#define F		first
#define S 		second
#define debug(x)    cout << #x << "= " << x << ", "
#define ll 		long long
#define fast 		ios::sync_with_stdio(false), cin.tie(0),  cout.tie(0)
#define SZ(x)         (int) x.size()
#define wall 		cout << endl;
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

const int maxn = 605 , maxl = 1205 , mod = 1e9 + 7;
int n , ar[maxl] , fac[maxl] , dp[maxl][maxn] , f[maxn] , m2[maxn] , frev[maxl];

int mpo(int a , int b)
{
	int res = 1;
	while(b != 0)
	{
		if(b & 1)  res = 1LL * res * a % mod;
		b >>= 1;
		a = 1LL * a * a % mod;
	}
	return res;
}

int C(int a , int b)
{
	if(b > a || b < 0 || a < 0)  return 0;
	int res = 1LL * fac[a] * frev[b] % mod;
	res = 1LL * res * frev[a - b] % mod;
	return res;
}

int32_t main()
{
	fast;
	cin >> n;
	int m = n * 2;
	for(int i = 0 ; i < n ; i++)
	{
		int x ;  cin >> x;
		ar[x] = 1;
	}
	fac[0] = fac[1] = frev[0] = frev[1] = 1;
	for(int i = 2 ; i < maxl ; i++)
	{
		fac[i] = 1LL * fac[i - 1] * i % mod;
		frev[i] = mpo(fac[i] , mod - 2);
	}
	m2[0] = 1;
	for(int i = 1 ; i < maxn ; i++)  m2[i] = m2[i - 1] * 2 % mod;
	f[0] = 1;
	for(int i = 1 ; i < maxn ; i++)
	{
		for(int j = 0 ; 2 * j <= i ; j++)
		{
			int tmp = (C(2 * j , j) - C(2 * j , j - 1) + mod) % mod;
			tmp = 1LL * tmp * C(i , 2 * j) % mod;
			tmp = 1LL * tmp * m2[i - 2 * j] % mod;
			tmp = 1LL * tmp * fac[i] % mod;
			f[i] = (f[i] + tmp) % mod;
		}
	}

	if(ar[m] == 0)  
	{
		cout << 0 << endl;  return 0;
	}
	int cntz = 0 , cnto = 1;
	dp[m][0] = 1;  dp[m][1] = 2;
	for(int i = m - 1 ; i > 0 ; i--)
	{
		if(ar[i] == 0)  cntz++;
		else cnto++;
		if(ar[i] == 0)
			for(int j = cntz ; j <= cnto ; j++)
				dp[i][j] = 1LL * dp[i + 1][j] * (j - cntz + 1) % mod;
		else
		{
			for(int j = cntz ; j <= cnto ; j++)
			{
				dp[i][j] = dp[i + 1][j];
				for(int k = cntz ; k < j ; k++)
				{
					int tmp = 1LL * f[j - k - 1] * C(cnto - k - 1 , j - k - 1) % mod;
					tmp = 1LL * tmp * (j - k + 1) % mod;
					tmp = 1LL * tmp * dp[i + 1][k] % mod;
					dp[i][j] = (dp[i][j] + tmp) % mod;
				}
			}
		}
	}
	int ans = mpo(m2[n] , mod - 2);
	ans = 1LL * ans * dp[1][n] % mod;
	cout << ans << endl;
	return 0;
}

Subtask #1
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 340 KB Output is correct
2 Correct 3 ms 468 KB Output is correct
3 Correct 3 ms 340 KB Output is correct
4 Correct 2 ms 340 KB Output is correct
5 Correct 3 ms 340 KB Output is correct
6 Correct 2 ms 340 KB Output is correct
7 Correct 2 ms 340 KB Output is correct
8 Correct 2 ms 340 KB Output is correct
9 Correct 2 ms 340 KB Output is correct
10 Correct 2 ms 340 KB Output is correct

Subtask #2
52.0 / 52.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 340 KB Output is correct
2 Correct 3 ms 468 KB Output is correct
3 Correct 3 ms 340 KB Output is correct
4 Correct 2 ms 340 KB Output is correct
5 Correct 3 ms 340 KB Output is correct
6 Correct 2 ms 340 KB Output is correct
7 Correct 2 ms 340 KB Output is correct
8 Correct 2 ms 340 KB Output is correct
9 Correct 2 ms 340 KB Output is correct
10 Correct 2 ms 340 KB Output is correct
11 Correct 3 ms 596 KB Output is correct
12 Correct 3 ms 596 KB Output is correct
13 Correct 3 ms 596 KB Output is correct
14 Correct 2 ms 340 KB Output is correct
15 Correct 2 ms 340 KB Output is correct
16 Correct 3 ms 596 KB Output is correct
17 Correct 3 ms 340 KB Output is correct
18 Correct 3 ms 596 KB Output is correct
19 Correct 3 ms 596 KB Output is correct
20 Correct 3 ms 552 KB Output is correct

Subtask #3
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 340 KB Output is correct
2 Correct 3 ms 468 KB Output is correct
3 Correct 3 ms 340 KB Output is correct
4 Correct 2 ms 340 KB Output is correct
5 Correct 3 ms 340 KB Output is correct
6 Correct 2 ms 340 KB Output is correct
7 Correct 2 ms 340 KB Output is correct
8 Correct 2 ms 340 KB Output is correct
9 Correct 2 ms 340 KB Output is correct
10 Correct 2 ms 340 KB Output is correct
11 Correct 3 ms 596 KB Output is correct
12 Correct 3 ms 596 KB Output is correct
13 Correct 3 ms 596 KB Output is correct
14 Correct 2 ms 340 KB Output is correct
15 Correct 2 ms 340 KB Output is correct
16 Correct 3 ms 596 KB Output is correct
17 Correct 3 ms 340 KB Output is correct
18 Correct 3 ms 596 KB Output is correct
19 Correct 3 ms 596 KB Output is correct
20 Correct 3 ms 552 KB Output is correct
21 Correct 5 ms 3156 KB Output is correct
22 Correct 5 ms 3156 KB Output is correct
23 Correct 5 ms 3156 KB Output is correct
24 Correct 8 ms 3156 KB Output is correct
25 Correct 2 ms 340 KB Output is correct
26 Correct 4 ms 3156 KB Output is correct
27 Correct 2 ms 340 KB Output is correct
28 Correct 3 ms 3112 KB Output is correct
29 Correct 2 ms 340 KB Output is correct
30 Correct 458 ms 3136 KB Output is correct
31 Correct 230 ms 3100 KB Output is correct
32 Correct 331 ms 3092 KB Output is correct
33 Correct 420 ms 3216 KB Output is correct
34 Correct 224 ms 3148 KB Output is correct
35 Correct 334 ms 3136 KB Output is correct
36 Correct 416 ms 3052 KB Output is correct