oj.uz

Submission #527740

# Submission time Handle Problem Language Result Execution time Memory
527740 2022-02-18T07:01:49 Z pnm1384 Ruins 3 (JOI20_ruins3) C++14
100 / 100
 694 ms 6076 KB 
#include<bits/stdc++.h>
using namespace std;

typedef long long ll;

#define F first
#define S second

const int N = 600 + 5, mod = 1e9 + 7;
int n, h[N][N][2], dp[N][N], pre[N][N], a[N], pa[N], fact[N], inv[N];

inline void add(int &a, int b) {
	a = a+b > mod ? a+b-mod : a+b;
}
inline int mul(int a, int b) {
	return a*1ll*b%mod;
}
int bp(int a, int p) {
	int r = 1;
	while(p) {
		if(p&1) r = mul(a, r);
		a = mul(a, a), p>>=1;
	}
	return r;
}
void setup() {
	for(int i = 0; i < N; i++)
	{
		if(i < 2) fact[i] = inv[i] = 1;
		else fact[i] = i, inv[i] = mod - mul(mod / i, inv[mod % i]);
	}
	for(int* a : {fact, inv})
	{
		for(int i = 2; i < N; i++)
		{
			a[i] = mul(a[i-1], a[i]);
		}
	}
	return;
}
inline int nck(int n, int k) {
	return n < 0 || k > n ? 0 : mul(fact[n], mul(inv[n - k], inv[k]));
}
inline int A(int n, int k) {
	return n < 0 || k > n ? 0 : mul(fact[n], inv[n - k]);
}
void calch() {
	h[0][0][0] = 1;
	for(int i = 0; i < n; i++)
	{
		for(int j = i; j <= n; j++) 
		{
			for(int f = 0; f < 2; f++) 
			{
				add(h[i+1][j][f], mul(h[i][j][f], inv[2]));
				add(h[i+1][j+1][f], h[i][j][f]);
				add(h[i+1][j+2][f], mul(h[i][j][f], inv[2]));
			}
			add(h[i+1][j][1], mul(h[i][j][0], inv[2]));
			add(h[i+1][j+1][1], mul(h[i][j][0], inv[2]));
		}
	}
	return;
}
inline int prod(int l, int r) 
{
	if(r < l) return 1;
	if(l <= 0) return 0;
	return mul(fact[r], inv[l-1]);
}
inline int contrib(int lst, int i) 
{
	int N = lst - (i>1?pa[i-2]:0);
	return prod(N-a[i-1]+1, N);
}
void calcdp() 
{
	dp[0][0] = 1;
	for(int i = 0; i <= n; i++)
	{
		for(int lst = 0; lst <= i; lst++) 
		{
			int q;
			for(int olst = 0; olst < lst; olst++) 
			{
				int dif = lst-olst-1;
				q = pre[i][olst];
				q = mul(q, mul(h[dif][dif][0] + h[dif][dif][1], A(i-olst-1, dif)));
				q = mul(q, contrib(lst, i));
				add(dp[i][lst], q);
			}
			if(i == n || !dp[i][lst]) continue;
			q = 1;
			for(int ni = i+1; ni <= n; ni++) 
			{
				add(pre[ni][lst], mul(q, dp[i][lst]));
				q = mul(q, contrib(lst, ni));
			}
		}
	}
	return;
}
 
int main() {
	ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
	setup();
	cin >> n;
	for(int i = 0; i < n; i++) cin >> a[i];
	reverse(a, a + n);
	if (a[0] != 2 * n) return cout << 0, 0;
	for(int i = 0; i < n; i++) a[i] = a[i] - a[i + 1] - 1;
	pa[0] = a[0];
	for (int i = 1; i < n; i++) pa[i] = pa[i-1] + a[i];
	calch();
	calcdp();
	cout << dp[n][n];
}

Subtask #1
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB Output is correct
2 Correct 1 ms 332 KB Output is correct
3 Correct 1 ms 316 KB Output is correct
4 Correct 1 ms 320 KB Output is correct
5 Correct 1 ms 448 KB Output is correct
6 Correct 1 ms 456 KB Output is correct
7 Correct 0 ms 204 KB Output is correct
8 Correct 1 ms 332 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 1 ms 460 KB Output is correct

Subtask #2
52.0 / 52.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB Output is correct
2 Correct 1 ms 332 KB Output is correct
3 Correct 1 ms 316 KB Output is correct
4 Correct 1 ms 320 KB Output is correct
5 Correct 1 ms 448 KB Output is correct
6 Correct 1 ms 456 KB Output is correct
7 Correct 0 ms 204 KB Output is correct
8 Correct 1 ms 332 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 1 ms 460 KB Output is correct
11 Correct 1 ms 832 KB Output is correct
12 Correct 1 ms 844 KB Output is correct
13 Correct 2 ms 844 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 0 ms 324 KB Output is correct
16 Correct 2 ms 772 KB Output is correct
17 Correct 0 ms 204 KB Output is correct
18 Correct 1 ms 836 KB Output is correct
19 Correct 1 ms 844 KB Output is correct
20 Correct 2 ms 844 KB Output is correct

Subtask #3
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB Output is correct
2 Correct 1 ms 332 KB Output is correct
3 Correct 1 ms 316 KB Output is correct
4 Correct 1 ms 320 KB Output is correct
5 Correct 1 ms 448 KB Output is correct
6 Correct 1 ms 456 KB Output is correct
7 Correct 0 ms 204 KB Output is correct
8 Correct 1 ms 332 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 1 ms 460 KB Output is correct
11 Correct 1 ms 832 KB Output is correct
12 Correct 1 ms 844 KB Output is correct
13 Correct 2 ms 844 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 0 ms 324 KB Output is correct
16 Correct 2 ms 772 KB Output is correct
17 Correct 0 ms 204 KB Output is correct
18 Correct 1 ms 836 KB Output is correct
19 Correct 1 ms 844 KB Output is correct
20 Correct 2 ms 844 KB Output is correct
21 Correct 332 ms 5956 KB Output is correct
22 Correct 294 ms 5956 KB Output is correct
23 Correct 311 ms 5912 KB Output is correct
24 Correct 331 ms 5876 KB Output is correct
25 Correct 0 ms 204 KB Output is correct
26 Correct 320 ms 5880 KB Output is correct
27 Correct 1 ms 332 KB Output is correct
28 Correct 270 ms 5956 KB Output is correct
29 Correct 1 ms 332 KB Output is correct
30 Correct 511 ms 5952 KB Output is correct
31 Correct 656 ms 5964 KB Output is correct
32 Correct 671 ms 5876 KB Output is correct
33 Correct 643 ms 5964 KB Output is correct
34 Correct 668 ms 5928 KB Output is correct
35 Correct 694 ms 5956 KB Output is correct
36 Correct 623 ms 6076 KB Output is correct