oj.uz

Submission #212445

# Submission time Handle Problem Language Result Execution time Memory
212445 2020-03-23T04:05:23 Z zscoder Ruins 3 (JOI20_ruins3) C++17
100 / 100
 850 ms 504 KB 
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;
 
#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define fbo find_by_order
#define ook order_of_key
 
typedef long long ll;
typedef pair<int,int> ii;
typedef vector<int> vi;
typedef long double ld; 
typedef tree<ll, null_type, less<ll>, rb_tree_tag, tree_order_statistics_node_update> pbds;

vector<int> fact;
vector<int> ifact;
vector<int> inv;
vector<int> pow2;
const int MOD = (1e9 + 7);
int add(int a, int b)
{
	a+=b;
	while(a>=MOD) a-=MOD;
	return a;
}
void radd(int &a, int b)
{
	a=add(a,b); 
}
int mult(int a, int b)
{
	return (a*1LL*b)%MOD;
}
void rmult(int &a, int b)
{
	a=mult(a,b);
}
int modpow(int a, int b)
{
	int r=1;
	while(b)
	{
		if(b&1) r=mult(r,a);
		a=mult(a,a);
		b>>=1;
	}
	return r;
}
int choose(int a, int b)
{
	if(a<b) return 0;
	if(b==0) return 1;
	if(a==b) return 1;
	return mult(fact[a],mult(ifact[b],ifact[a-b]));
}
int inverse(int a)
{
	return modpow(a,MOD-2);
}
void init(int _n)
{
	fact.clear(); ifact.clear(); inv.clear(); pow2.clear();
	fact.resize(_n+1);
	ifact.resize(_n+1);
	inv.resize(_n+1);
	pow2.resize(_n+1);
	pow2[0]=1;
	ifact[0]=1;
	fact[0]=1;
	for(int i=1;i<=_n;i++)
	{
		pow2[i]=add(pow2[i-1],pow2[i-1]);
		fact[i]=mult(fact[i-1],i);
		//ifact[i]=mult(ifact[i-1],inv[i]);
	}
	ifact[_n] = inverse(fact[_n]);
	for(int i=_n-1;i>=1;i--)
	{
		ifact[i] = mult(ifact[i + 1], i + 1);
	}
	for(int i=1;i<=_n;i++)
	{
		inv[i] = mult(fact[i-1],ifact[i]);
	}
}
	
int ways[2222];

int p2(int x)
{
	if(x>=0) return pow2[x];
	else return inverse(pow2[-x]);
}

int ok[2222];
int main()
{
	ios_base::sync_with_stdio(0); cin.tie(0);
	init(2222);
	int n; cin>>n;
	vi f(n+1);
	vi g(n+1);
	g[0]=f[0]=1;
	//remember, cases like 3,3,4,4 are VALID
	//a[i]>=i, each a[i] appears at most 2 times, count such sequences then shuffle
	//count occurrences of a[i] in reverse order (e.g: 2,1,1,0)
	//we want sum of brk(S)
	for(int i=1;i<=n;i++) 
	{
		f[i]=mult(choose(2*(i+1),i+1),inv[i+2]);
		//cerr<<"F: "<<i<<' '<<f[i]<<'\n';
	}
	for(int i=1;i<=n;i++)
	{
		g[i]=f[i];
		for(int j=1;j<i;j++)
		{
			radd(g[i],MOD-mult(g[j],f[i-j]));
		}
		//cerr<<"G "<<i<<" = "<<g[i]<<'\n';
	}
	for(int i=1;i<=n;i++)
	{
		int ans=0;
		for(int j=1;j<=i;j++)
		{
			radd(ans,mult(j,mult(g[j],f[i-j])));
		}
		ans = mult(ans,fact[i-1]);
		ways[i]=ans;
	}
	for(int i=0;i<n;i++)
	{
		int x; cin>>x; x--;
		ok[x]=1;
	}
	vi old(n+1,0);
	old[0]=1;
	int surv=0;
	int ded=0;
	for(int i=2*n-1;i>=0;i--)
	{
		vi nw(n+1,0);
		if(ok[i])
		{
			for(int j=ded;j<=surv;j++)
			{
				radd(nw[j],old[j]);
				for(int k=j+1;k<=surv+1;k++)
				{
					//most recent one must be chosen, so k-j-1 slots left
					radd(nw[k],mult(old[j],mult(choose(surv-j,k-j-1),ways[k-j])));
				}
			}
		}
		else
		{
			for(int j=ded;j<=surv;j++)
			{
				radd(nw[j],mult(old[j],j-ded));
			}
		}
		if(ok[i]) surv++;
		else ded++;
		old=nw;
	}
	cout<<mult(old[n],p2(-n))<<'\n';
}

Subtask #1
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB Output is correct
2 Correct 5 ms 384 KB Output is correct
3 Correct 5 ms 384 KB Output is correct
4 Correct 4 ms 384 KB Output is correct
5 Correct 5 ms 384 KB Output is correct
6 Correct 4 ms 384 KB Output is correct
7 Correct 5 ms 384 KB Output is correct
8 Correct 5 ms 384 KB Output is correct
9 Correct 4 ms 384 KB Output is correct
10 Correct 5 ms 384 KB Output is correct

Subtask #2
52.0 / 52.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB Output is correct
2 Correct 5 ms 384 KB Output is correct
3 Correct 5 ms 384 KB Output is correct
4 Correct 4 ms 384 KB Output is correct
5 Correct 5 ms 384 KB Output is correct
6 Correct 4 ms 384 KB Output is correct
7 Correct 5 ms 384 KB Output is correct
8 Correct 5 ms 384 KB Output is correct
9 Correct 4 ms 384 KB Output is correct
10 Correct 5 ms 384 KB Output is correct
11 Correct 5 ms 384 KB Output is correct
12 Correct 5 ms 384 KB Output is correct
13 Correct 4 ms 384 KB Output is correct
14 Correct 5 ms 384 KB Output is correct
15 Correct 6 ms 384 KB Output is correct
16 Correct 5 ms 384 KB Output is correct
17 Correct 4 ms 384 KB Output is correct
18 Correct 5 ms 384 KB Output is correct
19 Correct 5 ms 384 KB Output is correct
20 Correct 5 ms 384 KB Output is correct

Subtask #3
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB Output is correct
2 Correct 5 ms 384 KB Output is correct
3 Correct 5 ms 384 KB Output is correct
4 Correct 4 ms 384 KB Output is correct
5 Correct 5 ms 384 KB Output is correct
6 Correct 4 ms 384 KB Output is correct
7 Correct 5 ms 384 KB Output is correct
8 Correct 5 ms 384 KB Output is correct
9 Correct 4 ms 384 KB Output is correct
10 Correct 5 ms 384 KB Output is correct
11 Correct 5 ms 384 KB Output is correct
12 Correct 5 ms 384 KB Output is correct
13 Correct 4 ms 384 KB Output is correct
14 Correct 5 ms 384 KB Output is correct
15 Correct 6 ms 384 KB Output is correct
16 Correct 5 ms 384 KB Output is correct
17 Correct 4 ms 384 KB Output is correct
18 Correct 5 ms 384 KB Output is correct
19 Correct 5 ms 384 KB Output is correct
20 Correct 5 ms 384 KB Output is correct
21 Correct 11 ms 384 KB Output is correct
22 Correct 9 ms 384 KB Output is correct
23 Correct 10 ms 384 KB Output is correct
24 Correct 17 ms 384 KB Output is correct
25 Correct 8 ms 384 KB Output is correct
26 Correct 9 ms 384 KB Output is correct
27 Correct 8 ms 384 KB Output is correct
28 Correct 7 ms 384 KB Output is correct
29 Correct 8 ms 384 KB Output is correct
30 Correct 850 ms 384 KB Output is correct
31 Correct 429 ms 384 KB Output is correct
32 Correct 632 ms 504 KB Output is correct
33 Correct 792 ms 444 KB Output is correct
34 Correct 439 ms 504 KB Output is correct
35 Correct 652 ms 468 KB Output is correct
36 Correct 786 ms 440 KB Output is correct