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Submission #76785

# Submission time Handle Problem Language Result Execution time Memory
76785 2018-09-17T20:19:55 Z vex Boat (APIO16_boat) C++14
100 / 100
 840 ms 12940 KB 
#include <bits/stdc++.h>
#define pii pair<int,int>
#define f first
#define s second
#define maxn 505
#define mod (long long)(1e9 + 7)
using namespace std;

long long ste(long long x,long long y)
{
    if(y==0)return 1LL;
    if(y%2==1)return (x*ste(x,y-1))%mod;

    long long ss=ste(x,y/2);
    return (ss*ss)%mod;
}
long long fact[2*maxn];
long long invf[2*maxn];
int d[2*maxn];
long long ff[2*maxn][maxn];
long long dff[2*maxn][maxn];
int n;
void precalc()
{
    fact[0]=1;
    for(int i=1;i<=1000;i++)
    {
        fact[i]=fact[i-1]*i;
        fact[i]%=mod;
    }
    for(int i=0;i<=1000;i++)
        invf[i]=ste(fact[i],mod-2);
        
    for(int i=1;i<=2*n-1;i++)
    {
    	ff[i][1]=d[i+1]-d[i];
    	dff[i][1]=d[i+1]-d[i]-1;
    	for(int j=1;j<500 && d[i+1]-d[i]-j>0;j++)
    	{
    		ff[i][j+1]=ff[i][j]*(d[i+1]-d[i]-j);
    		ff[i][j+1]%=mod;
    		
    		dff[i][j+1]=dff[i][j]*(d[i+1]-d[i]-j-1);
    		dff[i][j+1]%=mod;
    	}
    }
}
long long bc(int x,int y)
{
    if(x<y)return 0;
    if(x<=1000)return (((fact[x]*invf[y])%mod) * invf[x-y] )%mod;

	long long res=1;
	for(int i=0;i<y;i++)
	{
		res*=(x-i);
		res%=mod;
	}
	return (res*invf[y])%mod;
}


pii t[maxn];

long long dp[2*maxn][maxn];

vector<int>tre;
long long pre[maxn];
long long f[2*maxn],gf[2*maxn];

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    
    cin>>n;
    for(int i=1;i<=n;i++)
    {
        cin>>t[i].f>>t[i].s;
        d[2*i-1]=t[i].f;
        d[2*i]=t[i].s;
    }

    sort(d+1,d+1+2*n);
    precalc();

    for(int i=1;i<=n;i++)dp[0][i]=0LL;
    for(int i=1;i<=n;i++)if(t[i].f==d[1])dp[0][i]=1LL;
    dp[0][0]=1LL;
    //for(int i=1;i<=n;i++)cout<<dp[0][i]<<" "<<t[i].f<<" "<<d[0]<<endl;

    for(int i=1;i<=2*n-1;i++)
    {
        for(int j=0;j<=n;j++)dp[i][j]=dp[i-1][j];
        if(d[i]==d[i+1])continue;

        tre.clear();
        for(int j=0;j<=n;j++)
        {
            f[j]=0;
            pre[j]=0;
            gf[j]=0;
        }

        for(int j=1;j<=n;j++)
        {
            if(t[j].f==d[i+1]);
            else if(t[j].f<=d[i] && d[i+1]<=t[j].s);
            else continue;


            for(int k=0;k<j;k++)
            {
                pre[j]+=dp[i-1][k];
                pre[j]%=mod;
            }

            if(t[j].f==d[i+1])
            {
                int sz=tre.size();
                int dd=min(d[i+1]-d[i]-1,sz);
                for(int k=1;k<=dd;k++)
                {
                    long long sss=0;
                    /*for(int kk=sz-k;kk>=0;kk--)
                    {
                        sss+=pre[tre[kk]]*bc(sz-kk-1,k-1);
                        sss%=mod;
                    }*/
                    sss=f[k];
                    dp[i][j]+=(((sss*invf[k])%mod)*dff[i][k])%mod;
                    dp[i][j]%=mod;
                }
                
                dp[i][j]+=pre[j];
                dp[i][j]%=mod;
            }
            else if(t[j].f<=d[i] && d[i+1]<=t[j].s)
            {
                int sz=tre.size();
                int dd=min(d[i+1]-d[i],sz+1);

                for(int k=2;k<=dd;k++)
                {
                    long long sss=0;
                    /*for(int kk=sz+1-k;kk>=0;kk--)
                    {
                        sss+=pre[tre[kk]]*bc(sz-1-kk,k-2);
                        sss%=mod;
                    }*/
                    sss=gf[k];
                    dp[i][j]+=(((sss*invf[k])%mod)*ff[i][k])%mod;
                    dp[i][j]%=mod;
                }
		
	    dp[i][j]+=pre[j]*(d[i+1]-d[i]);
	    dp[i][j]%=mod;
                tre.push_back(j);
                
                for(int k=dd;k>2;k--)
                {
                	gf[k]+=gf[k-1];
                	gf[k]%=mod;
                }
                gf[2]+=pre[j];
                gf[2]%=mod;
                if(sz+2<=d[i+1]-d[i])
                {
                	gf[sz+2]=pre[tre[0]];
                }
                
                
                dd=min(d[i+1]-d[i]-1,sz);
                for(int k=dd;k>1;k--)
                {
                	f[k]+=f[k-1];
                	f[k]%=mod;
                }
                f[1]+=pre[j];
                f[1]%=mod;
                if(sz+1<=d[i+1]-d[i]-1)
                {
            	f[sz+1]=pre[tre[0]];	
                }
            }
        }
    }

    long long sol=0;
    for(int i=1;i<=n;i++)
    {
        sol+=dp[2*n-1][i];
        sol%=mod;
    }
    cout<<sol<<endl;
    return 0;
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 12280 KB Output is correct
2 Correct 16 ms 12280 KB Output is correct
3 Correct 17 ms 12352 KB Output is correct
4 Correct 17 ms 12368 KB Output is correct
5 Correct 16 ms 12428 KB Output is correct
6 Correct 15 ms 12444 KB Output is correct
7 Correct 16 ms 12444 KB Output is correct
8 Correct 15 ms 12444 KB Output is correct
9 Correct 15 ms 12488 KB Output is correct
10 Correct 15 ms 12504 KB Output is correct
11 Correct 17 ms 12504 KB Output is correct
12 Correct 15 ms 12520 KB Output is correct
13 Correct 16 ms 12648 KB Output is correct
14 Correct 16 ms 12648 KB Output is correct
15 Correct 15 ms 12648 KB Output is correct
16 Correct 12 ms 12648 KB Output is correct
17 Correct 13 ms 12648 KB Output is correct
18 Correct 14 ms 12648 KB Output is correct
19 Correct 13 ms 12648 KB Output is correct
20 Correct 12 ms 12648 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 12280 KB Output is correct
2 Correct 16 ms 12280 KB Output is correct
3 Correct 17 ms 12352 KB Output is correct
4 Correct 17 ms 12368 KB Output is correct
5 Correct 16 ms 12428 KB Output is correct
6 Correct 15 ms 12444 KB Output is correct
7 Correct 16 ms 12444 KB Output is correct
8 Correct 15 ms 12444 KB Output is correct
9 Correct 15 ms 12488 KB Output is correct
10 Correct 15 ms 12504 KB Output is correct
11 Correct 17 ms 12504 KB Output is correct
12 Correct 15 ms 12520 KB Output is correct
13 Correct 16 ms 12648 KB Output is correct
14 Correct 16 ms 12648 KB Output is correct
15 Correct 15 ms 12648 KB Output is correct
16 Correct 12 ms 12648 KB Output is correct
17 Correct 13 ms 12648 KB Output is correct
18 Correct 14 ms 12648 KB Output is correct
19 Correct 13 ms 12648 KB Output is correct
20 Correct 12 ms 12648 KB Output is correct
21 Correct 241 ms 12648 KB Output is correct
22 Correct 229 ms 12648 KB Output is correct
23 Correct 215 ms 12648 KB Output is correct
24 Correct 231 ms 12648 KB Output is correct
25 Correct 224 ms 12648 KB Output is correct
26 Correct 315 ms 12648 KB Output is correct
27 Correct 323 ms 12648 KB Output is correct
28 Correct 322 ms 12648 KB Output is correct
29 Correct 315 ms 12648 KB Output is correct
30 Correct 23 ms 12648 KB Output is correct
31 Correct 19 ms 12648 KB Output is correct
32 Correct 20 ms 12648 KB Output is correct
33 Correct 22 ms 12648 KB Output is correct
34 Correct 22 ms 12648 KB Output is correct
35 Correct 19 ms 12648 KB Output is correct
36 Correct 18 ms 12648 KB Output is correct
37 Correct 16 ms 12648 KB Output is correct
38 Correct 17 ms 12648 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 12648 KB Output is correct
2 Correct 8 ms 12648 KB Output is correct
3 Correct 8 ms 12648 KB Output is correct
4 Correct 9 ms 12648 KB Output is correct
5 Correct 9 ms 12648 KB Output is correct
6 Correct 12 ms 12648 KB Output is correct
7 Correct 12 ms 12648 KB Output is correct
8 Correct 12 ms 12648 KB Output is correct
9 Correct 11 ms 12648 KB Output is correct
10 Correct 11 ms 12648 KB Output is correct
11 Correct 11 ms 12648 KB Output is correct
12 Correct 8 ms 12648 KB Output is correct
13 Correct 8 ms 12648 KB Output is correct
14 Correct 8 ms 12648 KB Output is correct
15 Correct 9 ms 12648 KB Output is correct
16 Correct 6 ms 12648 KB Output is correct
17 Correct 6 ms 12648 KB Output is correct
18 Correct 6 ms 12648 KB Output is correct
19 Correct 6 ms 12648 KB Output is correct
20 Correct 6 ms 12648 KB Output is correct

Subtask #4
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 12280 KB Output is correct
2 Correct 16 ms 12280 KB Output is correct
3 Correct 17 ms 12352 KB Output is correct
4 Correct 17 ms 12368 KB Output is correct
5 Correct 16 ms 12428 KB Output is correct
6 Correct 15 ms 12444 KB Output is correct
7 Correct 16 ms 12444 KB Output is correct
8 Correct 15 ms 12444 KB Output is correct
9 Correct 15 ms 12488 KB Output is correct
10 Correct 15 ms 12504 KB Output is correct
11 Correct 17 ms 12504 KB Output is correct
12 Correct 15 ms 12520 KB Output is correct
13 Correct 16 ms 12648 KB Output is correct
14 Correct 16 ms 12648 KB Output is correct
15 Correct 15 ms 12648 KB Output is correct
16 Correct 12 ms 12648 KB Output is correct
17 Correct 13 ms 12648 KB Output is correct
18 Correct 14 ms 12648 KB Output is correct
19 Correct 13 ms 12648 KB Output is correct
20 Correct 12 ms 12648 KB Output is correct
21 Correct 241 ms 12648 KB Output is correct
22 Correct 229 ms 12648 KB Output is correct
23 Correct 215 ms 12648 KB Output is correct
24 Correct 231 ms 12648 KB Output is correct
25 Correct 224 ms 12648 KB Output is correct
26 Correct 315 ms 12648 KB Output is correct
27 Correct 323 ms 12648 KB Output is correct
28 Correct 322 ms 12648 KB Output is correct
29 Correct 315 ms 12648 KB Output is correct
30 Correct 23 ms 12648 KB Output is correct
31 Correct 19 ms 12648 KB Output is correct
32 Correct 20 ms 12648 KB Output is correct
33 Correct 22 ms 12648 KB Output is correct
34 Correct 22 ms 12648 KB Output is correct
35 Correct 19 ms 12648 KB Output is correct
36 Correct 18 ms 12648 KB Output is correct
37 Correct 16 ms 12648 KB Output is correct
38 Correct 17 ms 12648 KB Output is correct
39 Correct 8 ms 12648 KB Output is correct
40 Correct 8 ms 12648 KB Output is correct
41 Correct 8 ms 12648 KB Output is correct
42 Correct 9 ms 12648 KB Output is correct
43 Correct 9 ms 12648 KB Output is correct
44 Correct 12 ms 12648 KB Output is correct
45 Correct 12 ms 12648 KB Output is correct
46 Correct 12 ms 12648 KB Output is correct
47 Correct 11 ms 12648 KB Output is correct
48 Correct 11 ms 12648 KB Output is correct
49 Correct 11 ms 12648 KB Output is correct
50 Correct 8 ms 12648 KB Output is correct
51 Correct 8 ms 12648 KB Output is correct
52 Correct 8 ms 12648 KB Output is correct
53 Correct 9 ms 12648 KB Output is correct
54 Correct 6 ms 12648 KB Output is correct
55 Correct 6 ms 12648 KB Output is correct
56 Correct 6 ms 12648 KB Output is correct
57 Correct 6 ms 12648 KB Output is correct
58 Correct 6 ms 12648 KB Output is correct
59 Correct 446 ms 12648 KB Output is correct
60 Correct 412 ms 12712 KB Output is correct
61 Correct 396 ms 12712 KB Output is correct
62 Correct 457 ms 12712 KB Output is correct
63 Correct 439 ms 12712 KB Output is correct
64 Correct 818 ms 12712 KB Output is correct
65 Correct 822 ms 12816 KB Output is correct
66 Correct 806 ms 12840 KB Output is correct
67 Correct 840 ms 12840 KB Output is correct
68 Correct 807 ms 12840 KB Output is correct
69 Correct 360 ms 12876 KB Output is correct
70 Correct 364 ms 12876 KB Output is correct
71 Correct 363 ms 12876 KB Output is correct
72 Correct 381 ms 12928 KB Output is correct
73 Correct 386 ms 12940 KB Output is correct
74 Correct 57 ms 12940 KB Output is correct
75 Correct 55 ms 12940 KB Output is correct
76 Correct 136 ms 12940 KB Output is correct
77 Correct 57 ms 12940 KB Output is correct
78 Correct 59 ms 12940 KB Output is correct