Submission #76784

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
76784	2018-09-17T19:51:27 Z	vex	Boat (APIO16_boat)	C++14	58 / 100	2000 ms	12748 KB

boat

#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;
                    }
                    dp[i][j]+=(((sss*invf[k])%mod)*dff[i][k])%mod;//bc(d[i+1]-d[i]-1,k);
                    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;
                    }
                    dp[i][j]+=(((sss*invf[k])%mod)*ff[i][k])%mod;//bc(d[i+1]-d[i],k);
                    dp[i][j]%=mod;
                }
		
	    dp[i][j]+=pre[j]*(d[i+1]-d[i]);
	    dp[i][j]%=mod;
                tre.push_back(j);
            }
            /*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++)
                {
                    dp[i][j]+=bc(d[i+1]-d[i]-1,k)*f[k];
                    dp[i][j]%=mod;
                }

                dp[i][j]+=pre[j];
            }

            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);

                dp[i][j]+=(d[i+1]-d[i])*pre[j];
                dp[i][j]%=mod;

                for(int k=2;k<=dd;k++)
                {
                    dp[i][j]+=bc(d[i+1]-d[i],k)*gf[k];
                    dp[i][j]%=mod;
                }

                for(int k=dd;k>2;k--)
                {
                    gf[k]+=gf[k-1];
                    gf[k]%=mod;
                }
                gf[2]+=pre[j];
                gf[2]%=mod;

                ///!!!!!
                ///BAGA OVDE

                tre.push_back(j);
                sz++;
                if(sz+1<=d[i+1]-d[i])
                {
                    gf[sz+2]=pre[tre[0]];
                }


                for(int k=dd;k>1;k--)
                {
                    f[k]+=f[k-1];
                    f[k]%=mod;
                }
                f[1]+=pre[j];
                f[1]%=mod;
                if(sz<=d[i+1]-d[i])
                {
                    f[sz]=pre[tre[0]];
                }
            }*/
        }


        //for(int j=1;j<=n;j++)cout<<pre[j]<<" ";cout<<endl;
    }


    //for(int i=1;i<=n;i++)cout<<i<<"   "<<t[i].f<<" "<<t[i].s<<endl;
    //for(int i=1;i<=2*n;i++)cout<<d[i]<<" ";cout<<endl;
    /*for(int i=0;i<=2*n-1;i++)
    {
        cout<<i<<"     ";
        for(int j=1;j<=n;j++)cout<<dp[i][j]<<" ";
        cout<<endl;
    }*/


    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	17 ms	12284 KB	Output is correct
2	Correct	16 ms	12284 KB	Output is correct
3	Correct	16 ms	12344 KB	Output is correct
4	Correct	16 ms	12464 KB	Output is correct
5	Correct	16 ms	12548 KB	Output is correct
6	Correct	15 ms	12548 KB	Output is correct
7	Correct	16 ms	12548 KB	Output is correct
8	Correct	16 ms	12548 KB	Output is correct
9	Correct	21 ms	12548 KB	Output is correct
10	Correct	15 ms	12548 KB	Output is correct
11	Correct	19 ms	12548 KB	Output is correct
12	Correct	16 ms	12612 KB	Output is correct
13	Correct	15 ms	12612 KB	Output is correct
14	Correct	15 ms	12640 KB	Output is correct
15	Correct	15 ms	12640 KB	Output is correct
16	Correct	12 ms	12640 KB	Output is correct
17	Correct	12 ms	12640 KB	Output is correct
18	Correct	12 ms	12640 KB	Output is correct
19	Correct	13 ms	12640 KB	Output is correct
20	Correct	12 ms	12640 KB	Output is correct

Subtask #2
22.0 / 22.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	17 ms	12284 KB	Output is correct
2	Correct	16 ms	12284 KB	Output is correct
3	Correct	16 ms	12344 KB	Output is correct
4	Correct	16 ms	12464 KB	Output is correct
5	Correct	16 ms	12548 KB	Output is correct
6	Correct	15 ms	12548 KB	Output is correct
7	Correct	16 ms	12548 KB	Output is correct
8	Correct	16 ms	12548 KB	Output is correct
9	Correct	21 ms	12548 KB	Output is correct
10	Correct	15 ms	12548 KB	Output is correct
11	Correct	19 ms	12548 KB	Output is correct
12	Correct	16 ms	12612 KB	Output is correct
13	Correct	15 ms	12612 KB	Output is correct
14	Correct	15 ms	12640 KB	Output is correct
15	Correct	15 ms	12640 KB	Output is correct
16	Correct	12 ms	12640 KB	Output is correct
17	Correct	12 ms	12640 KB	Output is correct
18	Correct	12 ms	12640 KB	Output is correct
19	Correct	13 ms	12640 KB	Output is correct
20	Correct	12 ms	12640 KB	Output is correct
21	Correct	900 ms	12748 KB	Output is correct
22	Correct	881 ms	12748 KB	Output is correct
23	Correct	776 ms	12748 KB	Output is correct
24	Correct	892 ms	12748 KB	Output is correct
25	Correct	878 ms	12748 KB	Output is correct
26	Correct	1524 ms	12748 KB	Output is correct
27	Correct	1448 ms	12748 KB	Output is correct
28	Correct	1435 ms	12748 KB	Output is correct
29	Correct	1481 ms	12748 KB	Output is correct
30	Correct	19 ms	12748 KB	Output is correct
31	Correct	19 ms	12748 KB	Output is correct
32	Correct	18 ms	12748 KB	Output is correct
33	Correct	19 ms	12748 KB	Output is correct
34	Correct	19 ms	12748 KB	Output is correct
35	Correct	18 ms	12748 KB	Output is correct
36	Correct	17 ms	12748 KB	Output is correct
37	Correct	17 ms	12748 KB	Output is correct
38	Correct	17 ms	12748 KB	Output is correct

Subtask #3
27.0 / 27.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	27 ms	12748 KB	Output is correct
2	Correct	18 ms	12748 KB	Output is correct
3	Correct	24 ms	12748 KB	Output is correct
4	Correct	25 ms	12748 KB	Output is correct
5	Correct	30 ms	12748 KB	Output is correct
6	Correct	86 ms	12748 KB	Output is correct
7	Correct	88 ms	12748 KB	Output is correct
8	Correct	88 ms	12748 KB	Output is correct
9	Correct	84 ms	12748 KB	Output is correct
10	Correct	86 ms	12748 KB	Output is correct
11	Correct	30 ms	12748 KB	Output is correct
12	Correct	19 ms	12748 KB	Output is correct
13	Correct	25 ms	12748 KB	Output is correct
14	Correct	25 ms	12748 KB	Output is correct
15	Correct	30 ms	12748 KB	Output is correct
16	Correct	15 ms	12748 KB	Output is correct
17	Correct	12 ms	12748 KB	Output is correct
18	Correct	14 ms	12748 KB	Output is correct
19	Correct	12 ms	12748 KB	Output is correct
20	Correct	19 ms	12748 KB	Output is correct

Subtask #4
0 / 42.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	17 ms	12284 KB	Output is correct
2	Correct	16 ms	12284 KB	Output is correct
3	Correct	16 ms	12344 KB	Output is correct
4	Correct	16 ms	12464 KB	Output is correct
5	Correct	16 ms	12548 KB	Output is correct
6	Correct	15 ms	12548 KB	Output is correct
7	Correct	16 ms	12548 KB	Output is correct
8	Correct	16 ms	12548 KB	Output is correct
9	Correct	21 ms	12548 KB	Output is correct
10	Correct	15 ms	12548 KB	Output is correct
11	Correct	19 ms	12548 KB	Output is correct
12	Correct	16 ms	12612 KB	Output is correct
13	Correct	15 ms	12612 KB	Output is correct
14	Correct	15 ms	12640 KB	Output is correct
15	Correct	15 ms	12640 KB	Output is correct
16	Correct	12 ms	12640 KB	Output is correct
17	Correct	12 ms	12640 KB	Output is correct
18	Correct	12 ms	12640 KB	Output is correct
19	Correct	13 ms	12640 KB	Output is correct
20	Correct	12 ms	12640 KB	Output is correct
21	Correct	900 ms	12748 KB	Output is correct
22	Correct	881 ms	12748 KB	Output is correct
23	Correct	776 ms	12748 KB	Output is correct
24	Correct	892 ms	12748 KB	Output is correct
25	Correct	878 ms	12748 KB	Output is correct
26	Correct	1524 ms	12748 KB	Output is correct
27	Correct	1448 ms	12748 KB	Output is correct
28	Correct	1435 ms	12748 KB	Output is correct
29	Correct	1481 ms	12748 KB	Output is correct
30	Correct	19 ms	12748 KB	Output is correct
31	Correct	19 ms	12748 KB	Output is correct
32	Correct	18 ms	12748 KB	Output is correct
33	Correct	19 ms	12748 KB	Output is correct
34	Correct	19 ms	12748 KB	Output is correct
35	Correct	18 ms	12748 KB	Output is correct
36	Correct	17 ms	12748 KB	Output is correct
37	Correct	17 ms	12748 KB	Output is correct
38	Correct	17 ms	12748 KB	Output is correct
39	Correct	27 ms	12748 KB	Output is correct
40	Correct	18 ms	12748 KB	Output is correct
41	Correct	24 ms	12748 KB	Output is correct
42	Correct	25 ms	12748 KB	Output is correct
43	Correct	30 ms	12748 KB	Output is correct
44	Correct	86 ms	12748 KB	Output is correct
45	Correct	88 ms	12748 KB	Output is correct
46	Correct	88 ms	12748 KB	Output is correct
47	Correct	84 ms	12748 KB	Output is correct
48	Correct	86 ms	12748 KB	Output is correct
49	Correct	30 ms	12748 KB	Output is correct
50	Correct	19 ms	12748 KB	Output is correct
51	Correct	25 ms	12748 KB	Output is correct
52	Correct	25 ms	12748 KB	Output is correct
53	Correct	30 ms	12748 KB	Output is correct
54	Correct	15 ms	12748 KB	Output is correct
55	Correct	12 ms	12748 KB	Output is correct
56	Correct	14 ms	12748 KB	Output is correct
57	Correct	12 ms	12748 KB	Output is correct
58	Correct	19 ms	12748 KB	Output is correct
59	Execution timed out	2062 ms	12748 KB	Time limit exceeded
60	Halted	0 ms	0 KB	-

Submission #76784

Compilation message

Subtask #1 9.0 / 9.0

Subtask #2 22.0 / 22.0

Subtask #3 27.0 / 27.0

Subtask #4 0 / 42.0

Subtask #1
9.0 / 9.0

Subtask #2
22.0 / 22.0

Subtask #3
27.0 / 27.0

Subtask #4
0 / 42.0