Submission #219914

#	Time	Username	Problem	Language	Result	Execution time	Memory
219914		MKopchev	Boat (APIO16_boat)	C++14	58 / 100	2089 ms	17656 KiB

boat

#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
#pragma GCC optimize ("unroll-loops")

#include<bits/stdc++.h>
using namespace std;
const int nmax=1e3+42,mod=1e9+7;

int my_pow(long long a,int b)
{
    long long ret=1;
    while(b)
    {
        if(b%2)ret=ret*a%mod;
        a=a*a%mod;
        b=b/2;
    }
    return ret;
}

int n;
pair<int,int> inp[nmax];

set< pair<int,int> > seen;

pair<int,int> groups[nmax];
int pointer=0;

int inv[nmax];

int dp[nmax][nmax][2];

int coeff[nmax][nmax];

int rec(int which_number,int last_used_group,bool can_place_zero)
{
    if(which_number>n)return 1;//properly chosen
    if(last_used_group==pointer)return can_place_zero;//skipped too much

    if(dp[which_number][last_used_group][can_place_zero]!=-1)return dp[which_number][last_used_group][can_place_zero];

    long long ret=0;

    //place zero
    if(can_place_zero)ret=(ret+rec(which_number+1,last_used_group,1))%mod;

    //place non-zero for other group
    ret=(ret+rec(which_number,last_used_group+1,0))%mod;//ignore this group

    //place non-zero
    if(inp[which_number].first<=groups[last_used_group+1].first&&groups[last_used_group+1].second<=inp[which_number].second)
    {
        int nums=0;
        for(int use=which_number;use<=n;use++)
        {
            if(inp[use].first<=groups[last_used_group+1].first&&groups[last_used_group+1].second<=inp[use].second)
            {
                nums++;
                ret=(ret+1LL*coeff[last_used_group+1][nums]*rec(use+1,last_used_group+1,1))%mod;
            }
            //cout<<"which_number= "<<which_number<<" last_used_group= "<<last_used_group<<" use= "<<use<<" mult= "<<coeff[last_used_group+1][nums]<<" can_place_zero= "<<can_place_zero<<" finish= "<<rec(use+1,last_used_group+1,1)<<endl;
        }
    }
    dp[which_number][last_used_group][can_place_zero]=ret;

    //cout<<which_number<<" "<<last_used_group<<" "<<can_place_zero<<" -> "<<ret<<endl;

    return ret;
}

int C[nmax][nmax];

int ask_C(int n_,int k_)
{
    if(0>k_||k_>n_)return 0;
    return C[n_][k_];
}
//mod= 1000000007

const long long M=18446743944;//(1<<64)/mod

const unsigned int MX_VAL_INT=4294967295;
const unsigned long long MX_VAL_LONG=18446744073709551615;

const unsigned long long M1=M>>32;
const unsigned long long M2=M&MX_VAL_INT;

int barreet(long long a)
{
    unsigned int a1=a>>32;
    unsigned int a2=a&MX_VAL_INT;

    unsigned long long val_32=M1*a2+M2*a1;
    unsigned long long val_0=M2*a2;

    unsigned long long q=M1;
    q=q*a1;

    q=q+(val_32>>32);
    val_32=val_32&MX_VAL_INT;

    val_32=val_32>>32;

    if(MX_VAL_LONG-val_0<val_32)q++;

    unsigned int r=a-q*mod;
    if(r >= mod) r= r - mod;

    //assert(r==a%mod);

    return r;
}
/*
typedef unsigned long long ull;
typedef __uint128_t L;
struct FastMod {
	ull b, m;
	FastMod(ull b) : b(b), m(ull((L(1) << 64) / b)) {}
	ull reduce(ull a) {
		ull q = (ull)((L(m) * a) >> 64), r = a - q * b;
		return r >= b ? r - b : r;
	}
};
*/
int main()
{
    memset(dp,-1,sizeof(dp));

    for(int i=0;i<nmax;i++)
        for(int j=0;j<=i;j++)
            if(j==0||j==i)C[i][j]=1;
            else C[i][j]=(C[i-1][j]+C[i-1][j-1])%mod;

    scanf("%i",&n);

    for(int i=1;i<nmax;i++)
    {
        inv[i]=my_pow(i,mod-2);
    }

    int prv=1e9;
    for(int i=1;i<=n;i++)
    {
        scanf("%i%i",&inp[i].first,&inp[i].second);

        seen.insert({inp[i].first,-1});
        seen.insert({inp[i].second,0});

        prv=min(prv,inp[i].first);
        prv=min(prv,inp[i].second);
    }

    for(auto k:seen)
    {
        int other=k.first+k.second;
        if(prv<=other)
        {
            pointer++;
            groups[pointer]={prv,other};
            prv=other+1;
        }
    }
    /*
    for(int i=1;i<=n;i++)
        for(int j=1;j<=pointer;j++)
        {
            int le=max(inp[i].first,groups[j].first);
            int ri=min(inp[i].second,groups[j].second);

            if(le>ri)continue;

            assert(le==groups[j].first&&ri==groups[j].second);
        }

    cout<<"---"<<endl;
    for(int i=1;i<=pointer;i++)cout<<groups[i].first<<" "<<groups[i].second<<endl;
    */
    for(int which=1;which<=pointer;which++)
        for(int nums=1;nums<=n;nums++)
        {
            int total=groups[which].second-groups[which].first+1;

            if(nums==1)coeff[which][1]=total;
            else
            {
                long long coeff_help=total;
                for(int zero=nums-2;zero>=0;zero--)
                {
                    if(total<nums-zero)coeff_help=0;
                    else if(total==nums-zero)coeff_help=1;
                    else coeff_help=barreet(1LL*barreet(coeff_help*(total-(nums-zero)+1))*inv[nums-zero]);

                    //cout<<"zero= "<<zero<<" "<<total-(nums-zero)+1<<" , "<<nums-zero<<" actual= "<<inv[nums-zero]<<endl;
                    //cout<<"zero= "<<zero<<" "<<coeff_help<<" "<<ask_C(total,nums-zero)<<endl;

                    //if(coeff_help!=ask_C(total,nums-zero))system("pause");
                    coeff[which][nums]=barreet(coeff[which][nums]+1LL*ask_C(nums-2,zero)*coeff_help);
                }
            }

            //cout<<which<<" "<<nums<<" -> "<<coeff[which][nums]<<endl;
            //cout<<"---"<<endl;
        }

    int out=rec(1,0,1);

    out=(out-1+mod)%mod;

    printf("%i\n",out);
    return 0;
}

Compilation message (stderr)

boat.cpp:83:38: warning: integer constant is so large that it is unsigned
 const unsigned long long MX_VAL_LONG=18446744073709551615;
                                      ^~~~~~~~~~~~~~~~~~~~
boat.cpp: In function 'int main()':
boat.cpp:134:10: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     scanf("%i",&n);
     ~~~~~^~~~~~~~~
boat.cpp:144:14: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
         scanf("%i%i",&inp[i].first,&inp[i].second);
         ~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

• Subtask 1: 9 / 9
• Subtask 2: 22 / 22
• Subtask 3: 27 / 27
• Subtask 4: 0 / 42