[UOJ 160][清华集训2015]斗地主

Posted 2021-03-19 lanrtabe

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文字数字较多，加载略慢

题目链接

Emm怎么没人做啊，网上都找不到题解~~我怎么抄~~

首先大力模拟，写一个对抗搜索，记录当前玩家的牌，对手的牌，当前玩家，对手上一次出的牌

然后加一个记忆化搜索，这样可以轻松跑出前两个Subtask（当然你可以加上O2优化跑得快一点）

然后我大力跑一下Subtask3，每个点都在(1s~2s)左右，然后跑了几十分钟也跑出来了

当然或许是因为i5-8250U然后开一大堆窗口的原因（复杂度爆炸（不过低压U确实慢

然后改成二分答案+判定，这样可以在搜索时加很多剪枝，比如当前玩家是自己且目前结果已经(ge Ans)就返回，其他类推

但还是很慢，我就放着跑，大概跑了(90min)终于出了Subtask4

总感觉什么地方写炸了，但是找不出来

复杂度大概是(O(2^{n+m} imes 15^3log^2))？

~~试了一下，Subtask5可能要跑一天~~

~~后来试了一下，跑到Test128炸内存了~~

官方题解说Subtask5中有的牌出现了多次，这些牌只用计算一次，然而我没看懂怎么实现

这个题写到后面代码已经乱得不行了，修改极其麻烦

就放一下暴力代码吧。u1s1，这种题放在考试里面我觉得不行

搜索+记忆化：

#pragma GCC optimize(3,"Ofast")
#include <map>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
typedef long long ll;
typedef std::pair<int,int> pii;

struct Cards
{
    int c[20];
    inline Cards(){memset(c,0,sizeof c);}
    inline int Cnt(int Res=0){for(int i=3;i<=17;++i)Res+=c[i];return Res;}
    //[3~17] -> [3, 4, 5, 6, 7, 8, 9, T, J, Q, K, A, 2, w, W]
};
struct Play//Play Cards
{
    int Type,A,B;
    //Type = 0 : None
    //      none
    //Type = 1 : Rocket
    //      none
    //Type = 2 : Bomb
    //      AAAA
    //Type = 3 : Single
    //      A
    //Type = 4 : Double
    //      AA
    //Type = 5 : Triple
    //      AAA
    //Type = 6 : 3+1
    //      AAA+?
    //Type = 7 : 3+2
    //      AAA+??
    //Type = 8 : Junko(Single)
    //      A~B
    //Type = 9 : Junko(Double)
    //      AA~BB
    //Type = 10 : Junko(Triple)
    //      AAA~BBB
    //Type = 11 : 4+1+1
    //      AAAA+?+?
    //Type = 12 : 4+2+2
    //      AAAA+??+??
    //Type = 13 : Plane(Single)
    //      AAA~BBB+?...
    //Type = 14 : Plane(Double)
    //      AAA~BBB+??...
};
struct Status
{
    ll A,B,C;//Status compression
    inline Status(const Cards& _A,const Cards& _B,const int Np,const Play& Last)
    {
        A=B=0,C=Np*8000+Last.Type*400+Last.A*20+Last.B;
        for(int i=3;i<=17;++i)A=A*5+_A.c[i],B=B*5+_B.c[i];
    }
    inline bool operator<(const Status& o)const{return A!=o.A?A<o.A:(B!=o.B?B<o.B:C<o.C);}
};

inline int ID(char c)
{
    if(c>='3'&&c<='9')return c^48;
    if(c=='T')return 10;
    if(c=='J')return 11;
    if(c=='Q')return 12;
    if(c=='K')return 13;
    if(c=='A')return 14;
    if(c=='2')return 15;
    return c=='w'?16:17;
}

std::vector<int> Cs;
inline void Choose(std::vector<std::vector<int> >& Plans,Cards& P,const int Tc,const int Ec,int x)
{
    //Plans of Choosing Tc Pair(s) (Each contains Ec Elements) in P
    if((int)Cs.size()==Tc)return Plans.push_back(Cs);
    for(int i=x;i<=17;++i)
        if(P.c[i]>=Ec)
        {
            P.c[i]-=Ec,Cs.push_back(i);
            Choose(Plans,P,Tc,Ec,i);
            P.c[i]+=Ec,Cs.pop_back();
        }
}

std::map<Status,int> Result;
int DFS(Cards& A,Cards& B,int Np,const Play Last)
{
    //Max Score A Could Get
    //A -> Now_Player B -> Next_Player
    //Np -> Now_Player_ID Last -> Last_Played_Cards
    
    if(!B.Cnt())return -A.Cnt();//Now_Player Losed With A.Cnt() Cards
    Status Ns=Status(A,B,Np,Last);
    if(Result.find(Ns)!=Result.end())return Result[Ns];
    int Res=-100;
    if(Last.Type)Res=std::max(Res,-DFS(B,A,Np^1,(Play){0,0,0}));//Pass
    if(A.c[16]&&A.c[17])//Type 1 Always The Strongest
    {
        A.c[16]=A.c[17]=0;
        Res=std::max(Res,-DFS(B,A,Np^1,(Play){1,0,0}));
        A.c[16]=A.c[17]=1;
    }
    for(int i=3;i<=15;++i)//Type 2
        if(A.c[i]==4&&!(Last.Type==1||(Last.Type==2&&Last.A>i)))
            A.c[i]=0,Res=std::max(Res,-DFS(B,A,Np^1,(Play){2,i,0})),A.c[i]=4;
    for(int i=3;i<=17;++i)
    {
        if(A.c[i]&&(!Last.Type||(Last.Type==3&&Last.A<i)))//Type 3
            --A.c[i],Res=std::max(Res,-DFS(B,A,Np^1,(Play){3,i,0})),++A.c[i];
        if(A.c[i]>=2&&(!Last.Type||(Last.Type==4&&Last.A<i)))//Type 4
            A.c[i]-=2,Res=std::max(Res,-DFS(B,A,Np^1,(Play){4,i,0})),A.c[i]+=2;
        if(A.c[i]>=3)
        {
            A.c[i]-=3;
            if(!Last.Type||(Last.Type==5&&Last.A<i))//Type 5
                Res=std::max(Res,-DFS(B,A,Np^1,(Play){5,i,0}));
            for(int j=3;j<=17;++j)
            {
                if(j==i)continue;
                if(A.c[j]&&(!Last.Type||(Last.Type==6&&Last.A<i)))//Type 6
                    --A.c[j],Res=std::max(Res,-DFS(B,A,Np^1,(Play){6,i,0})),++A.c[j];
                if(A.c[j]>=2&&(!Last.Type||(Last.Type==7&&Last.A<i)))//Type 7
                    A.c[j]-=2,Res=std::max(Res,-DFS(B,A,Np^1,(Play){7,i,0})),A.c[j]+=2;
            }
            A.c[i]+=3;
        }
    }
    for(int i=3;i<=14;++i)
    {
        int Minc=4;
        for(int j=i;j<=14;++j)
        {
            Minc=std::min(Minc,A.c[j]);
            if(Minc&&(!Last.Type||(Last.Type==8&&j-i==Last.B-Last.A&&Last.A<i))&&j-i+1>=5)//Type 8
            {
                for(int k=i;k<=j;++k)--A.c[k];
                Res=std::max(Res,-DFS(B,A,Np^1,(Play){8,i,j}));
                for(int k=i;k<=j;++k)++A.c[k];
            }
            if(Minc>=2&&(!Last.Type||(Last.Type==9&&j-i==Last.B-Last.A&&Last.A<i))&&j-i+1>=3)//Type 9
            {
                for(int k=i;k<=j;++k)A.c[k]-=2;
                Res=std::max(Res,-DFS(B,A,Np^1,(Play){9,i,j}));
                for(int k=i;k<=j;++k)A.c[k]+=2;
            }
            if(Minc>=3&&j-i+1>=2)
            {
                for(int k=i;k<=j;++k)A.c[k]-=3;
                if(!Last.Type||(Last.Type==10&&j-i==Last.B-Last.A&&Last.A<i))//Type 10
                    Res=std::max(Res,-DFS(B,A,Np^1,(Play){10,i,j}));
                if(!Last.Type||(Last.Type==13&&j-i==Last.B-Last.A&&Last.A<i))//Type 13
                {
                    std::vector<std::vector<int> > Plans;
                    Choose(Plans,A,j-i+1,1,3);
                    for(auto p:Plans)
                    {
                        for(auto ps:p)--A.c[ps];
                        Res=std::max(Res,-DFS(B,A,Np^1,(Play){13,i,j}));
                        for(auto ps:p)++A.c[ps];
                    }
                }
                if(!Last.Type||(Last.Type==14&&j-i==Last.B-Last.A&&Last.A<i))//Type 14
                {
                    std::vector<std::vector<int> > Plans;
                    Choose(Plans,A,j-i+1,2,3);
                    for(auto p:Plans)
                    {
                        for(auto ps:p)A.c[ps]-=2;
                        Res=std::max(Res,-DFS(B,A,Np^1,(Play){14,i,j}));
                        for(auto ps:p)A.c[ps]+=2;
                    }
                }
                for(int k=i;k<=j;++k)A.c[k]+=3;
            }
        }
    }
    for(int i=3;i<=15;++i)
        if(A.c[i]==4)
        {
            A.c[i]=0;
            for(int j=3;j<=17;++j)
            {
                if(A.c[j])
                {
                    --A.c[j];
                    for(int k=j;k<=17;++k)
                        if(A.c[k]&&(!Last.Type||(Last.Type==11&&Last.A<i)))//Type 11
                            --A.c[k],Res=std::max(Res,-DFS(B,A,Np^1,(Play){11,i,0})),++A.c[k];
                    ++A.c[j];
                }
                if(A.c[j]>=2)
                {
                    A.c[j]-=2;
                    for(int k=j;k<=15;++k)
                        if(A.c[k]>=2&&(!Last.Type||(Last.Type==12&&Last.A<i)))//Type 12
                            A.c[k]-=2,Res=std::max(Res,-DFS(B,A,Np^1,(Play){12,i,0})),A.c[k]+=2;
                    A.c[j]+=2;
                }
            }
            A.c[i]=4;
        }
    return Result[Ns]=Res;
}

int main()
{
    freopen("in.txt","r",stdin);
    freopen("out.txt","w",stdout);
    for(int n,m,Cas=1;scanf("%d%d",&n,&m),n||m;++Cas)
    {
        char s[30];
        Cards P0,P1;
        Result.clear();
        scanf("%s",s+1);
        for(int i=1;i<=n;++i)++P0.c[ID(s[i])];
        scanf("%s",s+1);
        for(int i=1;i<=m;++i)++P1.c[ID(s[i])];
        printf("%d
",DFS(P0,P1,0,(Play){0,0,0}));
        std::cerr<<"Solve "<<Cas<<'
';
    }
    return 0;
}

搜索+记忆化+二分答案+剪枝

#pragma GCC optimize(3,"Ofast")
#include <map>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
typedef long long ll;
typedef std::pair<int,int> pii;

struct Cards
{
    int c[20];
    inline Cards(){memset(c,0,sizeof c);}
    inline int Cnt(int Res=0){for(int i=3;i<=17;++i)Res+=c[i];return Res;}
    //[3~17] -> [3, 4, 5, 6, 7, 8, 9, T, J, Q, K, A, 2, w, W]
};
struct Play//Play Cards
{
    int Type,A,B;
    //Type = 0 : None
    //      none
    //Type = 1 : Rocket
    //      none
    //Type = 2 : Bomb
    //      AAAA
    //Type = 3 : Single
    //      A
    //Type = 4 : Double
    //      AA
    //Type = 5 : Triple
    //      AAA
    //Type = 6 : 3+1
    //      AAA+?
    //Type = 7 : 3+2
    //      AAA+??
    //Type = 8 : Junko(Single)
    //      A~B
    //Type = 9 : Junko(Double)
    //      AA~BB
    //Type = 10 : Junko(Triple)
    //      AAA~BBB
    //Type = 11 : 4+1+1
    //      AAAA+?+?
    //Type = 12 : 4+2+2
    //      AAAA+??+??
    //Type = 13 : Plane(Single)
    //      AAA~BBB+?...
    //Type = 14 : Plane(Double)
    //      AAA~BBB+??...
};
struct Status
{
    ll A,B,C;//Status compression
    inline Status(const Cards& _A,const Cards& _B,const int Np,const Play& Last)
    {
        A=B=0,C=Np*8000+Last.Type*400+Last.A*20+Last.B;
        for(int i=3;i<=17;++i)A=A*5+_A.c[i],B=B*5+_B.c[i];
    }
    inline bool operator<(const Status& o)const{return A!=o.A?A<o.A:(B!=o.B?B<o.B:C<o.C);}
};

inline int ID(char c)
{
    if(c>='3'&&c<='9')return c^48;
    if(c=='T')return 10;
    if(c=='J')return 11;
    if(c=='Q')return 12;
    if(c=='K')return 13;
    if(c=='A')return 14;
    if(c=='2')return 15;
    return c=='w'?16:17;
}

std::vector<int> Cs;
inline void Choose(std::vector<std::vector<int> >& Plans,Cards& P,const int Tc,const int Ec,int x)
{
    //Plans of Choosing Tc Pair(s) (Each contains Ec Elements) in P
    if((int)Cs.size()==Tc)return Plans.push_back(Cs);
    for(int i=x;i<=17;++i)
        if(P.c[i]>=Ec)
        {
            P.c[i]-=Ec,Cs.push_back(i);
            Choose(Plans,P,Tc,Ec,i);
            P.c[i]+=Ec,Cs.pop_back();
        }
}

int Ans;

std::map<Status,int> Result;
int DFS(Cards& A,Cards& B,int Np,const Play Last)
{
    //Max Score A Could Get
    //A -> Now_Player B -> Next_Player
    //Np -> Now_Player_ID Last -> Last_Played_Cards
    int Ac=A.Cnt(),Bc=B.Cnt();
    if(!Np&&Bc<Ans)return -100;
    if(!Np&&-Ac>=Ans)return 100;
    if(Np&&Ac<Ans)return 100;
    if(Np&&-Bc>=Ans)return -100;
    if(!Bc)return -Ac;//Now_Player Losed With A.Cnt() Cards
    Status Ns=Status(A,B,Np,Last);
    if(Result.find(Ns)!=Result.end())return Result[Ns];
    int &Res=Result[Ns]=-100;
    if(Last.Type)Res=std::max(Res,-DFS(B,A,Np^1,(Play){0,0,0}));//Pass
    if((!Np&&Res>=Ans)||(Np&&-Res<Ans))return Res;
    if(A.c[16]&&A.c[17])//Type 1 Always The Strongest
    {
        A.c[16]=A.c[17]=0;
        Res=std::max(Res,-DFS(B,A,Np^1,(Play){1,0,0}));
        A.c[16]=A.c[17]=1;
    }
    if((!Np&&Res>=Ans)||(Np&&-Res<Ans))return Res;
    for(int i=3;i<=15;++i)//Type 2
        if(A.c[i]==4&&!(Last.Type==1||(Last.Type==2&&Last.A>i)))
        {
            A.c[i]=0,Res=std::max(Res,-DFS(B,A,Np^1,(Play){2,i,0})),A.c[i]=4;
            if((!Np&&Res>=Ans)||(Np&&-Res<Ans))return Res;
        }
    for(int i=3;i<=17;++i)
    {
        if(A.c[i]&&(!Last.Type||(Last.Type==3&&Last.A<i)))//Type 3
        {
            --A.c[i],Res=std::max(Res,-DFS(B,A,Np^1,(Play){3,i,0})),++A.c[i];
            if((!Np&&Res>=Ans)||(Np&&-Res<Ans))return Res;
        }
        if(A.c[i]>=2&&(!Last.Type||(Last.Type==4&&Last.A<i)))//Type 4
        {
            A.c[i]-=2,Res=std::max(Res,-DFS(B,A,Np^1,(Play){4,i,0})),A.c[i]+=2;
            if((!Np&&Res>=Ans)||(Np&&-Res<Ans))return Res;
        }
        if(A.c[i]>=3)
        {
            A.c[i]-=3;
            if(!Last.Type||(Last.Type==5&&Last.A<i))//Type 5
            {
                Res=std::max(Res,-DFS(B,A,Np^1,(Play){5,i,0}));
                if((!Np&&Res>=Ans)||(Np&&-Res<Ans))return A.c[i]+=3,Res;
            }
            for(int j=3;j<=17;++j)
            {
                if(j==i)continue;
                if(A.c[j]&&(!Last.Type||(Last.Type==6&&Last.A<i)))//Type 6
                {
                    --A.c[j],Res=std::max(Res,-DFS(B,A,Np^1,(Play){6,i,0})),++A.c[j];
                    if((!Np&&Res>=Ans)||(Np&&-Res<Ans))return A.c[i]+=3,Res;
                }
                if(A.c[j]>=2&&(!Last.Type||(Last.Type==7&&Last.A<i)))//Type 7
                {
                    A.c[j]-=2,Res=std::max(Res,-DFS(B,A,Np^1,(Play){7,i,0})),A.c[j]+=2;
                    if((!Np&&Res>=Ans)||(Np&&-Res<Ans))return A.c[i]+=3,Res;
                }
            }
            A.c[i]+=3;
        }
    }
    for(int i=3;i<=14;++i)
    {
        int Minc=4;
        for(int j=i;j<=14;++j)
        {
            Minc=std::min(Minc,A.c[j]);
            if(Minc&&(!Last.Type||(Last.Type==8&&j-i==Last.B-Last.A&&Last.A<i))&&j-i+1>=5)//Type 8
            {
                for(int k=i;k<=j;++k)--A.c[k];
                Res=std::max(Res,-DFS(B,A,Np^1,(Play){8,i,j}));
                for(int k=i;k<=j;++k)++A.c[k];
                if((!Np&&Res>=Ans)||(Np&&-Res<Ans))return Res;
            }
            if(Minc>=2&&(!Last.Type||(Last.Type==9&&j-i==Last.B-Last.A&&Last.A<i))&&j-i+1>=3)//Type 9
            {
                for(int k=i;k<=j;++k)A.c[k]-=2;
                Res=std::max(Res,-DFS(B,A,Np^1,(Play){9,i,j}));
                for(int k=i;k<=j;++k)A.c[k]+=2;
                if((!Np&&Res>=Ans)||(Np&&-Res<Ans))return Res;
            }
            if(Minc>=3&&j-i+1>=2)
            {
                if(!Last.Type||(Last.Type==10&&j-i==Last.B-Last.A&&Last.A<i))//Type 10
                {
                    for(int k=i;k<=j;++k)A.c[k]-=3;
                    Res=std::max(Res,-DFS(B,A,Np^1,(Play){10,i,j}));
                    for(int k=i;k<=j;++k)A.c[k]+=3;
                    if((!Np&&Res>=Ans)||(Np&&-Res<Ans))return Res;
                }
                if(!Last.Type||(Last.Type==13&&j-i==Last.B-Last.A&&Last.A<i))//Type 13
                {
                    std::vector<std::vector<int> > Plans;
                    for(int k=i;k<=j;++k)A.c[k]-=3;
                    Choose(Plans,A,j-i+1,1,3);
                    for(int k=i;k<=j;++k)A.c[k]+=3;
                    for(auto p:Plans)
                    {
                        for(auto ps:p)--A.c[ps];
                        for(int k=i;k<=j;++k)A.c[k]-=3;
                        Res=std::max(Res,-DFS(B,A,Np^1,(Play){13,i,j}));
                        for(auto ps:p)++A.c[ps];
                        for(int k=i;k<=j;++k)A.c[k]+=3;
                        if((!Np&&Res>=Ans)||(Np&&-Res<Ans))return Res;
                    }
                }
                if(!Last.Type||(Last.Type==14&&j-i==Last.B-Last.A&&Last.A<i))//Type 14
                {
                    std::vector<std::vector<int> > Plans;
                    for(int k=i;k<=j;++k)A.c[k]-=3;
                    Choose(Plans,A,j-i+1,2,3);
                    for(int k=i;k<=j;++k)A.c[k]+=3;
                    for(auto p:Plans)
                    {
                        for(auto ps:p)A.c[ps]-=2;
                        for(int k=i;k<=j;++k)A.c[k]-=3;
                        Res=std::max(Res,-DFS(B,A,Np^1,(Play){14,i,j}));
                        for(auto ps:p)A.c[ps]+=2;
                        for(int k=i;k<=j;++k)A.c[k]+=3;
                        if((!Np&&Res>=Ans)||(Np&&-Res<Ans))return Res;
                    }
                }
            }
        }
    }
    for(int i=3;i<=15;++i)
        if(A.c[i]==4)
        {
            A.c[i]=0;
            for(int j=3;j<=17;++j)
            {
                if(A.c[j])
                {
                    --A.c[j];
                    for(int k=j;k<=17;++k)
                        if(A.c[k]&&(!Last.Type||(Last.Type==11&&Last.A<i)))//Type 11
                        {
                            --A.c[k],Res=std::max(Res,-DFS(B,A,Np^1,(Play){11,i,0})),++A.c[k];
                            if((!Np&&Res>=Ans)||(Np&&-Res<Ans))
                            {
                                ++A.c[j],A.c[i]=4;
                                return Res;
                            }
                        }
                    ++A.c[j];
                }
                if(A.c[j]>=2)
                {
                    A.c[j]-=2;
                    for(int k=j;k<=15;++k)
                        if(A.c[k]>=2&&(!Last.Type||(Last.Type==12&&Last.A<i)))//Type 12
                        {
                            A.c[k]-=2,Res=std::max(Res,-DFS(B,A,Np^1,(Play){12,i,0})),A.c[k]+=2;
                            if((!Np&&Res>=Ans)||(Np&&-Res<Ans))
                            {
                                A.c[j]+=2,A.c[i]=4;
                                return Res;
                            }
                        }
                    A.c[j]+=2;
                }
            }
            A.c[i]=4;
            if((!Np&&Res>=Ans))return Res;
        }
    return Res;
}

int main()
{
    freopen("in.txt","r",stdin);
    freopen("out.txt","w",stdout);
    for(int n,m,Cas=1;scanf("%d%d",&n,&m),n||m;++Cas)
    {
        char s[30];
        Cards P0,P1;
        scanf("%s",s+1);
        for(int i=1;i<=n;++i)++P0.c[ID(s[i])];
        scanf("%s",s+1);
        for(int i=1;i<=m;++i)++P1.c[ID(s[i])];
        int l=-6,r=21;
        while(l<r)
        {
            Ans=((l+60+r+60)>>1)-60,Result.clear();
            if(DFS(P0,P1,0,(Play){0,0,0})>=Ans)l=Ans+1;
            else r=Ans;
        }
        printf("%d
",l-1);
        std::cerr<<"Solve "<<Cas<<'
';
    }
    return 0;
}

landlords1.out

landlords2.out

landlords3.out

landlords4.out

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2
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15
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-1
-1

landlords5.out

AWSL

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