题解 P7336 【[JRKSJ R1] 1+1】
正常的赛时题解大家可以在这里看 https://www.luogu.com.cn/blog/2-6-5-3-5/ti-xie-t411-post
其实还有一个小优化就是那个 dfs 是可以记忆化的。
其他的东西 cmll02 都写了
这里说一下我是怎么优化的
首先大家的做法基本都要预处理必胜必败局面吧？
这里我开一个搜 16 层的东西在旁边跑，跑了 20s 出来了。
给一下打表程序：
#include<bits/stdc++.h>
#define write cout<<"player:\n"<<pl[0]<<' '<<pl[1]<<"\ncomputer:\n"<<cp[0]<<' '<<cp[1]<<'\n'<<'\n'
using namespace std;
const int w=16;
int dp[10][10][10][10];
int lx(int a[2])
{
int b[2];
b[0]=a[0],b[1]=a[1];
if(b[0]>b[1]) swap(b[0],b[1]);
if(b[0]==3&&b[1]==3||b[0]==3&&b[1]==5||b[0]==1&&b[1]==6) return 1;
if(b[0]==1&&b[1]==9) return 2;
if(b[0]==1&&b[1]==5) return -1;
if(b[0]==5&&b[1]==5) return -2;
return 0;
}
int jm(int a[2],int b[2])
{
if(lx(a)<=0) return 0;
if(lx(a)+lx(b)>0) return 1;
if(lx(a)==1)
{
if(lx(b)==-1) b[0]=b[1]=1;
else b[0]=5,b[1]=1;
}
else b[0]=b[1]=1;
return 0;
}
int dp2[10][10][10][10][10];
int dfs(int c,int a[2],int b[2],int f)
{
int ca[2],cb[2],i,j,sum=0;
ca[0]=a[0],ca[1]=a[1],cb[0]=b[0],cb[1]=b[1];
if(c==w) return 0;
if(dp2[c][a[0]][a[1]][b[0]][b[1]]!=-1) return dp2[c][a[0]][a[1]][b[0]][b[1]];
if(c%2==0)
{
for(i=0;i<2;i++)
for(j=0;j<2;j++)
{
cb[i]=(cb[i]+ca[j])%10;
if(dp[ca[0]][ca[1]][cb[0]][cb[1]]) return dp2[c][a[0]][a[1]][b[0]][b[1]]=0;
ca[0]=a[0],ca[1]=a[1],cb[0]=b[0],cb[1]=b[1];
}
for(i=0;i<2;i++)
for(j=0;j<2;j++)
{
cb[i]=(cb[i]+ca[j])%10;
jm(cb,ca);
sum+=dfs(c+1,ca,cb,f/4);
ca[0]=a[0],ca[1]=a[1],cb[0]=b[0],cb[1]=b[1];
}
}
else
{
for(i=0;i<2;i++)
for(j=0;j<2;j++)
{
ca[i]=(ca[i]+cb[j])%10;
if(dp[cb[0]][cb[1]][ca[0]][ca[1]]) return dp2[c][a[0]][a[1]][b[0]][b[1]]=f;
ca[0]=a[0],ca[1]=a[1],cb[0]=b[0],cb[1]=b[1];
}
for(i=0;i<2;i++)
for(j=0;j<2;j++)
{
ca[i]=(ca[i]+cb[j])%10;
jm(ca,cb);
sum+=dfs(c+1,ca,cb,f/4);
ca[0]=a[0],ca[1]=a[1],cb[0]=b[0],cb[1]=b[1];
}
}
return dp2[c][a[0]][a[1]][b[0]][b[1]]=sum;
}
bool ask(int a[2],int b[2],int deep)
{
if(deep%2&&jm(b,a)) return 1;
if(deep%2==0&&jm(a,b)) return 0;
if(deep>w) return 0;
int ca[2],cb[2],i,j;
if(deep%2)
{
for(i=0;i<2;i++)
for(j=0;j<2;j++)
{
ca[0]=a[0],ca[1]=a[1],cb[0]=b[0],cb[1]=b[1];
ca[i]=(ca[i]+cb[j])%10;
if(ask(ca,cb,deep+1)==0) return 0;
}
return 1;
}
else
{
for(i=0;i<2;i++)
for(j=0;j<2;j++)
{
ca[0]=a[0],ca[1]=a[1],cb[0]=b[0],cb[1]=b[1];
cb[i]=(cb[i]+ca[j])%10;
if(ask(ca,cb,deep+1)==1) return 1;
}
return 0;
}
}
void jfca(int a[2],int b[2])
{
int ca[2],cb[2],s=0,mx=-1073741825,x,y,i,j,sum;
for(i=0;i<2;i++)
for(j=0;j<2;j++)
{
ca[0]=a[0],ca[1]=a[1],cb[0]=b[0],cb[1]=b[1];
ca[i]=(ca[i]+cb[j])%10;
if(jm(ca,cb))
{
a[i]=(a[i]+b[j])%10;
cout<<i<<' '<<j<<endl;
return;
}
}
for(i=0;i<2;i++)
for(j=0;j<2;j++)
{
ca[0]=a[0],ca[1]=a[1],cb[0]=b[0],cb[1]=b[1];
ca[i]=(ca[i]+cb[j])%10;
jm(ca,cb);
sum=dfs(0,ca,cb,1073741824);
if(sum>mx)
{
mx=sum;
x=i,y=j;
}
}
cout<<x<<' '<<y<<endl;
a[x]=(a[x]+b[y])%10;
}
void init()
{
memset(dp2,-1,sizeof(dp2));
int i,j,k,l,a[2],b[2],sum=0;
for(i=0;i<10;i++)
for(j=0;j<10;j++)
for(k=0;k<10;k++)
for(l=0;l<10;l++)
{
a[0]=i;
a[1]=j;
b[0]=k;
b[1]=l;
dp[i][j][k][l]=ask(a,b,1);
cout<<dp[i][j][k][l]<<',';
}
}
int main()
{
freopen("out.txt","w",stdout);
init();
}然后跑到了七十多 ms。
然后发现了一件神奇的事情：这题可以打表！太牛逼了！！1后知后觉
对于每个状态给出反应措施。
#include<bits/stdc++.h>
#define write cout<<"player:\n"<<pl[0]<<' '<<pl[1]<<"\ncomputer:\n"<<cp[0]<<' '<<cp[1]<<'\n'<<'\n'
using namespace std;
int w=10;
int 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0,1,0,0,0,0,0,0,0,0};
int lx(int a[2])
{
int b[2];
b[0]=a[0],b[1]=a[1];
if(b[0]>b[1]) swap(b[0],b[1]);
if(b[0]==3&&b[1]==3||b[0]==3&&b[1]==5||b[0]==1&&b[1]==6) return 1;
if(b[0]==1&&b[1]==9) return 2;
if(b[0]==1&&b[1]==5) return -1;
if(b[0]==5&&b[1]==5) return -2;
return 0;
}
int jm(int a[2],int b[2])
{
if(lx(a)<=0) return 0;
if(lx(a)+lx(b)>0) return 1;
if(lx(a)==1)
{
if(lx(b)==-1) b[0]=b[1]=1;
else b[0]=5,b[1]=1;
}
else b[0]=b[1]=1;
return 0;
}
int dp2[10][10][10][10][10];
int dfs(int c,int a[2],int b[2],int f)
{
int ca[2],cb[2],i,j,sum=0;
ca[0]=a[0],ca[1]=a[1],cb[0]=b[0],cb[1]=b[1];
if(c==w) return 0;
if(dp2[c][a[0]][a[1]][b[0]][b[1]]!=-1) return dp2[c][a[0]][a[1]][b[0]][b[1]];
if(c%2==0)
{
for(i=0;i<2;i++)
for(j=0;j<2;j++)
{
cb[i]=(cb[i]+ca[j])%10;
if(dp[ca[0]][ca[1]][cb[0]][cb[1]]) return dp2[c][a[0]][a[1]][b[0]][b[1]]=0;
ca[0]=a[0],ca[1]=a[1],cb[0]=b[0],cb[1]=b[1];
}
for(i=0;i<2;i++)
for(j=0;j<2;j++)
{
cb[i]=(cb[i]+ca[j])%10;
jm(cb,ca);
sum+=dfs(c+1,ca,cb,f/4);
ca[0]=a[0],ca[1]=a[1],cb[0]=b[0],cb[1]=b[1];
}
}
else
{
for(i=0;i<2;i++)
for(j=0;j<2;j++)
{
ca[i]=(ca[i]+cb[j])%10;
if(dp[cb[0]][cb[1]][ca[0]][ca[1]]) return dp2[c][a[0]][a[1]][b[0]][b[1]]=f;
ca[0]=a[0],ca[1]=a[1],cb[0]=b[0],cb[1]=b[1];
}
for(i=0;i<2;i++)
for(j=0;j<2;j++)
{
ca[i]=(ca[i]+cb[j])%10;
jm(ca,cb);
sum+=dfs(c+1,ca,cb,f/4);
ca[0]=a[0],ca[1]=a[1],cb[0]=b[0],cb[1]=b[1];
}
}
return dp2[c][a[0]][a[1]][b[0]][b[1]]=sum;
}
pair<int,int> jfca(int a[2],int b[2])
{
int ca[2],cb[2],s=0,mx=-1073741825,x,y,i,j,sum;
for(i=0;i<2;i++)
for(j=0;j<2;j++)
{
ca[0]=a[0],ca[1]=a[1],cb[0]=b[0],cb[1]=b[1];
ca[i]=(ca[i]+cb[j])%10;
if(jm(ca,cb))
{
a[i]=(a[i]+b[j])%10;
return make_pair(i,j);
}
}
for(i=0;i<2;i++)
for(j=0;j<2;j++)
{
ca[0]=a[0],ca[1]=a[1],cb[0]=b[0],cb[1]=b[1];
ca[i]=(ca[i]+cb[j])%10;
jm(ca,cb);
sum=dfs(0,ca,cb,1073741824);
if(sum>mx)
{
mx=sum;
x=i,y=j;
}
}
a[x]=(a[x]+b[y])%10;
return make_pair(x,y);
}
int main()
{
freopen("out2.txt","w",stdout);
memset(dp2,-1,sizeof(dp2));
int i,j,k,l,a[2],b[2],sum=0;
pair<int,int> ans;
for(i=0;i<10;i++)
for(j=0;j<10;j++)
for(k=0;k<10;k++)
for(l=0;l<10;l++)
{
a[0]=i;
a[1]=j;
b[0]=k;
b[1]=l;
ans=jfca(a,b);
cout<<ans.first<<',';
}
freopen("out3.txt","w",stdout);
for(i=0;i<10;i++)
for(j=0;j<10;j++)
for(k=0;k<10;k++)
for(l=0;l<10;l++)
{
a[0]=i;
a[1]=j;
b[0]=k;
b[1]=l;
ans=jfca(a,b);
cout<<ans.second<<',';
}
}开十层放心大胆的跑，很快就出来了。
然后一交，47 行，跑的飞快。