1 条题解
-
0
自动搬运
来自洛谷，原作者为
critnos
咔菲好喝。搬运于
2025-08-24 22:28:53，当前版本为作者最后更新于2021-02-16 11:33:56，作者可能在搬运后再次修改，您可在原文处查看最新版自动搬运只会搬运当前题目点赞数最高的题解，您可前往洛谷题解查看更多
以下是正文
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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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。
15011418730
LV 7
@ 2025-8-24 22:28:53
- 1
