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第14章博弈论基础（《C++编程与信息学竞赛数学基础》）

news 2026/6/5 3:40:16

1、T557802 062-14-C01-取硬币游戏
https://www.luogu.com.cn/problem/T557802

#include <bits/stdc++.h> using namespace std; int main() { int n; while(cin>>n&&n!=0) { if(n<=2) cout<<"Alice"<<endl; else cout<<"Bob"<<endl; } return 0; }

2、T553290 06-14-C02-遥控机器人
https://www.luogu.com.cn/problem/T553290

#include <bits/stdc++.h> #define ll long long using namespace std; int solve(){ ll d,k,n,x,y; cin>>d>>k; n=d/(sqrt(2)*k); x=(n+1)*k; y=n*k; if(x*x+y*y>d*d){ cout<<"Bob"<<'\n'; }else{ cout<<"Alice"<<'\n'; } return 0; } int main() { int t; cin>>t; while(t--){ solve(); } return 0; }

3、T553291 06-14-C03-欧几里德游戏
https://www.luogu.com.cn/problem/T553291

#include <bits/stdc++.h> using namespace std; bool f(int x,int y){ if(x<y){ swap(x,y); } if(x%y==0){ return 1; } if(x<2*y){ return !f(x-y,y); } return 1; } int main() { int x,y; cin>>x>>y; if(f(x,y)){ cout<<"Alice wins"; }else{ cout<<"Bob wins"; } return 0; }

4、T553292 06-14-C04-Nim取石头游戏
https://www.luogu.com.cn/problem/T553292

#include <bits/stdc++.h> using namespace std; int n,a[105],t; int main() { int i,j; cin>>n; cin>>a[1]; t=a[1]; for(int i=2;i<=n;i++){ cin>>a[i]; t^=a[i]; } if(t==0){ cout<<"B wins"; return 0; } cout<<"A wins"<<'\n'; int k=31; while(!(t&1<<k)){ k--; } for(int i=1;i<=n;i++){ if(a[i]&1<<k){ j=i; break; } } cout<<j<<" "<<a[j]-(a[j]^t)<<'\n'; return 0; }

5、T553293 06-14-C05-改数游戏
https://www.luogu.com.cn/problem/T553293

#include <bits/stdc++.h> using namespace std; long long n,a[100],b[100],t; int main() { int i,j,x=0; cin>>n; while(n) { b[++x]=n%10; n/=10; } for(i=1;i<=x;i++){ t^=b[i]; } if(t==0){ cout<<"B wins"; return 0; } cout<<"A wins"<<'\n'; int k=6; while(!(t&1<<k)){ k--; } for(i=1;i<=x;i++){ if(b[i]&1<<k){ j=i; break; } } cout<<j<<" "<<(b[j]^t)<<'\n'; return 0; }

6、T557803 062-14-D01-Nim取石头游戏(2)
https://www.luogu.com.cn/problem/T557803

#include <bits/stdc++.h> using namespace std; void solve(int n) { int a[105],t; int i,j; cin>>a[1]; t=a[1]; for(int i=2;i<=n;i++){ cin>>a[i]; t^=a[i]; } if(t==0){ cout<<"0"<<'\n'; return; } int ans=0; for(int i=1;i<=n;i++){ if((a[i]^t)<a[i]){ ans++; } } cout<<ans<<'\n'; return; } int main() { int n; while(cin>>n){ if(n==0)break; solve(n); } }