博弈题目小结

　　关于入门资料，推荐看<这里>，取火柴的那10个定理必须理解。

五篇国家集训队论文：

　　张一飞：《由感性认识到理性认识——透析一类搏弈游戏的解答过程》
　　王晓珂：《解析一类组合游戏》
　　方展鹏：《浅谈如何解决不平等博弈问题》
　　贾志豪：《组合游戏略述——浅谈SG游戏的若干拓展及变形》
　　曹钦翔：《从“k倍动态减法游戏”出发探究一类组合游戏问题》

　　下面是题目总结：

1.HDU 1404 预处理，推出所有情况的胜负情况。

  1 //STATUS:C++_AC_468MS_4140KB
  2 #include <functional>
  3 #include <algorithm>
  4 #include <iostream>
  5 //#include <ext/rope>
  6 #include <fstream>
  7 #include <sstream>
  8 #include <iomanip>
  9 #include <numeric>
 10 #include <cstring>
 11 #include <cassert>
 12 #include <cstdio>
 13 #include <string>
 14 #include <vector>
 15 #include <bitset>
 16 #include <queue>
 17 #include <stack>
 18 #include <cmath>
 19 #include <ctime>
 20 #include <list>
 21 #include <set>
 22 #include <map>
 23 using namespace std;
 24 //using namespace __gnu_cxx;
 25 //define
 26 #define pii pair<int,int>
 27 #define mem(a,b) memset(a,b,sizeof(a))
 28 #define lson l,mid,rt<<1
 29 #define rson mid+1,r,rt<<1|1
 30 #define PI acos(-1.0)
 31 //typedef
 32 typedef long long LL;
 33 typedef unsigned long long ULL;
 34 //const
 35 const int N=1000010;
 36 const int INF=0x3f3f3f3f;
 37 const int MOD=100000,STA=8000010;
 38 const LL LNF=1LL<<60;
 39 const double EPS=1e-8;
 40 const double OO=1e15;
 41 const int dx[4]={-1,0,1,0};
 42 const int dy[4]={0,1,0,-1};
 43 const int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
 44 //Daily Use ...
 45 inline int sign(double x){return (x>EPS)-(x<-EPS);}
 46 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
 47 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}
 48 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}
 49 template<class T> inline T Min(T a,T b){return a<b?a:b;}
 50 template<class T> inline T Max(T a,T b){return a>b?a:b;}
 51 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}
 52 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}
 53 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}
 54 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}
 55 //End
 56 
 57 int sta[N],ten[10];
 58 int n;
 59 
 60 int dfs(int u,int w)
 61 {
 62     if(!w || u/ten[w-1]==0)return 1;
 63     if(sta[u]!=-1)return sta[u];
 64     int i,j,t,v;
 65     for(i=w-1;i>=0;i--){
 66         t=u/ten[i]%10;
 67         if(t==0){
 68             v=u/ten[i+1];
 69             if(dfs(v,w-i-1)==0)return sta[u]=1;
 70         }
 71         v=u-ten[i];
 72         for(;t;t--,v-=ten[i])
 73             if(dfs(v,w)==0)return sta[u]=1;
 74     }
 75     return sta[u]=0;
 76 }
 77 
 78 int getw(int a)
 79 {
 80     if(a/10==0)return 1;
 81     if(a/100==0)return 2;
 82     if(a/1000==0)return 3;
 83     if(a/10000==0)return 4;
 84     if(a/100000==0)return 5;
 85     return 6;
 86 }
 87 
 88 int main()
 89 {
 90   //  freopen("in.txt","r",stdin);
 91     int i,j,len;
 92     char s[10];
 93     for(i=ten[0]=1;i<8;i++)ten[i]=ten[i-1]*10;
 94     mem(sta,-1);sta[0]=1;
 95     for(i=1;i<1000000;i++){
 96         if(sta[i]==-1)dfs(i,getw(i));
 97     }
 98     while(~scanf("%s",s))
 99     {
100         len=strlen(s);
101         for(i=n=0;i<len;i++)n+=(s[len-i-1]-'0')*ten[i];
102 
103         printf("%s
",(s[0]=='0' || sta[n])?"Yes":"No");
104     }
105     return 0;
106 }

View Code

2.HDU 1907 尼姆博奕，最后取玩的位loser，必败态为：T2,S0；必胜态为：S2,S1,T0；

 1 //STATUS:C++_AC_0MS_228KB
 2 #include <functional>
 3 #include <algorithm>
 4 #include <iostream>
 5 //#include <ext/rope>
 6 #include <fstream>
 7 #include <sstream>
 8 #include <iomanip>
 9 #include <numeric>
10 #include <cstring>
11 #include <cassert>
12 #include <cstdio>
13 #include <string>
14 #include <vector>
15 #include <bitset>
16 #include <queue>
17 #include <stack>
18 #include <cmath>
19 #include <ctime>
20 #include <list>
21 #include <set>
22 #include <map>
23 using namespace std;
24 //using namespace __gnu_cxx;
25 //define
26 #define pii pair<int,int>
27 #define mem(a,b) memset(a,b,sizeof(a))
28 #define lson l,mid,rt<<1
29 #define rson mid+1,r,rt<<1|1
30 #define PI acos(-1.0)
31 //typedef
32 typedef long long LL;
33 typedef unsigned long long ULL;
34 //const
35 const int N=110;
36 const int INF=0x3f3f3f3f;
37 const int MOD=100000,STA=8000010;
38 const LL LNF=1LL<<60;
39 const double EPS=1e-8;
40 const double OO=1e15;
41 const int dx[4]={-1,0,1,0};
42 const int dy[4]={0,1,0,-1};
43 const int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
44 //Daily Use ...
45 inline int sign(double x){return (x>EPS)-(x<-EPS);}
46 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
47 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}
48 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}
49 template<class T> inline T Min(T a,T b){return a<b?a:b;}
50 template<class T> inline T Max(T a,T b){return a>b?a:b;}
51 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}
52 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}
53 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}
54 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}
55 //End
56 
57 int T,n;
58 
59 int main()
60 {
61  //   freopen("in.txt","r",stdin);
62     int i,j,sg,a,cou;
63     scanf("%d",&T);
64     while(T--)
65     {
66         scanf("%d",&n);
67         sg=cou=0;
68         while(n--){
69             scanf("%d",&a);
70             sg^=a;
71             if(a>1)cou++;
72         }
73         if((!cou&&sg) || (cou>=2&&!sg))
74             printf("Brother
");
75         else printf("John
");
76     }
77     return 0;
78 }

View Code

3.HDU 2509 和上一题一样。

 1 //STATUS:C++_AC_0MS_228KB
 2 #include <functional>
 3 #include <algorithm>
 4 #include <iostream>
 5 //#include <ext/rope>
 6 #include <fstream>
 7 #include <sstream>
 8 #include <iomanip>
 9 #include <numeric>
10 #include <cstring>
11 #include <cassert>
12 #include <cstdio>
13 #include <string>
14 #include <vector>
15 #include <bitset>
16 #include <queue>
17 #include <stack>
18 #include <cmath>
19 #include <ctime>
20 #include <list>
21 #include <set>
22 #include <map>
23 using namespace std;
24 //using namespace __gnu_cxx;
25 //define
26 #define pii pair<int,int>
27 #define mem(a,b) memset(a,b,sizeof(a))
28 #define lson l,mid,rt<<1
29 #define rson mid+1,r,rt<<1|1
30 #define PI acos(-1.0)
31 //typedef
32 typedef long long LL;
33 typedef unsigned long long ULL;
34 //const
35 const int N=110;
36 const int INF=0x3f3f3f3f;
37 const int MOD=100000,STA=8000010;
38 const LL LNF=1LL<<60;
39 const double EPS=1e-8;
40 const double OO=1e15;
41 const int dx[4]={-1,0,1,0};
42 const int dy[4]={0,1,0,-1};
43 const int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
44 //Daily Use ...
45 inline int sign(double x){return (x>EPS)-(x<-EPS);}
46 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
47 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}
48 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}
49 template<class T> inline T Min(T a,T b){return a<b?a:b;}
50 template<class T> inline T Max(T a,T b){return a>b?a:b;}
51 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}
52 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}
53 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}
54 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}
55 //End
56 
57 int n;
58 
59 int main()
60 {
61  //   freopen("in.txt","r",stdin);
62     int i,j,sg,a,cou;
63     while(~scanf("%d",&n))
64     {
65         sg=cou=0;
66         while(n--){
67             scanf("%d",&a);
68             sg^=a;
69             if(a>1)cou++;
70         }
71         if((!cou&&sg) || (cou>=2&&!sg))
72             printf("No
");
73         else printf("Yes
");
74     }
75     return 0;
76 }

View Code

4.HDU 1517 区间的博弈，从最大的范围推到，把每个区间的胜负情况推到出来：[n,+∞]（T态） —> [(n+1)/2，n-1]（S态，表示为[n,m]) —> [(n+8)/9,n-1]（T态）—>......。还可以HASH+DFS暴力搞出来。

  1 //STATUS:C++_AC_32MS_264KB
  2 #include <functional>
  3 #include <algorithm>
  4 #include <iostream>
  5 //#include <ext/rope>
  6 #include <fstream>
  7 #include <sstream>
  8 #include <iomanip>
  9 #include <numeric>
 10 #include <cstring>
 11 #include <cassert>
 12 #include <cstdio>
 13 #include <string>
 14 #include <vector>
 15 #include <bitset>
 16 #include <queue>
 17 #include <stack>
 18 #include <cmath>
 19 #include <ctime>
 20 #include <list>
 21 #include <set>
 22 #include <map>
 23 using namespace std;
 24 //using namespace __gnu_cxx;
 25 //define
 26 #define pii pair<int,int>
 27 #define mem(a,b) memset(a,b,sizeof(a))
 28 #define lson l,mid,rt<<1
 29 #define rson mid+1,r,rt<<1|1
 30 #define PI acos(-1.0)
 31 //typedef
 32 typedef long long LL;
 33 typedef unsigned long long ULL;
 34 //const
 35 const int N=100000010;
 36 const int INF=0x3f3f3f3f;
 37 const int MOD=5000,STA=100010;
 38 const LL LNF=1LL<<60;
 39 const double EPS=1e-8;
 40 const double OO=1e15;
 41 const int dx[4]={-1,0,1,0};
 42 const int dy[4]={0,1,0,-1};
 43 const int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
 44 //Daily Use ...
 45 inline int sign(double x){return (x>EPS)-(x<-EPS);}
 46 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
 47 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}
 48 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}
 49 template<class T> inline T Min(T a,T b){return a<b?a:b;}
 50 template<class T> inline T Max(T a,T b){return a>b?a:b;}
 51 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}
 52 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}
 53 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}
 54 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}
 55 //End
 56 
 57 struct Hash
 58 {
 59     int i,size,next[STA];
 60     int f[MOD],sg[STA];
 61     LL sta[STA];
 62     void init(){
 63         size=0;
 64         mem(f,-1);
 65     }
 66     int find(LL a){
 67         int s=a%MOD;
 68         for(i=f[s];i!=-1;i=next[i]){
 69             if(sta[i]==a){
 70                 return sg[i];
 71             }
 72         }
 73         sta[size]=a;sg[size]=0;
 74         next[size]=f[s];
 75         f[s]=size++;
 76         return -1;
 77     }
 78     void update(LL a){
 79         int s=a%MOD;
 80         for(i=f[s];i!=-1 && sta[i]!=a;i=next[i]);
 81         sg[i]=1;
 82     }
 83 }hs;
 84 
 85 LL n;
 86 
 87 int dfs(LL u)
 88 {
 89     if(u>=n)return 0;
 90     int i,t,sg,ret=0;
 91     if((t=hs.find(u))!=-1)return t;
 92     for(i=2;i<=9;i++){
 93         sg=dfs(u*i);
 94         if(!sg)ret=1,hs.update(u);
 95     }
 96     return ret;
 97 }
 98 
 99 int main()
100 {
101  //   freopen("in.txt","r",stdin);
102     int i,j;
103     while(~scanf("%I64d",&n))
104     {
105         hs.init();
106         printf("%s wins.
",dfs((LL)1)?"Stan":"Ollie");
107     }
108     return 0;
109 }

View Code

5.HDU 1849 尼姆博奕模型。

 1 //STATUS:C++_AC_0MS_228KB
 2 #include <functional>
 3 #include <algorithm>
 4 #include <iostream>
 5 //#include <ext/rope>
 6 #include <fstream>
 7 #include <sstream>
 8 #include <iomanip>
 9 #include <numeric>
10 #include <cstring>
11 #include <cassert>
12 #include <cstdio>
13 #include <string>
14 #include <vector>
15 #include <bitset>
16 #include <queue>
17 #include <stack>
18 #include <cmath>
19 #include <ctime>
20 #include <list>
21 #include <set>
22 #include <map>
23 using namespace std;
24 //using namespace __gnu_cxx;
25 //define
26 #define pii pair<int,int>
27 #define mem(a,b) memset(a,b,sizeof(a))
28 #define lson l,mid,rt<<1
29 #define rson mid+1,r,rt<<1|1
30 #define PI acos(-1.0)
31 //typedef
32 typedef long long LL;
33 typedef unsigned long long ULL;
34 //const
35 const int N=100000010;
36 const int INF=0x3f3f3f3f;
37 const int MOD=5000,STA=100010;
38 const LL LNF=1LL<<60;
39 const double EPS=1e-8;
40 const double OO=1e15;
41 const int dx[4]={-1,0,1,0};
42 const int dy[4]={0,1,0,-1};
43 const int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
44 //Daily Use ...
45 inline int sign(double x){return (x>EPS)-(x<-EPS);}
46 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
47 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}
48 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}
49 template<class T> inline T Min(T a,T b){return a<b?a:b;}
50 template<class T> inline T Max(T a,T b){return a>b?a:b;}
51 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}
52 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}
53 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}
54 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}
55 //End
56 
57 int main()
58 {
59  //   freopen("in.txt","r",stdin);
60     int n,a,sg;
61     while(~scanf("%d",&n) && n)
62     {
63         sg=0;
64         while(n--){
65             scanf("%d",&a);
66             sg^=a;
67         }
68 
69         printf("%s Win!
",sg?"Rabbit":"Grass");
70     }
71     return 0;
72 }

View Code

6.HDU 2188 巴什博奕模型。

 1 //STATUS:C++_AC_0MS_228KB
 2 #include <functional>
 3 #include <algorithm>
 4 #include <iostream>
 5 //#include <ext/rope>
 6 #include <fstream>
 7 #include <sstream>
 8 #include <iomanip>
 9 #include <numeric>
10 #include <cstring>
11 #include <cassert>
12 #include <cstdio>
13 #include <string>
14 #include <vector>
15 #include <bitset>
16 #include <queue>
17 #include <stack>
18 #include <cmath>
19 #include <ctime>
20 #include <list>
21 #include <set>
22 #include <map>
23 using namespace std;
24 //using namespace __gnu_cxx;
25 //define
26 #define pii pair<int,int>
27 #define mem(a,b) memset(a,b,sizeof(a))
28 #define lson l,mid,rt<<1
29 #define rson mid+1,r,rt<<1|1
30 #define PI acos(-1.0)
31 //typedef
32 typedef long long LL;
33 typedef unsigned long long ULL;
34 //const
35 const int N=100000010;
36 const int INF=0x3f3f3f3f;
37 const int MOD=5000,STA=100010;
38 const LL LNF=1LL<<60;
39 const double EPS=1e-8;
40 const double OO=1e15;
41 const int dx[4]={-1,0,1,0};
42 const int dy[4]={0,1,0,-1};
43 const int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
44 //Daily Use ...
45 inline int sign(double x){return (x>EPS)-(x<-EPS);}
46 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
47 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}
48 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}
49 template<class T> inline T Min(T a,T b){return a<b?a:b;}
50 template<class T> inline T Max(T a,T b){return a>b?a:b;}
51 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}
52 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}
53 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}
54 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}
55 //End
56 
57 int T,n,m;
58 
59 int main()
60 {
61  //   freopen("in.txt","r",stdin);
62     scanf("%d",&T);
63     while(T--)
64     {
65         scanf("%d%d",&n,&m);
66         printf("%s
",n%(m+1)?"Grass":"Rabbit");
67     }
68     return 0;
69 }

View Code

7.HDU 1851 n堆的巴什博奕，用SG函数。

 1 //STATUS:C++_AC_15MS_228KB
 2 #include <functional>
 3 #include <algorithm>
 4 #include <iostream>
 5 //#include <ext/rope>
 6 #include <fstream>
 7 #include <sstream>
 8 #include <iomanip>
 9 #include <numeric>
10 #include <cstring>
11 #include <cassert>
12 #include <cstdio>
13 #include <string>
14 #include <vector>
15 #include <bitset>
16 #include <queue>
17 #include <stack>
18 #include <cmath>
19 #include <ctime>
20 #include <list>
21 #include <set>
22 #include <map>
23 using namespace std;
24 //using namespace __gnu_cxx;
25 //define
26 #define pii pair<int,int>
27 #define mem(a,b) memset(a,b,sizeof(a))
28 #define lson l,mid,rt<<1
29 #define rson mid+1,r,rt<<1|1
30 #define PI acos(-1.0)
31 //typedef
32 typedef long long LL;
33 typedef unsigned long long ULL;
34 //const
35 const int N=100000010;
36 const int INF=0x3f3f3f3f;
37 const int MOD=5000,STA=100010;
38 const LL LNF=1LL<<60;
39 const double EPS=1e-8;
40 const double OO=1e15;
41 const int dx[4]={-1,0,1,0};
42 const int dy[4]={0,1,0,-1};
43 const int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
44 //Daily Use ...
45 inline int sign(double x){return (x>EPS)-(x<-EPS);}
46 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
47 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}
48 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}
49 template<class T> inline T Min(T a,T b){return a<b?a:b;}
50 template<class T> inline T Max(T a,T b){return a>b?a:b;}
51 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}
52 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}
53 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}
54 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}
55 //End
56 
57 int T,n,m;
58 
59 int main()
60 {
61  //   freopen("in.txt","r",stdin);
62     int a,sg;
63     scanf("%d",&T);
64     while(T--)
65     {
66         scanf("%d",&n);
67         sg=0;
68         while(n--){
69             scanf("%d%d",&a,&m);
70             sg^=a%(m+1);
71         }
72         printf("%s
",sg?"No":"Yes");
73     }
74     return 0;
75 }

View Code

8.HDU 2897 有下界限制的巴什博奕。

 1 //STATUS:C++_AC_62MS_228KB
 2 #include <functional>
 3 #include <algorithm>
 4 #include <iostream>
 5 //#include <ext/rope>
 6 #include <fstream>
 7 #include <sstream>
 8 #include <iomanip>
 9 #include <numeric>
10 #include <cstring>
11 #include <cassert>
12 #include <cstdio>
13 #include <string>
14 #include <vector>
15 #include <bitset>
16 #include <queue>
17 #include <stack>
18 #include <cmath>
19 #include <ctime>
20 #include <list>
21 #include <set>
22 #include <map>
23 using namespace std;
24 //using namespace __gnu_cxx;
25 //define
26 #define pii pair<int,int>
27 #define mem(a,b) memset(a,b,sizeof(a))
28 #define lson l,mid,rt<<1
29 #define rson mid+1,r,rt<<1|1
30 #define PI acos(-1.0)
31 //typedef
32 typedef long long LL;
33 typedef unsigned long long ULL;
34 //const
35 const int N=100000010;
36 const int INF=0x3f3f3f3f;
37 const int MOD=5000,STA=100010;
38 const LL LNF=1LL<<60;
39 const double EPS=1e-8;
40 const double OO=1e15;
41 const int dx[4]={-1,0,1,0};
42 const int dy[4]={0,1,0,-1};
43 const int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
44 //Daily Use ...
45 inline int sign(double x){return (x>EPS)-(x<-EPS);}
46 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
47 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}
48 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}
49 template<class T> inline T Min(T a,T b){return a<b?a:b;}
50 template<class T> inline T Max(T a,T b){return a>b?a:b;}
51 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}
52 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}
53 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}
54 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}
55 //End
56 
57 int T,n;
58 
59 int main()
60 {
61  //   freopen("in.txt","r",stdin);
62     int x,y,a,p,q,sg;
63     while(~scanf("%d%d%d",&a,&p,&q))
64     {
65         sg=0;
66         x=1,y=p;
67         while(a<x || a>y){
68             x=y+1;
69             if(sg)y+=p;
70             else y+=q;
71             sg^=1;
72         }
73         printf("%s
",sg?"WIN":"LOST");
74     }
75     return 0;
76 }

View Code

9.HDU 2516 找规律，S态为Fibonacci数列。

 1 //STATUS:C++_AC_0MS_228KB
 2 #include <functional>
 3 #include <algorithm>
 4 #include <iostream>
 5 //#include <ext/rope>
 6 #include <fstream>
 7 #include <sstream>
 8 #include <iomanip>
 9 #include <numeric>
10 #include <cstring>
11 #include <cassert>
12 #include <cstdio>
13 #include <string>
14 #include <vector>
15 #include <bitset>
16 #include <queue>
17 #include <stack>
18 #include <cmath>
19 #include <ctime>
20 #include <list>
21 #include <set>
22 #include <map>
23 using namespace std;
24 //using namespace __gnu_cxx;
25 //define
26 #define pii pair<int,int>
27 #define mem(a,b) memset(a,b,sizeof(a))
28 #define lson l,mid,rt<<1
29 #define rson mid+1,r,rt<<1|1
30 #define PI acos(-1.0)
31 //typedef
32 typedef long long LL;
33 typedef unsigned long long ULL;
34 //const
35 const int N=110;
36 const int INF=0x3f3f3f3f;
37 const int MOD=5000,STA=100010;
38 const LL LNF=1LL<<60;
39 const double EPS=1e-8;
40 const double OO=1e15;
41 const int dx[4]={-1,0,1,0};
42 const int dy[4]={0,1,0,-1};
43 const int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
44 //Daily Use ...
45 inline int sign(double x){return (x>EPS)-(x<-EPS);}
46 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
47 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}
48 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}
49 template<class T> inline T Min(T a,T b){return a<b?a:b;}
50 template<class T> inline T Max(T a,T b){return a>b?a:b;}
51 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}
52 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}
53 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}
54 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}
55 //End
56 
57 int f[N];
58 int n;
59 
60 int main()
61 {
62  //   freopen("in.txt","r",stdin);
63     int i,ok;
64     f[0]=f[1]=1;
65     for(i=2;i<46;i++)f[i]=f[i-1]+f[i-2];
66     while(~scanf("%d",&n) && n)
67     {
68         ok=1;
69         for(i=0;i<46;i++)if(f[i]==n){ok=0;break;}
70         printf("%s win
",ok?"First":"Second");
71     }
72     return 0;
73 }

View Code

10.HDU 2149 区间博弈，巴什博奕。

 1 //STATUS:C++_AC_0MS_232KB
 2 #include <functional>
 3 #include <algorithm>
 4 #include <iostream>
 5 //#include <ext/rope>
 6 #include <fstream>
 7 #include <sstream>
 8 #include <iomanip>
 9 #include <numeric>
10 #include <cstring>
11 #include <cassert>
12 #include <cstdio>
13 #include <string>
14 #include <vector>
15 #include <bitset>
16 #include <queue>
17 #include <stack>
18 #include <cmath>
19 #include <ctime>
20 #include <list>
21 #include <set>
22 #include <map>
23 using namespace std;
24 //using namespace __gnu_cxx;
25 //define
26 #define pii pair<int,int>
27 #define mem(a,b) memset(a,b,sizeof(a))
28 #define lson l,mid,rt<<1
29 #define rson mid+1,r,rt<<1|1
30 #define PI acos(-1.0)
31 //typedef
32 typedef long long LL;
33 typedef unsigned long long ULL;
34 //const
35 const int N=100000010;
36 const int INF=0x3f3f3f3f;
37 const int MOD=5000,STA=100010;
38 const LL LNF=1LL<<60;
39 const double EPS=1e-8;
40 const double OO=1e15;
41 const int dx[4]={-1,0,1,0};
42 const int dy[4]={0,1,0,-1};
43 const int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
44 //Daily Use ...
45 inline int sign(double x){return (x>EPS)-(x<-EPS);}
46 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
47 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}
48 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}
49 template<class T> inline T Min(T a,T b){return a<b?a:b;}
50 template<class T> inline T Max(T a,T b){return a>b?a:b;}
51 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}
52 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}
53 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}
54 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}
55 //End
56 
57 int n,m;
58 
59 int main()
60 {
61  //   freopen("in.txt","r",stdin);
62     int i,j,sg,lx,ly,x,y;
63     while(~scanf("%d%d",&m,&n))
64     {
65         sg=1;
66         lx=m;ly=m+n;
67         x=Max(m-n,0);y=Max(0,m-1);
68         while(0<x){
69             lx=x,ly=y;
70             if(sg)x=y=x-1;
71             else {
72                 y=x-1;x-=n;
73             }
74             sg^=1;
75         }
76 
77         if(sg){
78             printf("%d",lx);
79             for(i=lx+1;i<=ly && i<=n;i++)
80                 printf(" %d",i);
81         }
82         else printf("none");
83         putchar('
');
84     }
85     return 0;
86 }

View Code

11.HDU 1850 求尼姆博弈开始必胜天态次数，先求出SG函数，然后遍历SG^num[i]==0的次数。

 1 //STATUS:C++_AC_0MS_232KB
 2 #include <functional>
 3 #include <algorithm>
 4 #include <iostream>
 5 //#include <ext/rope>
 6 #include <fstream>
 7 #include <sstream>
 8 #include <iomanip>
 9 #include <numeric>
10 #include <cstring>
11 #include <cassert>
12 #include <cstdio>
13 #include <string>
14 #include <vector>
15 #include <bitset>
16 #include <queue>
17 #include <stack>
18 #include <cmath>
19 #include <ctime>
20 #include <list>
21 #include <set>
22 #include <map>
23 using namespace std;
24 //using namespace __gnu_cxx;
25 //define
26 #define pii pair<int,int>
27 #define mem(a,b) memset(a,b,sizeof(a))
28 #define lson l,mid,rt<<1
29 #define rson mid+1,r,rt<<1|1
30 #define PI acos(-1.0)
31 //typedef
32 typedef long long LL;
33 typedef unsigned long long ULL;
34 //const
35 const int N=1000010;
36 const int INF=0x3f3f3f3f;
37 const int MOD=5000,STA=100010;
38 const LL LNF=1LL<<60;
39 const double EPS=1e-8;
40 const double OO=1e15;
41 const int dx[4]={-1,0,1,0};
42 const int dy[4]={0,1,0,-1};
43 const int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
44 //Daily Use ...
45 inline int sign(double x){return (x>EPS)-(x<-EPS);}
46 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
47 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}
48 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}
49 template<class T> inline T Min(T a,T b){return a<b?a:b;}
50 template<class T> inline T Max(T a,T b){return a>b?a:b;}
51 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}
52 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}
53 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}
54 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}
55 //End
56 
57 int num[N];
58 int n;
59 
60 int main()
61 {
62  //   freopen("in.txt","r",stdin);
63     int i,j,sg,w,ans;
64     while(~scanf("%d",&n) && n)
65     {
66         sg=0;
67         for(i=0;i<n;i++){
68             scanf("%d",&num[i]);
69             sg^=num[i];
70         }
71         if(sg){
72             for(i=0;i<31;i++)
73                 if(sg&(1<<i))w=(1<<i);
74             for(i=ans=0;i<n;i++){
75                 if(num[i]&w)ans++;
76             }
77         }
78 
79         printf("%d
",sg?ans:0);
80     }
81     return 0;
82 }

View Code

12.HDU 4023 贪心+博弈，贪心的细想。仔细观察15钟棋盘的布局，然后把它们分类：

　　　　15 对双方的是一样的

　　　　3,4,5,6 分偏向Bob和偏向Alice

　　　　11,12,13,14 偏向双方

　　　　7,9,9,10 如果一方得到一个，另一方也能得到一个

　　　　1,2 属于各自的。

 1 //STATUS:C++_AC_0MS_228KB
 2 #include <functional>
 3 #include <algorithm>
 4 #include <iostream>
 5 //#include <ext/rope>
 6 #include <fstream>
 7 #include <sstream>
 8 #include <iomanip>
 9 #include <numeric>
10 #include <cstring>
11 #include <cassert>
12 #include <cstdio>
13 #include <string>
14 #include <vector>
15 #include <bitset>
16 #include <queue>
17 #include <stack>
18 #include <cmath>
19 #include <ctime>
20 #include <list>
21 #include <set>
22 #include <map>
23 using namespace std;
24 //using namespace __gnu_cxx;
25 //define
26 #define pii pair<int,int>
27 #define mem(a,b) memset(a,b,sizeof(a))
28 #define lson l,mid,rt<<1
29 #define rson mid+1,r,rt<<1|1
30 #define PI acos(-1.0)
31 //typedef
32 typedef long long LL;
33 typedef unsigned long long ULL;
34 //const
35 const int N=20;
36 const int INF=0x3f3f3f3f;
37 const int MOD=5000,STA=100010;
38 const LL LNF=1LL<<60;
39 const double EPS=1e-8;
40 const double OO=1e15;
41 const int dx[4]={-1,0,1,0};
42 const int dy[4]={0,1,0,-1};
43 const int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
44 //Daily Use ...
45 inline int sign(double x){return (x>EPS)-(x<-EPS);}
46 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
47 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}
48 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}
49 template<class T> inline T Min(T a,T b){return a<b?a:b;}
50 template<class T> inline T Max(T a,T b){return a>b?a:b;}
51 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}
52 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}
53 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}
54 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}
55 //End
56 
57 int num[N],g[5];
58 int T,n=15;
59 
60 int main()
61 {
62  //   freopen("in.txt","r",stdin);
63     int i,j,cou[2],w,ca=1;
64     scanf("%d",&T);
65     while(T--)
66     {
67         for(i=1;i<=n;i++)
68             scanf("%d",&num[i]);
69         g[1]=num[15];
70         g[2]=num[5]+num[6]-num[3]-num[4];
71         g[3]=num[11]+num[12]+num[13]+num[14];
72         g[4]=num[7]+num[8]-num[9]-num[10];
73      //   printf("%d %d %d %d
",g[1],g[2],g[3],g[4]);
74         cou[0]=num[1]*2;cou[1]=num[2]*2;
75         w=0;
76         if(g[1]&1){cou[w]++;w^=1;}
77         if(g[2]){
78             if(g[2]>0)cou[0]+=g[2]/2;
79             else cou[1]+=(-g[2])/2;
80             if(g[2]&1){
81                 if((!w && g[2]>0) || (w && g[2]<0))cou[w]++;
82                 w^=1;
83             }
84         }
85         if(g[3]&1)w^=1;
86         if(g[4]){
87             if(g[4]>0)cou[0]+=g[4]/2;
88             else cou[1]+=(-g[4])/2;
89             if(g[4]&1){
90                 if((w && g[4]>0) || (!w && g[4]<0))cou[!w]++;
91                 w^=1;
92             }
93         }
94 
95         printf("Case #%d: %s
",ca++,((cou[0]>cou[1]) || (cou[0]==cou[1] && w))?"Alice":"Bob");
96     }
97     return 0;
98 }

View Code

13.HDU 1847 SG函数找找规律就出来了。

 1 //STATUS:C++_AC_0MS_228KB
 2 #include <functional>
 3 #include <algorithm>
 4 #include <iostream>
 5 //#include <ext/rope>
 6 #include <fstream>
 7 #include <sstream>
 8 #include <iomanip>
 9 #include <numeric>
10 #include <cstring>
11 #include <cassert>
12 #include <cstdio>
13 #include <string>
14 #include <vector>
15 #include <bitset>
16 #include <queue>
17 #include <stack>
18 #include <cmath>
19 #include <ctime>
20 #include <list>
21 #include <set>
22 #include <map>
23 using namespace std;
24 //using namespace __gnu_cxx;
25 //define
26 #define pii pair<int,int>
27 #define mem(a,b) memset(a,b,sizeof(a))
28 #define lson l,mid,rt<<1
29 #define rson mid+1,r,rt<<1|1
30 #define PI acos(-1.0)
31 //typedef
32 typedef long long LL;
33 typedef unsigned long long ULL;
34 //const
35 const int N=20;
36 const int INF=0x3f3f3f3f;
37 const int MOD=5000,STA=100010;
38 const LL LNF=1LL<<60;
39 const double EPS=1e-8;
40 const double OO=1e15;
41 const int dx[4]={-1,0,1,0};
42 const int dy[4]={0,1,0,-1};
43 const int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
44 //Daily Use ...
45 inline int sign(double x){return (x>EPS)-(x<-EPS);}
46 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
47 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}
48 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}
49 template<class T> inline T Min(T a,T b){return a<b?a:b;}
50 template<class T> inline T Max(T a,T b){return a>b?a:b;}
51 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}
52 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}
53 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}
54 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}
55 //End
56 
57 int n;
58 
59 int main()
60 {
61  //   freopen("in.txt","r",stdin);
62     while(~scanf("%d",&n))
63     {
64         printf("%s
",n%3?"Kiki":"Cici");
65     }
66     return 0;
67 }

View Code

14.HDU 2147 转化为尼姆博弈。

 1 //STATUS:C++_AC_15MS_228KB
 2 #include <functional>
 3 #include <algorithm>
 4 #include <iostream>
 5 //#include <ext/rope>
 6 #include <fstream>
 7 #include <sstream>
 8 #include <iomanip>
 9 #include <numeric>
10 #include <cstring>
11 #include <cassert>
12 #include <cstdio>
13 #include <string>
14 #include <vector>
15 #include <bitset>
16 #include <queue>
17 #include <stack>
18 #include <cmath>
19 #include <ctime>
20 #include <list>
21 #include <set>
22 #include <map>
23 using namespace std;
24 //using namespace __gnu_cxx;
25 //define
26 #define pii pair<int,int>
27 #define mem(a,b) memset(a,b,sizeof(a))
28 #define lson l,mid,rt<<1
29 #define rson mid+1,r,rt<<1|1
30 #define PI acos(-1.0)
31 //typedef
32 typedef long long LL;
33 typedef unsigned long long ULL;
34 //const
35 const int N=20;
36 const int INF=0x3f3f3f3f;
37 const int MOD=5000,STA=100010;
38 const LL LNF=1LL<<60;
39 const double EPS=1e-8;
40 const double OO=1e15;
41 const int dx[4]={-1,0,1,0};
42 const int dy[4]={0,1,0,-1};
43 const int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
44 //Daily Use ...
45 inline int sign(double x){return (x>EPS)-(x<-EPS);}
46 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
47 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}
48 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}
49 template<class T> inline T Min(T a,T b){return a<b?a:b;}
50 template<class T> inline T Max(T a,T b){return a>b?a:b;}
51 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}
52 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}
53 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}
54 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}
55 //End
56 
57 int n;
58 
59 int main()
60 {
61  //   freopen("in.txt","r",stdin);
62     int a,b;
63     while(scanf("%d%d",&a,&b) && a && b)
64     {
65         printf("%s
",(a&1 && b&1)?"What a pity!":"Wonderful!");
66     }
67     return 0;
68 }

View Code

15.HDU 1525 简单博弈推导题，考虑到经过的数是一样的。

 1 //STATUS:C++_AC_15MS_228KB
 2 #include <functional>
 3 #include <algorithm>
 4 #include <iostream>
 5 //#include <ext/rope>
 6 #include <fstream>
 7 #include <sstream>
 8 #include <iomanip>
 9 #include <numeric>
10 #include <cstring>
11 #include <cassert>
12 #include <cstdio>
13 #include <string>
14 #include <vector>
15 #include <bitset>
16 #include <queue>
17 #include <stack>
18 #include <cmath>
19 #include <ctime>
20 #include <list>
21 #include <set>
22 #include <map>
23 using namespace std;
24 //using namespace __gnu_cxx;
25 //define
26 #define pii pair<int,int>
27 #define mem(a,b) memset(a,b,sizeof(a))
28 #define lson l,mid,rt<<1
29 #define rson mid+1,r,rt<<1|1
30 #define PI acos(-1.0)
31 //typedef
32 typedef long long LL;
33 typedef unsigned long long ULL;
34 //const
35 const int N=210;
36 const int INF=0x3f3f3f3f;
37 const int MOD=5000,STA=100010;
38 const LL LNF=1LL<<60;
39 const double EPS=1e-8;
40 const double OO=1e15;
41 const int dx[4]={-1,0,1,0};
42 const int dy[4]={0,1,0,-1};
43 const int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
44 //Daily Use ...
45 inline int sign(double x){return (x>EPS)-(x<-EPS);}
46 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
47 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}
48 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}
49 template<class T> inline T Min(T a,T b){return a<b?a:b;}
50 template<class T> inline T Max(T a,T b){return a>b?a:b;}
51 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}
52 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}
53 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}
54 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}
55 //End
56 
57 int main()
58 {
59   //  freopen("in.txt","r",stdin);
60     int ok,a,b,w;
61     while(~scanf("%d%d",&a,&b) && (a||b))
62     {
63         ok=w=0;
64         while(a && b){
65             if(a>b)swap(a,b);
66             if(b/a>=2){
67                 if(!w)ok=1;
68                 else ok=2;
69                 break;
70             }
71             b-=b/a*a;
72             w^=1;
73         }
74         if(!ok){
75             if(w)ok=1;
76             else ok=2;
77         }
78 
79         printf("%s wins
",ok==1?"Stan":"Ollie");
80     }
81     return 0;
82 }

View Code

16.HDU 3032 可以将一堆石子分成多堆——Multi-SG游戏，将SG函数适当变形，然后找规律。

 1 //STATUS:C++_AC_0MS_228KB
 2 #include <functional>
 3 #include <algorithm>
 4 #include <iostream>
 5 //#include <ext/rope>
 6 #include <fstream>
 7 #include <sstream>
 8 #include <iomanip>
 9 #include <numeric>
10 #include <cstring>
11 #include <cassert>
12 #include <cstdio>
13 #include <string>
14 #include <vector>
15 #include <bitset>
16 #include <queue>
17 #include <stack>
18 #include <cmath>
19 #include <ctime>
20 #include <list>
21 #include <set>
22 #include <map>
23 using namespace std;
24 //using namespace __gnu_cxx;
25 //define
26 #define pii pair<int,int>
27 #define mem(a,b) memset(a,b,sizeof(a))
28 #define lson l,mid,rt<<1
29 #define rson mid+1,r,rt<<1|1
30 #define PI acos(-1.0)
31 //typedef
32 typedef long long LL;
33 typedef unsigned long long ULL;
34 //const
35 const int N=210;
36 const int INF=0x3f3f3f3f;
37 const int MOD=5000,STA=100010;
38 const LL LNF=1LL<<60;
39 const double EPS=1e-8;
40 const double OO=1e15;
41 const int dx[4]={-1,0,1,0};
42 const int dy[4]={0,1,0,-1};
43 const int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
44 //Daily Use ...
45 inline int sign(double x){return (x>EPS)-(x<-EPS);}
46 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
47 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}
48 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}
49 template<class T> inline T Min(T a,T b){return a<b?a:b;}
50 template<class T> inline T Max(T a,T b){return a>b?a:b;}
51 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}
52 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}
53 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}
54 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}
55 //End
56 
57 int T,n;
58 
59 int main()
60 {
61  //   freopen("in.txt","r",stdin);
62     LL a,sg;
63     scanf("%d",&T);
64     while(T--)
65     {
66         scanf("%d",&n);
67         sg=0;
68         while(n--){
69             scanf("%I64d",&a);
70             if(a%4==0)sg^=a-1;
71             else if(a%4==3)sg^=a+1;
72             else sg^=a;
73         }
74 
75         printf("%s
",sg?"Alice":"Bob");
76     }
77     return 0;
78 }

View Code

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原文地址：https://www.cnblogs.com/zhsl/p/3176518.html

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