【HDOJ6224】Legends of the Three Kingdoms（概率DP）

题意：三国杀，给定4个白板武将的血量，4个角色轮流行动，每回合行动时如果该人存活则可以选择使阵营不同的角色血量-1，血量为0则死亡。每个人按自己获胜概率最大化行动，如果有多种方案概率相同则等概率选择这些策略，问最后主公、反贼、内奸三个阵营分别获胜的概率

0 < h1 < 40, 0 ≤ h2 < 40, 0 ≤ h3 < 40, 0 ≤ h4 < 40

思路：当前的决策与概率只与血量和当前行动的人有关

注意行动顺序是主公，反贼，忠臣，内奸

其他的具体看代码注释吧

 #include<cstdio>
 #include<cstring>
 #include<string>
 #include<cmath>
 #include<iostream>
 #include<algorithm>
 #include<map>
 #include<set>
 #include<queue>
 #include<vector>
 using namespace std;
 typedef long long ll;
 typedef unsigned int uint;
 typedef unsigned long long ull;
 typedef pair<int,int> PII;
 typedef vector<int> VI;
 #define fi first
 #define se second
 #define MP make_pair
 #define N   11000
 #define M   41
 #define MOD 1e9+7
 #define eps 1e-13
 #define pi acos(-1)

 double dp[][][][][][];
 bool vis[][][][][];

 int read()
 {
    int v=,f=;
    char c=getchar();
    while(c<||<c) {if(c=='-') f=-; c=getchar();}
    while(<=c&&c<=) v=(v<<)+v+v+c-,c=getchar();
    return v*f;
 }

 void dfs(int a,int b,int c,int d,int i)
 {
     if(vis[a][b][c][d][i]) return;

     vis[a][b][c][d][i]=;

     if(!c&&!d)    //Both of the Rebel and the Traitor are dead
     {
         dp[a][b][c][d][i][]=1.0;
         dp[a][b][c][d][i][]=dp[a][b][c][d][i][]=0.0;
         return;     //Monarch and the Minister win
     }

     if(!a)    //The Monarch is dead
     {
         if(a+b+c==)    //If the Traitor is surviving and all the other players are dead
         {
             dp[a][b][c][d][i][]=1.0;
             dp[a][b][c][d][i][]=dp[a][b][c][d][i][]=0.0;
             return; //the Traitor wins
         }
          else
          {
              dp[a][b][c][d][i][]=1.0;
              dp[a][b][c][d][i][]=dp[a][b][c][d][i][]=0.0;
              return;    //the Rebel wins
          }
     }

     if(i==&&a==||i==&&c==||i==&&b==||i==&&d==)         //deadman turn
     {
         dfs(a,b,c,d,(i+)%);
         for(int j=;j<=;j++) dp[a][b][c][d][i][j]=dp[a][b][c][d][(i+)%][j];
         return;
     }

     int j=(i+)%;
     double s1=0.0;
     double s2=0.0;
     double s3=0.0;
     int x=;

     if(i==||i==)    //Monarch and the Minister
     {
         double t=-1.0;

         if(c)
         {
             dfs(a,b,c-,d,j);
             double k=dp[a][b][c-][d][j][];

             if(k-t>eps)
             {
                 x=;
                 t=k;
                 s1=dp[a][b][c-][d][j][];
                 s2=dp[a][b][c-][d][j][];
                 s3=dp[a][b][c-][d][j][];
             }
             else
             if(fabs(k-t)<eps)
             {
                 x++;
                 s1+=dp[a][b][c-][d][j][];
                 s2+=dp[a][b][c-][d][j][];
                 s3+=dp[a][b][c-][d][j][];
             }
         }

         if(d)
         {
             dfs(a,b,c,d-,j);
             double k=dp[a][b][c][d-][j][];

             if(k-t>eps)
             {
                 x=;
                 t=k;
                 s1=dp[a][b][c][d-][j][];
                 s2=dp[a][b][c][d-][j][];
                 s3=dp[a][b][c][d-][j][];
             }
             else
             if(fabs(k-t)<eps)
             {
                 x++;
                 s1+=dp[a][b][c][d-][j][];
                 s2+=dp[a][b][c][d-][j][];
                 s3+=dp[a][b][c][d-][j][];
             }
         }
     }

     if(i==)    //Rebel
     {
         double t=-1.0;

         if(a)
         {
             dfs(a-,b,c,d,j);
             double k=dp[a-][b][c][d][j][];

             if(k-t>eps)
             {
                 x=;
                 t=k;
                 s1=dp[a-][b][c][d][j][];
                 s2=dp[a-][b][c][d][j][];
                 s3=dp[a-][b][c][d][j][];
             }
             else
             if(fabs(k-t)<eps)
             {
                 x++;
                 s1+=dp[a-][b][c][d][j][];
                 s2+=dp[a-][b][c][d][j][];
                 s3+=dp[a-][b][c][d][j][];
             }
         }

         if(b)
         {
             dfs(a,b-,c,d,j);
             double k=dp[a][b-][c][d][j][];

             if(k-t>eps)
             {
                 x=;
                 t=k;
                 s1=dp[a][b-][c][d][j][];
                 s2=dp[a][b-][c][d][j][];
                 s3=dp[a][b-][c][d][j][];
             }
             else
             if(fabs(k-t)<eps)
             {
                 x++;
                 s1+=dp[a][b-][c][d][j][];
                 s2+=dp[a][b-][c][d][j][];
                 s3+=dp[a][b-][c][d][j][];
             }
         }

         if(d)
         {
             dfs(a,b,c,d-,j);
             double k=dp[a][b][c][d-][j][];

             if(k-t>eps)
             {
                 x=;
                 t=k;
                 s1=dp[a][b][c][d-][j][];
                 s2=dp[a][b][c][d-][j][];
                 s3=dp[a][b][c][d-][j][];
             }
             else
             if(fabs(k-t)<eps)
             {
                 x++;
                 s1+=dp[a][b][c][d-][j][];
                 s2+=dp[a][b][c][d-][j][];
                 s3+=dp[a][b][c][d-][j][];
             }
         }
     }

     if(i==)    //Traitor
     {
         double t=-1.0;

         if(a)
         {
             dfs(a-,b,c,d,j);
             double k=dp[a-][b][c][d][j][];

             if(k-t>eps)
             {
                 x=;
                 t=k;
                 s1=dp[a-][b][c][d][j][];
                 s2=dp[a-][b][c][d][j][];
                 s3=dp[a-][b][c][d][j][];
             }
             else
             if(fabs(k-t)<eps)
             {
                 x++;
                 s1+=dp[a-][b][c][d][j][];
                 s2+=dp[a-][b][c][d][j][];
                 s3+=dp[a-][b][c][d][j][];
             }
         }

         if(b)
         {
             dfs(a,b-,c,d,j);
             double k=dp[a][b-][c][d][j][];

             if(k-t>eps)
             {
                 x=;
                 t=k;
                 s1=dp[a][b-][c][d][j][];
                 s2=dp[a][b-][c][d][j][];
                 s3=dp[a][b-][c][d][j][];
             }
             else
             if(fabs(k-t)<eps)
             {
                 x++;
                 s1+=dp[a][b-][c][d][j][];
                 s2+=dp[a][b-][c][d][j][];
                 s3+=dp[a][b-][c][d][j][];
             }
         }

         if(c)
         {
             dfs(a,b,c-,d,j);
             double k=dp[a][b][c-][d][j][];

             if(k-t>eps)
             {
                 x=;
                 t=k;
                 s1=dp[a][b][c-][d][j][];
                 s2=dp[a][b][c-][d][j][];
                 s3=dp[a][b][c-][d][j][];
             }
             else
             if(fabs(k-t)<eps)
             {
                 x++;
                 s1+=dp[a][b][c-][d][j][];
                 s2+=dp[a][b][c-][d][j][];
                 s3+=dp[a][b][c-][d][j][];
             }
         }
     }

     dp[a][b][c][d][i][]=s1/x;
     dp[a][b][c][d][i][]=s2/x;
     dp[a][b][c][d][i][]=s3/x;
     //printf("%d %d %d %d %d %.3lf %.3lf %.3lf\n",a,b,c,d,i,dp[a][b][c][d][i][0],dp[a][b][c][d][i][1],dp[a][b][c][d][i][2]);
 }

 int main()
 {
     freopen("hdoj6224.in","r",stdin);
     freopen("hdoj6224.out","w",stdout);
     int cas;
     scanf("%d",&cas);

     memset(vis,,sizeof(vis));

     while(cas--)
     {
         int A,B,C,D;
          scanf("%d%d%d%d",&A,&B,&C,&D);
          dfs(A,B,C,D,);
          printf("%.6lf %.6lf %.6lf\n",dp[A][B][C][D][][],dp[A][B][C][D][][],dp[A][B][C][D][][]);
     }
     return ;
 }