[THOJ 1599] dices 期望DP

  1 #include <cstdio>
  2 #include <cstring>
  3 #include <cstdlib>
  4 #include <cctype>
  5 #include <map>
  6 using namespace std;
  7 #define F(i, a, b) for (register int i = (a); i <= (b); i++)
  8 #define D(i, a, b) for (register int i = (a); i >= (b); i--)
  9 #define db double
 10 
 11 db p[10];
 12 
 13 int cnt[10];
 14 int idx, id[500], pos[50000];
 15 db P[500], w[500][15];
 16 
 17 void Prework(int dep, db Ps) {
 18     if (dep > 5) {
 19         int St = 0; F(i, 1, 6) St = St * 6 + cnt[i];
 20         
 21         bool tag = (pos[St] > 0);
 22         if (!tag) id[++idx] = St, pos[St] = idx;
 23         
 24         int Loc = pos[St];
 25         P[Loc] += Ps;
 26         
 27         if (!tag) {
 28             int sum = 0; F(i, 1, 6) sum += i * cnt[i];
 29             
 30             w[Loc][14] = sum;
 31             
 32             bool Same = false;
 33             F(i, 1, 6) if (cnt[i] == 5) Same = true;
 34             if (Same) w[Loc][13] = 50;
 35             
 36             bool Five = (cnt[2] > 0 && cnt[3] > 0 && cnt[4] > 0 && cnt[5] > 0);
 37             if (Five && (cnt[1] > 0 || cnt[6] > 0))
 38                 w[Loc][12] = 40;
 39             
 40             bool Four = (cnt[1] > 0 && cnt[2] > 0 && cnt[3] > 0 && cnt[4] > 0);
 41             Four |= (cnt[2] > 0 && cnt[3] > 0 && cnt[4] > 0 && cnt[5] > 0);
 42             Four |= (cnt[3] > 0 && cnt[4] > 0 && cnt[5] > 0 && cnt[6] > 0);
 43             if (Four) w[Loc][11] = 30;
 44             
 45             bool Three = false, Two = false;
 46             F(i, 1, 6) {
 47                 if (cnt[i] == 3) Three = true;
 48                 if (cnt[i] == 2) Two = true;
 49             }
 50             if (Three && Two) w[Loc][10] = 25;
 51             
 52             Four = false;
 53             F(i, 1, 6) if (cnt[i] >= 4) Four = true;
 54             if (Four) w[Loc][9] = sum;
 55             
 56             Three = false;
 57             F(i, 1, 6) if (cnt[i] >= 3) Three = true;
 58             if (Three) w[Loc][8] = sum;
 59             
 60             int twocnt = 0;
 61             F(i, 1, 6) twocnt += (cnt[i] >= 2);
 62             if (twocnt >= 2) w[Loc][7] = sum;
 63             
 64             F(i, 1, 6) w[Loc][i] = i * cnt[i];
 65         }
 66         
 67         return;
 68     }
 69     F(w, 1, 6) {
 70         cnt[w]++;
 71         Prework(dep+1, Ps * p[w]);
 72         cnt[w]--;
 73     }
 74 }
 75 
 76 db f[20000];
 77 
 78 int main(void) {
 79     #ifndef ONLINE_JUDGE
 80         freopen("dices.in", "r", stdin);
 81     #endif
 82     
 83     int nT; scanf("%d", &nT);
 84     F(cas, 1, nT) {
 85         F(i, 1, 6) scanf("%lf", p+i);
 86         
 87         idx = 0, memset(id, 0, sizeof id), memset(pos, 0, sizeof pos);
 88         memset(P, 0, sizeof P), memset(w, 0, sizeof w);
 89         Prework(1, 1);
 90         
 91         memset(f, 0, sizeof f);
 92         D(St, (1 << 14) - 2, 0)
 93             F(Loc, 1, idx) {
 94                 db Max = 0;
 95                 F(Dec, 1, 14) if (~St >> Dec-1 & 1)
 96                     Max = max(Max, w[Loc][Dec] + f[St | (1 << Dec-1)]);
 97                 f[St] += P[Loc] * Max;
 98             }
 99         printf("Case #%d: %0.6lf\n", cas, f[0]);
100     }
101     
102     return 0;
103 }