// Elimination // Solution by Jacob Plachta #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; #define LL long long #define LD long double #define PR pair #define Fox(i,n) for (i=0; i=0; i--) #define FoxR1(i,n) for (i=n; i>0; i--) #define FoxRI(i,a,b) for (i=b; i>=a; i--) #define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++) #define Min(a,b) a=min(a,b) #define Max(a,b) a=max(a,b) #define Sz(s) int((s).size()) #define All(s) (s).begin(),(s).end() #define Fill(s,v) memset(s,v,sizeof(s)) #define pb push_back #define mp make_pair #define x first #define y second template T Abs(T x) { return(x < 0 ? -x : x); } template T Sqr(T x) { return(x * x); } string plural(string s) { return(Sz(s) && s[Sz(s) - 1] == 'x' ? s + "en" : s + "s"); } const int INF = (int)1e9; const LD EPS = 1e-12; const LD PI = acos(-1.0); #define GETCHAR getchar_unlocked #define LIM 8001 // dyn[b][w] = expected number of remaining rounds // when there are b better and w worse players than you LD dyn[LIM][LIM]; int NumPairs(int c) { return(c * (c - 1) / 2); } // inv indicates that b/w have been swapped to capture worse players winning LD Comp(int b, int w, bool inv) { LD p = (LD)1 / NumPairs(b + w + 1), d = 0; // elimination of better player than you if (b > 0) d += NumPairs(b) * p * (inv ? dyn[w][b - 1] : dyn[b - 1][w]); // elimination of worse player than you if (w > 0) d += (w * (b + 1) + NumPairs(w)) * p * (inv ? dyn[w - 1][b] : dyn[b][w - 1]); return(d); } void ProcessCase() { int N, i, b, w; LD P; // input scanf("%d%Lf", &N, &P); // DP Fill(dyn, 0); Fox(b, N) { Fox(w, N - b) { if (b + w) { dyn[b][w] = 1 + Comp(b, w, false) * P + // better players winning Comp(w, b, true) * (1 - P); // worse players winning } } } // output Fox(i, N) printf("%.8Lf\n", dyn[N - i - 1][i]); } int main() { int T, t; scanf("%d\n", &T); Fox1(t, T) { printf("Case #%d:\n", t); ProcessCase(); } return(0); }