#include #include #include #include #include #include #include #include #include // require sort next_permutation count __gcd reverse etc. #include // require abs exit atof atoi #include // require scanf printf #include #include // require accumulate #include // require fabs #include #include #include #include // require setw #include // require stringstream #include // require memset #include // require tolower, toupper #include // require freopen #include // require srand #define rep(i,n) for(int i=0;i<(n);i++) #define ALL(A) A.begin(), A.end() using namespace std; typedef long long ll; typedef pair P; /* No.65 回数の期待値の練習 No.72 の確率固定版。 E[1] = 1 E[2] = E[1]*P1 + 1 = E[1]/6 + 1 E[3] = E[2]*P1 + E[1]*P2 + 1 = (E[2] + E[1] )/6 + 1 E[4] = E[3]*P1 + E[2]*P2 + E[1]*P3 + 1 = (E[3] + E[2] + E[1] )/6 + 1 E[5] = E[4]*P1 + E[3]*P2 + E[2]*P3 + E[1]*P4 + 1 = (E[4] + E[3] + E[2] + E[1] )/6 + 1 E[6] = E[5]*P1 + E[4]*P2 + E[3]*P3 + E[2]*P4 + E[1]*P5 + 1 = (E[5] + E[4] + E[3] + E[2] + E[1] )/6 + 1 E[7] = E[6]*P1 + E[5]*P2 + E[4]*P3 + E[3]*P4 + E[2]*P5 + E[1]*P6 + 1 = (E[6] + E[5] + E[4] + E[3] + E[2] + E[1] )/6 + 1 問題文は x >= 7 のとき E[x] = E[x-1]*1/6 + E[x-2]*1/6 + E[x-3]*1/6 + E[x-4]*1/6 + E[x-5]*1/6 + E[x-6]*1/6 + 1 の誤植かな? */ const int MAX_K = 22; double E[MAX_K]; int main() { memset (E, 0., sizeof (E ) ); ios_base::sync_with_stdio(0); E[1] = 1.; E[2] = E[1]/6. + 1.; E[3] = (E[2] + E[1] )/6. + 1.; E[4] = (E[3] + E[2] + E[1] )/6. + 1.; E[5] = (E[4] + E[3] + E[2] + E[1] )/6. + 1.; E[6] = (E[5] + E[4] + E[3] + E[2] + E[1] )/6. + 1.; for (int i = 7; i < MAX_K; i++ ){ for (int j = 1; j <= 6; j++ ){ E[i] += E[i-j]/6.; } // end for E[i] += 1.; } // end for int K; cin >> K; printf ("%.6lf\n", E[K] ); return 0; }