C - Bath Queue

https://codeforces.com/contest/28/submission/181061158

Codeforces/28/C/C.cpp

@@ -0,0 +1,59 @@
+#include <iostream>
+#include <cmath>
+#include <iomanip>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 55;
+
+int n, m, a[N];
+long long c[N][N];
+double f[N][N][N], sum, ans;
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    c[0][0] = 1;
+    for (int i = 1; i < N; ++i) {
+        c[i][0] = 1;
+
+        for (int j = 1; j <= i; ++j) {
+            c[i][j] = c[i - 1][j - 1] + c[i - 1][j];
+        }
+    }
+
+    cin >> n >> m;
+
+    for (int i = 1; i <= m; i++) {
+        cin >> a[i];
+    }
+
+    f[0][0][0] = 1;
+
+    for (int i = 1; i <= m; i++) {
+        for (int j = 0; j <= n; j++) {
+            for (int k = 0; k <= j; k++) {
+                for (int l = 0; l <= n - j; l++) {
+                    int p = std::max(static_cast<int>(std::ceil(static_cast<double>(l) / a[i])), k);
+
+                    f[i][j + l][p] += f[i - 1][j][k] * c[n - j][l];
+                }
+            }
+        }
+    }
+
+    for (int i = 0; i <= n; i++) {
+        sum += f[m][n][i];
+    }
+
+    for (int i = 1; i <= n; i++) {
+        ans += static_cast<double>(i) * f[m][n][i];
+    }
+
+    cout << std::fixed << std::setprecision(20) << ans / sum << endl;
+
+    return 0;
+}