From ea9baef29c8f2d6e3b6e59ffa7b78c1b45e4757e Mon Sep 17 00:00:00 2001
From: Baoshuo <i@baoshuo.ren>
Date: Tue, 15 Nov 2022 17:16:40 +0800
Subject: [PATCH] C - Bath Queue

https://codeforces.com/contest/28/submission/181061158
---
 Codeforces/28/C/C.cpp | 59 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 59 insertions(+)
 create mode 100644 Codeforces/28/C/C.cpp

diff --git a/Codeforces/28/C/C.cpp b/Codeforces/28/C/C.cpp
new file mode 100644
index 00000000..c410f19d
--- /dev/null
+++ b/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;
+}