From 41841f5dd5e859aaa44b5ef1abf1576e09f94d6e Mon Sep 17 00:00:00 2001
From: ADI <114460573+adityapatil4545@users.noreply.github.com>
Date: Mon, 24 Oct 2022 15:59:20 +0530
Subject: [PATCH] added Hat Check Problem
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This problem can be solved by counting the number n of derangements of an n–element set. A derangement is a permutation of a set’s elements, such that no element appears in its original position.
---
 Hat_Check_Problem.c | 22 ++++++++++++++++++++++
 1 file changed, 22 insertions(+)
 create mode 100644 Hat_Check_Problem.c

diff --git a/Hat_Check_Problem.c b/Hat_Check_Problem.c
new file mode 100644
index 0000000..ccb2ddb
--- /dev/null
+++ b/Hat_Check_Problem.c
@@ -0,0 +1,22 @@
+#include <stdio.h>
+ 
+// Recursive function to count the derangements of an n–element set
+int derangements(int n)
+{
+    // base case
+    if (n == 1 || n == 2) {
+        return n - 1;
+    }
+ 
+    // recur using the recurrence relation
+    return (n - 1) * (derangements(n - 1) + derangements(n - 2));
+}
+ 
+int main(void)
+{
+    int n = 4;
+    printf("The total number of derangements of a %d–element set is %d",
+        n, derangements(n));
+ 
+    return 0;
+}