Create 01 - Recursive Approach.cpp

Author: JawadSher

24 - Dynamic Programming Problems/09 - Dis-arrangement of Balls/01 - Recursive Approach.cpp

@@ -0,0 +1,22 @@
+class Solution {
+  public:
+    // Function to calculate the number of derangements for n items
+    int countDer(int n) {
+        // Base case: For n = 1, there is no valid dearrangement
+        if(n == 1) return 0;
+
+        // Base case: For n = 2, there is exactly one valid dearrangement: {2, 1}
+        if(n == 2) return 1;
+
+        // Recursive relation for derangement:
+        // totalRelations = (n-1) * (countDer(n-1) + countDer(n-2))
+        // Explanation:
+        // - (n-1): Choose a position for the first item (other than its original position).
+        // - countDer(n-1): Solve the subproblem for the remaining (n-1) items.
+        // - countDer(n-2): Solve the subproblem for (n-2) items when swapping is involved.
+        int totalRelations = (n-1) * (countDer(n-1) + countDer(n-2));
+        
+        // Return the total number of derangements for n items
+        return totalRelations;
+    }
+};