Create 02 - Top-Down | DP | Approach.cpp

Author: JawadSher

24 - Dynamic Programming Problems/09 - Dis-arrangement of Balls/02 - Top-Down | DP | Approach.cpp

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+class Solution {
+  public:
+    // Helper function to calculate derangements recursively with memoization
+    int solve(int n, vector<int>& dp) {
+        // Base case: For n = 1, no valid dearrangements exist
+        if(n == 1) return 0;
+
+        // Base case: For n = 2, exactly one valid dearrangement exists
+        if(n == 2) return 1;
+
+        // If the result for this value of n has already been computed, return it
+        if(dp[n] != -1) return dp[n];
+
+        // Use the recursive relation:
+        // D(n) = (n-1) * (D(n-1) + D(n-2))
+        dp[n] = (n-1) * (solve(n-1, dp) + solve(n-2, dp));
+
+        // Return the computed result
+        return dp[n];
+    }
+
+    // Main function to compute derangements of n items
+    int countDer(int n) {
+        // Create a memoization array initialized with -1
+        // dp[i] will store the number of derangements for i items
+        vector<int> dp(n+1, -1);
+
+        // Call the helper function to compute the result
+        return solve(n, dp);
+    }
+};