Create 03 - Bottom-Up | DP | Approach.cpp

Author: JawadSher

24 - Dynamic Programming Problems/09 - Dis-arrangement of Balls/03 - Bottom-Up | DP | Approach.cpp

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+class Solution {
+  public:
+    // Function to calculate derangements using tabulation (iterative dynamic programming)
+    int solve(int n) {
+        // Create a DP array to store the number of derangements for each value from 0 to n
+        vector<int> dp(n + 1, -1);
+
+        // Base cases:
+        // For n = 1, there are no valid derangements
+        dp[1] = 0;
+
+        // For n = 2, there is exactly one valid derangement
+        dp[2] = 1;
+
+        // Fill the DP array iteratively using the relation:
+        // D(i) = (i-1) * (D(i-1) + D(i-2))
+        for (int i = 3; i <= n; i++) {
+            dp[i] = (i - 1) * (dp[i - 1] + dp[i - 2]);
+        }
+
+        // Return the result for n
+        return dp[n];
+    }
+
+    // Main function to calculate derangements
+    int countDer(int n) {
+        // Delegate the computation to the solve function
+        return solve(n);
+    }
+};