Create 04 - Space Optimized | DP | Approach.cpp

Author: JawadSher

24 - Dynamic Programming Problems/09 - Dis-arrangement of Balls/04 - Space Optimized | DP | Approach.cpp

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+class Solution {
+public:
+    // Function to calculate derangements using space-optimized approach
+    int solve(int n) {
+        // Base case: For n = 1, there are no valid derangements
+        if (n == 1) return 0;
+
+        // Base case: For n = 2, there is exactly one valid derangement
+        if (n == 2) return 1;
+
+        // Initialize variables to store results for the last two states
+        // prev: D(n-2), curr: D(n-1)
+        int prev = 0; // D(1)
+        int curr = 1; // D(2)
+
+        // Loop to calculate D(n) iteratively using the relation:
+        // D(i) = (i-1) * (D(i-1) + D(i-2))
+        for (int i = 3; i <= n; i++) {
+            // Compute the next derangement value
+            int next = (i - 1) * (curr + prev);
+
+            // Update prev and curr for the next iteration
+            prev = curr;
+            curr = next;
+        }
+
+        // Return the result for D(n)
+        return curr;
+    }
+    
+    // Main function to calculate derangements
+    int countDer(int n) {
+        // Delegate the computation to the solve function
+        return solve(n);    
+    }
+};