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

Author: JawadSher

24 - Dynamic Programming Problems/10 - Painting the Fence/02 - Top-Down | DP | Approach.cpp

@@ -0,0 +1,41 @@
+class Solution {
+  public:
+    // Helper function to add two integers
+    int add(int a, int b){
+        return (a + b);  // Returns the sum of a and b
+    }
+    
+    // Helper function to multiply two integers
+    int multi(int a, int b){
+        return (a * b);  // Returns the product of a and b
+    }
+    
+    // Recursive function with memoization to calculate the number of ways to paint the fence
+    // n: number of posts, k: number of colors, dp: memoization array
+    int solve(int n, int k, vector<int>& dp){
+        // Base case 1: If there is only one post, there are k ways to paint it with k colors
+        if(n == 1) return k;
+
+        // Base case 2: If there are two posts, there are k * k ways to paint them
+        if(n == 2) return add(k, multi(k, k-1));
+        
+        // If the result for the current number of posts is already computed (cached), return it
+        if(dp[n] != -1) return dp[n];
+        
+        // Recursive case: Use the recurrence relation to calculate the number of ways to paint n posts
+        // D(n) = (D(n-1) * (k-1)) + (D(n-2) * (k-1))
+        dp[n] = add(multi(solve(n-2, k, dp), k-1), multi(solve(n-1, k, dp), k-1));
+        
+        // Return the result for the current number of posts
+        return dp[n];
+    }
+
+    // Main function to initialize the DP array and call the solve function
+    int countWays(int n, int k) {
+        // Create a memoization array to store the result for each number of posts (initially -1)
+        vector<int> dp(n+1, -1);
+        
+        // Call the solve function to calculate and return the result
+        return solve(n, k, dp);
+    }
+};