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

Author: JawadSher

24 - Dynamic Programming Problems/10 - Painting the Fence/03 - Bottom-Up | DP | Approach.cpp

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+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
+    }
+    
+    // Function to calculate the number of ways to paint the fence with n posts and k colors
+    int solve(int n, int k){
+        // Initialize a dynamic programming (DP) array to store the number of ways to paint i posts
+        // dp[i] will store the number of ways to paint i posts
+        vector<int> dp(n+1, -1);
+        
+        // Base case: For 1 post, there are k ways to paint it using k colors
+        dp[1] = k;
+        
+        // Base case: For 2 posts, there are k * k ways to paint them
+        // The first post can be painted with any of the k colors, and the second post can be painted with any of the k colors
+        dp[2] = add(k, multi(k, k-1));
+        
+        // Fill the DP array iteratively for posts from 3 to n
+        // Use the recurrence relation:
+        // dp[i] = (dp[i-1] * (k-1)) + (dp[i-2] * (k-1))
+        for(int i = 3; i <= n; i++){
+            // Calculate the number of ways to paint i posts:
+            // - The first part (dp[i-1] * (k-1)) represents the case where the i-th post is painted with a different color than the (i-1)-th post
+            // - The second part (dp[i-2] * (k-1)) represents the case where the i-th post is painted with a different color than the (i-1)-th post
+            dp[i] = add(multi(dp[i-2], k-1), multi(dp[i-1], k-1));
+        }
+        
+        // Return the result for the nth post
+        return dp[n];
+    }
+    
+    // Main function to compute the number of ways to paint the fence
+    int countWays(int n, int k) {
+        // Call the solve function to compute the result
+        return solve(n, k);
+    }
+};