Create 01 - Recursive Approach (caused TLE).cpp

Author: JawadSher

24 - Dynamic Programming Problems/10 - Painting the Fence/01 - Recursive Approach (caused TLE).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){
+        // Base case: If there is only one post, there are k ways to paint it with k colors
+        if(n == 1) return k;
+        
+        // Base case: If there are two posts, there are k * k ways to paint them
+        // (each post can be painted with any of the k colors)
+        if(n == 2) return add(k, multi(k, k-1));
+        
+        // Recurrence relation:
+        // The number of ways to paint n posts is calculated as:
+        // dp[n] = (dp[n-1] * (k-1)) + (dp[n-2] * (k-1))
+        // This is based on the fact that we can paint the nth post in (k-1) ways to avoid
+        // repeating the color of the (n-1)th post.
+        int ans = add(multi(solve(n-2, k), k-1), multi(solve(n-1, k), k-1));
+        
+        // Return the calculated number of ways to paint n posts
+        return ans;
+    }
+
+    // Main function to initiate the calculation and return the result
+    int countWays(int n, int k) {
+        return solve(n, k);  // Call the solve function to calculate the result
+    }
+};