Create 04 - Space Optimized | DP | Approach.cpp

Author: JawadSher

24 - Dynamic Programming Problems/10 - Painting the Fence/04 - Space Optimized | 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){
+        // Base case: When there is only 1 post, there are k ways to paint it with k colors
+        if(n == 1) return k;
+
+        // Base case: When there are 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
+        if(n == 2) return add(k, multi(k, k-1));
+        
+        // Initializing the values for the first two posts (dp[1] and dp[2])
+        // prev2 represents dp[i-2] (previous to the current value)
+        // prev1 represents dp[i-1] (the previous value)
+        int prev2 = k;  // Ways to paint the first post
+        int prev1 = add(k, multi(k, k-1));  // Ways to paint two posts
+
+        // Iteratively calculate the number of ways to paint posts from 3 to n
+        for(int i = 3; i <= n; i++){
+            // Calculate the number of ways to paint the i-th post:
+            // - The first part (multi(prev2, 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 (multi(prev1, k-1)) represents the case where the i-th post is painted with a different color than the (i-1)-th post
+            int current = add(multi(prev2, k-1), multi(prev1, k-1));
+            
+            // Move the values forward for the next iteration
+            prev2 = prev1;  // Update prev2 to the value of prev1
+            prev1 = current;  // Update prev1 to the new current value
+        }
+
+        // Return the result for the nth post, which is stored in prev1
+        return prev1;
+    }
+
+    // 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);
+    }
+};