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

Author: JawadSher

24 - Dynamic Programming Problems/28 - Unique Binary Search Trees/03 - Bottom-Up | DP | Approach.cpp

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+class Solution {
+public:
+    // Function to calculate the number of unique BSTs for 'n' nodes using a bottom-up approach.
+    int solve(int n) {
+        // Create a dp array of size (n+1) to store the results for subproblems.
+        // dp[i] will hold the number of unique BSTs that can be formed with 'i' nodes.
+        vector<int> dp(n+1, 0);
+
+        // Base cases:
+        // When there are 0 nodes, there is 1 unique BST (an empty tree).
+        // When there is 1 node, there is 1 unique BST (the single node as the root).
+        dp[0] = dp[1] = 1;
+
+        // Fill the dp array for all values from 2 to n (Bottom-Up approach).
+        for (int i = 2; i <= n; i++) {
+            // Calculate the number of unique BSTs for 'i' nodes.
+            for (int j = 1; j <= i; j++) {
+                // Treat 'j' as the root node.
+                // The left subtree has (j-1) nodes.
+                // The right subtree has (i-j) nodes.
+                dp[i] += dp[j-1] * dp[i-j];
+            }
+        }
+
+        // Return the result for 'n' nodes.
+        return dp[n];
+    }
+
+    // Main function to calculate the number of unique BSTs for 'n' nodes.
+    int numTrees(int n) {
+        return solve(n); // Call the helper function with the input 'n'.
+    }
+};