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

Author: JawadSher

24 - Dynamic Programming Problems/28 - Unique Binary Search Trees/02 - Top-Down | DP | Approach.cpp

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+class Solution {
+public:
+    // Helper function to calculate the number of unique BSTs for 'n' nodes using memoization.
+    int solve(int n, vector<int>& dp) {
+        // Base case: If there are 0 or 1 nodes, there is only 1 unique BST possible.
+        if(n <= 1) return 1;
+
+        // Check if the result for 'n' is already computed and stored in dp.
+        if(dp[n] != -1) return dp[n];
+
+        int ans = 0; // Initialize the variable to store the total number of unique BSTs.
+
+        // Loop through each number i from 1 to n.
+        // Treat 'i' as the root of the BST.
+        for(int i = 1; i <= n; i++) {
+            // Recursively calculate the number of unique BSTs for the left and right subtrees.
+            // Left subtree has (i-1) nodes.
+            // Right subtree has (n-i) nodes.
+            ans += solve(i-1, dp) * solve(n-i, dp);
+        }
+
+        // Store the computed result for 'n' in the dp array for future use.
+        return dp[n] = ans;
+    }
+
+    // Main function to calculate the number of unique BSTs for 'n' nodes.
+    int numTrees(int n) {
+        // Create a dp array initialized with -1 to indicate uncomputed results.
+        vector<int> dp(n+1, -1);
+
+        // Call the helper function with the initial value of 'n' and the dp array.
+        return solve(n, dp);
+    }
+};