Create 04 - Catalan Number Approach.cpp

Author: JawadSher

24 - Dynamic Programming Problems/28 - Unique Binary Search Trees/04 - Catalan Number Approach.cpp

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+class Solution {
+public:
+    // Function to calculate the nth Catalan number using a mathematical formula.
+    int solve(int n) {
+        // Initialize a variable to store the computed Catalan number.
+        // Using 'long long' to handle intermediate results that might exceed int limits.
+        long long catalan = 1;
+
+        // Compute the value of (2n)! / n! in a loop.
+        // This is a part of the Catalan number formula: C(n) = (2n)! / ((n+1)! * n!).
+        for (int i = 0; i < n; i++) {
+            // Update 'catalan' using the current term of the formula.
+            // Multiply by (2n - i) and divide by (i + 1) iteratively.
+            catalan = catalan * (2 * n - i) / (i + 1);
+        }
+
+        // Divide the computed value by (n + 1) to complete the Catalan number calculation.
+        return catalan / (n + 1);
+    }
+
+    // Main function to calculate the number of unique BSTs for 'n' nodes.
+    int numTrees(int n) {
+        // Call the helper function 'solve' to compute the nth Catalan number.
+        return solve(n);
+    }
+};