🚀 **Catalan Numbers & Unique BSTs!** 🌳🧮 Did you know the number of unique Binary Search Trees (BSTs) with `n` nodes can be found using Catalan numbers? Here's how! ### Formula The nth Catalan number is given by: \[ C_n = \frac{1}{n + 1} \binom{2n}{n} \] In Python:

Explanation - Time Complexity: (O(n)) because we iterate `n` times. - Space Complexity: (O(1)) because we're using a constant amount of space to store the interim result.

### Real-World Use Case **Expression Parsing**: Unique BSTs are crucial in compiler design for parsing arithmetic expressions. They help in generating different parse trees for expressions, ensuring that code gets compiled correctly and efficiently.

For instance,parsing the expression `a + b * c` couldyield different trees basedon operator precedence, ultimately affecting the compiledoutput. Unleash the power of Catalan numbers in your projects! 🚀🌟 #Python #Algorithms #DataStructures #CodingTips #DevTricks #CompilerDesign