Understanding Expression Trees
An expression tree is a specific kind of binary tree used to represent expressions. The leaves of the tree are operands (such as constants or variable names), and the other internal nodes contain operators.
How it Works
1. Infix to Postfix Conversion
The visualizer first converts the user-provided infix expression (e.g., (a+b)*c)
into postfix notation (e.g., ab+c*) using the Shunting-yard algorithm.
This simplifies the tree construction process as postfix notation removes the need for
parentheses and handles operator precedence.
2. Postfix to Tree Construction
Using a stack, we iterate through the postfix expression:
- If the token is an operand, create a node and push it onto the stack.
- If the token is an operator, pop two nodes from the stack, make them the right and left children of a new operator node, and push the operator node back onto the stack.
JS Implementation
- Custom Stack-based algorithm
- SVG-based dynamic rendering
- Recursive tree traversal for layout
- State snapshotting for history
Complexity Analysis
Time Complexity
O(n)
Linear pass through expression
Space Complexity
O(n)
Storage for the tree structure