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Operations & Algorithms of Expression Trees - (BCA / B.Tech)

Operations & Algorithms of Expression Trees in Data Structures:

Expression Tree:

An expression tree is a binary tree used to represent a mathematical or logical expression. It contains operator nodes and operand nodes (numbers or variables).

Structure of an Expression Tree:

Internal nodes are operators, and leaf nodes are operands. For example, `A + B * C` is represented with `+` at the root, `A` as its left child, and `*` as its right child, which in turn has `B` and `C` as its children.

Operations of an Expression Tree:

Construction: Expression trees are usually built from postfix, prefix, or infix expressions. Postfix is common as it can be easily constructed using a stack.

Evaluation: The main use of an expression tree is to calculate the value of the expression. This is done by traversing the tree (Inorder, Postorder, Preorder). Postorder traversal is most common for evaluation.

Traversal: Inorder, Postorder, and Preorder traversals can be used to reconstruct the expression in different formats.

Algorithm for Expression Tree Construction:

An expression tree can be easily built from a postfix expression using a stack:

Create an empty stack.
Scan the postfix expression from left to right.
If an operand is found, convert it into a node and push it onto the stack.
If an operator is found:
- Pop two nodes from the stack.
- Create a new node for the operator.
- Set the popped nodes as its children.
- Push this new node onto the stack.
Finally, the one node left in the stack is the root of the expression tree.

Advantages and Disadvantages:

Advantages: Useful for storing and managing expressions, easy evaluation, flexibility in reconstructing expressions, and widely used in compilers.

Disadvantages: Increased complexity for large expressions, higher resource usage, and time-consuming for evaluation of large trees.

Expression Tree Program in C/C++:

The provided C++ code demonstrates how to construct an expression tree from a postfix expression using a stack and then perform an inorder traversal on it.

Operations & Algorithms of Expression Trees

Operations & Algorithms of Expression Trees in Data Structures:

In this Chapter