Expression tree
- 1. Expression tree Nagajothi N 1 M.Sc., IT 1
- 2. Objectives What is expression tree What are expressions in data structures? What kind of expression tree What type of data structure is tree? Construction of expression tree Traversal of expression tree Algebraic expression tree Boolean expression tree 2
- 3. What is expression tree A binary expression tree is a specific kind of a binary tree used to represent expressions. .. These trees can represent expressions that contain both unary and binary operators Each node of a binary tree, and hence of a binary expression tree, has zero, one, or two children. 3
- 4. What are expressions in data structures? An expression is a collection of operators and operands that represents a specific value. operator is a symbol which performs a particular task like arithmetic operation or logical operation or conditional operation etc., Operands are the values on which the operators can perform the task 4
- 6. There are three kinds of expressions An arithmetic expression evaluates to a single arithmetic value.(x, x 2, xy, or 3xy 2,) A character expression evaluates to a single value of type character. A logical or relational expression evaluates to a single logical value(TRUE or FALSE) 6
- 7. What type of data structure is tree? A tree is a hierarchical data structure which can represent relationships between different nodes 7
- 9. Construction of expression tree Now For constructing an expression tree we use a stack. If a character is an operator pop two values from the stack make them its child and push the current node again 9
- 10. example 10
- 11. Algebraic expression Algebraic expression trees represent expressions that contain numbers,variables, and unary and binary operators. Some of the common operators are × (multiplication), ÷ (division), + (addition), − (subtraction), ^ (exponentiation), and - (negation) 11
- 12. Boolean expressions Boolean expressions use true and false as constant values, and the operators include (AND), (OR), (NOT). 12
- 13. Traversal of expression tree infix expression Postfix expression Prefix expression 13
- 14. infix expression X + Y. Operators are written in-between their operands An expression such as A * ( B + C ) / D is usually taken to mean something like: "First add B and C together, then multiply the result by A, then divide by D to give the final answer." 14
- 15. example 15
- 16. Postfix expression X Y + Operators are written after their operands. The infix expression given above is equivalent to A B C + * D / 16
- 17. example 17
- 18. Prefix expression + X Y Operators are written before their operands. The expressions given above are equivalent to / * A + B C D 18
- 19. example 19
- 20. Thankyou ! 20