The document discusses expression trees, which are binary trees used to represent expressions. Each node in an expression tree contains either an operator or operand. There are three types of expressions - arithmetic, character, and logical/relational - which evaluate to a number, character, or true/false value. The document describes how to construct an expression tree using a stack, and provides examples of algebraic and Boolean expression trees. It also discusses traversing expression trees using infix, postfix, and prefix notation and provides examples of each.

1. Expression tree
Nagajothi N
1 M.Sc., IT
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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
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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.
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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
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5. Operators
Operands
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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)
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7. What type of data structure is tree?
 A tree is a hierarchical data structure which can
represent relationships between different
nodes
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8. Tree structure
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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
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10. example
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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)
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12. Boolean expressions
 Boolean expressions use true and false as
constant values, and the operators
include (AND), (OR), (NOT).
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13. Traversal of expression tree
infix
expression
Postfix
expression
Prefix
expression
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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."
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15. example
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16. Postfix expression
 X Y + Operators are written after their
operands. The infix expression given above is
equivalent to A B C + * D /
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17. example
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18. Prefix expression
 + X Y Operators are written before their
operands. The expressions given above are
equivalent to / * A + B C D
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19. example
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20. Thankyou !
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