Expression tree

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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