Stack Applications

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Stack Applications

• CS501
• Irena Pevac

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Arithmetic Expressions

• Arithmetic expressions have
• operands (variables or numeric constants).
• Operators
• Binary , -, , / ,
• Unary -
• Priority convention
• - Unary minus (sign for negative numbers) has
  highest priority
• , /, have medium priority
• , - have lowest priority

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Infix, Prefix, Postfix

• Example arithmetic expression a b consists of
  operands a, b and operator .
• Infix notation is format where operator is
  specified in between the two operands. ab
• Prefix notation is format where operator is
  specified before the two operands. a b
• Postfix notation is format where operator is
  specified after the two operands. Postfix
  notation is also called RPN or Reverse Polish
  Notation. a b

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Arithmetic Expressions
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Boolean Expressions

• Boolean expressions have
• Operands (variables of boolean type or boolean
  constants TRUE, FALSE).
• Operators Binary , V, gt, ?
• Unary
• Convention for operator priorities
• has highest priority, has next priority
  level, v has next priority level, gt has next
  priority level, ? has lowest priority.

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Infix, Prefix, Postfix for Boolean Expressions

• Example Boolean expression a b consists of
  operands a, b and operator .
• Infix notation is format where operator is
  specified in between the two operands. ab
• Prefix notation is format where operator is
  specified before the two operands. a b
• Postfix notation is format where operator is
  specified after the two operands. Postfix
  notation is also called RPN or Reverse Polish
  Notation. a b

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Boolean Expressions
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Evaluating Arithmetic Expressions in Postfix
Notation

• Algorithm
• INPUT list of tokens that are either numbers or
  binary arithmetic operators , -,, /, and .
  List represents postfix notation of an arithmetic
  expression
• OUTPUT value of expression.

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• Create an empty stack that will contain operands.
  
• Take one by one token from the left to right.
• If token is an operand push it to the stack.
• If token is an operator op
• Pop the top item from the stack as operand2.
• Pop again the top item from the stack as
  operand1.
• Perform operation operand1 op operand2.
• Push result back to stack.
• When all tokens in input expression are processed
  stack should contain a single item, which is the
  value of expression.

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Evaluate 3 2 - 4
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Evaluating Boolean Expressions in Postfix Notation

• Algorithm is same as for arithmetic expressions
• INPUT list of tokens that are either TRUE or
  FALSE or operators , V, gt, ?. List represents
  postfix notation of an arithmetic expression.
• OUTPUT value of expression that is either TRUE
  or FALSE.

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• Create an empty stack that will contain boolean
  operands.
• Take one by one token from the left to right.
• If token is an operand push it to the stack.
• If token is an operator op
• Pop the top item from the stack as operand2.
• Pop again the top item from the stack as
  operand1.
• Perform operation operand1 op operand2.
• Push result back to stack.
• When all tokens in input expression are processed
  stack should contain a single item, which is the
  boolean value of expression.

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Evaluate True True False gt
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ALGORITHM TO CONVERT AN INFIX EXPRESSION TO RPN

• Accepts An infix expression
• Convert the expression to RPN
• Uses a stack to store operations
• Output The RPN expression

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INFIX EXPRESSION TO RPN
Initialize an empty stack of operators. While no
error has occurred and the end of the infix
expression has not been reached, do the
followinga. Get the next input Token (constant,
variable, arithmetic operator, left
and right parenthesis) in the infix
expression.
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INFIX EXPRESSION TO RPN

• b. If Token is(i) a left parenthesis Push it
  onto the stack(ii) a right parenthesis Pop and
  display stack elements until a left
  parenthesis is popped, but do not display it.
  (It is an error if the stack becomes empty
  with no left parenthesis found.)(iii) an
  operator If the stack is empty or
• Token
  has a higher priority than the top stack,
  push Token onto the stack. Otherwise, pop and
  display the top stack
• 
  element then repeat the
  comparison of Token
• 
  with the new top stack item. A left
  parenthesis in the stack is assumed to have a
  lower priority than that of operators.(iv) an
  operand Display it.

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INFIX EXPRESSION TO RPN

• c. When the end of the infix expression is
  reached, pop and display stack items until the
  stack is empty.

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Example

• Convert infix expression into postfix
• (71)(6(3-2)) gtgt RPN

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(No Transcript)
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(71)(6(3-2)) gtgt RPN
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(71)(6(3-2)) gtgt RPN

• 7 1 6 3 - displayed
• Stack content
• Add that to display
• 7 1 6 3 - is RPN

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Checking Parenteses

• Create an empty stack
• Until a special symbol appears (indicating the
  end of expression) doRead one by one token from
  the input expressionIf token is
• If the stack is empty push token to the
  stack
• If the stack is non empty pop a top stack
  element
• If the popped element is ( or type an
  error message such as Rule 2 is not satisfied
  at positionOtherwise push it back and push the
  token to the stack.
• (

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Checking Parenteses

• If the stack is empty rule 1 is not satisfied.
  Type a message If the stack is not empty pop
  the top stack element and If it is then read
  next token Otherwise type Rule 1 is not
  satisfied at position
• )
• Other Skip to the next token
• If the stack is non empty after the end of
  expression has been encountered then print an
  error message such as Rule 1 is violated at the
  end of expressionelse Check control
  is O.K.