data structure stack appplication in python

data structure stack appplication in python

• 1.
  Infix to Prefix STACKAPPLICATION
• 2.
  Terminology • Infix: Thenotation commonly used in mathematical formulae • Operand: The value on which an operator is performed • Operator: A symbol like minus that shows an operation • Postfix: A mathematical notation in which operators follow operands • Prefix: A mathematical notation in which operands follow operators. • Reverse Polish Notation (RPN): A mathematical notation in which operators follow operands
• 3.
  Example • Infix: (A+B)*C-D+F • Prefix: -*+ABC+D • Postfix: AB+C*D-F+ Converting an infix expression to a prefix expression and infix to postfix expression involves changing the order of operators and operands while maintaining the precedence and associativity of the operators.
• 4.
  Infix to prefixconversion using stack • The steps are: Reverse the infix expression. Replace '(' with ')' and ')' with '(' to maintain the correct grouping. Convert the reversed infix expression to postfix notation. Reverse the postfix expression to get the prefix expression.
• 5.
  Steps are : Reversethe infix expression.  Replace '(' with ')' and ')' with ‘(‘. Convert the reversed infix expression to postfix notation . Reverse the postfix expression to get the prefix expression: Prefix Expression.
• 6.
  Convert infix topostfix • If character is operand then add them to the output expression. • If character is ‘)’ then Pop operators from the stack until an open parenthesis is encountered and add them to the output expression. • Discard the open parenthesis. • If character is operator then push onto the stack. • Check the precendence of operator with stack top element is operator. 1.If precendence of operator is higher than stack top element then operator just push onto the stack. 2. If precendence of operator is lower than stack top element then pop stack top element operator add them to the output expression.
• 7.
  Infix to prefixexample • Example: (A+B)*C-D+F • Reverse expression : F+D-C*)B+A( • Replace ) with ( and ) with ( • Final Reverse string :F+D-C*(B+A)
• 8.
  Example of infixto prefix expression Steps Current character Operation on stack Stack representation Postfix expression 1 F F 2 + PUSH + F 3 D FD 4 - PUSH – AND POP + (Because + has higher precedence than -.) - FD+ 5 C FD+C 6 * PUSH * (Because - has lower precedence than *) -* FD+C 7 ( PUSH -*( FD+C F+D-C*(B+A)
• 9.
  Example of infixto prefix expression Steps Current character Operation on stack Stack representation Postfix expression 8 B -*( FD+CB 9 + PUSH + -*(+ FD+CB 10 A FD+CBA 11 ) POP + ,( FD+CBA+ 12 POP * FD+CBA+* POP - FD+CBA+*- Empty stack Final postfix expression : FD+CBA+*- Reverse the postfix expression we get prefix expression : -*+ABC+DF