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3
Palindrome
same both forward and backward x y z a z y x lb ub
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Evaluating Postfix
Read from left to right:
the stack (the first number popped is the second binary operand)
push the result back onto the stack
on top of stack is the answer
5 3 + 10 *
5 3 + 4 + 1 +
- A palindrome is a string that reads the
- Two questions:
- How do you check equality?
- When do you stop?
- if a number is read, push it on the stack
- if an operator is read, pop two numbers off
- apply the operation to the numbers, and
- when the expression is complete, the number
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Infix to Postfix
post_fix := โโ Create(Op_Stack) for I in 1 .. Length loop If Is_Operand(expr(I)) = true then Append(post_fix, expr(I))
If Is_Operator(expr(I)) = true then Process_Next_Operator(expr(I)) end loop
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Process_Next_Operator
Done := False loop If Is_Empty(Op_Stack) or next_op is โ(โ, set Done to True Elsif precedence(next_op) > precedence(top_operator) Push next_op onto Op_stack-- ensures higher precedence operators evaluated first Set Done to True Else Pop the operator_stack If operator popped is โ(โ set Done to True Else Done = True
-- string post_fix has the result
push next_op onto Op_Stack
append operator popped to post_fix string exit when end loop
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Infix to Postfix: Example
Infix Expression 3 + 5 * โ 6 โ 7 * (8 + 5)
Postfix Expression
