data structures - Stack And Arithmetic Evaluation

Question

A stack is said to be the ideal data structure for Arithmetic Evaluation. Why is it so?
Why do we even need a data structure for Arithmetic Evaluation? I've been studying about this for some time now and still confused. I don't understand what is the use of Prefix and Postfix expressions because the Infix expression is quite readable.

question from:https://stackoverflow.com/questions/65933107/stack-and-arithmetic-evaluation

Answer 1

Answer for the part of why postfix/prefix over infix is quite well explained here.As a summary infix is readable but not easily parsed
As for why stack is used here is:
1: push,pop in O(1) time are quite useful for evaluation.
2: push: add the operand on stack.
3: pop: remove the operand and evaluate expression(binary) 4: final result is the only one left on stack after parsing