What is this written in postfix notation:
!(!((5-10)*(4-(9/2)) > 60)-(((5*7)/(4/(5+3)))=15))<((4-3)=1)
Holy crap!
Is ! the NOT operator? If so, we have
!(!((5-10)*(4-(9/2)) > 60)
has unbalanced parentheses
(((5*7)/(4/(5+3)))=15))
has unbalanced parentheses
In both cases there are not enough ('s
Better go over it and make sure things balance out
That's what I thought...
The given expression is written in postfix notation, which is a way of representing mathematical expressions without the use of parentheses. In postfix notation, the operators are placed after their operands.
Here's the given expression in postfix notation:
5 10 - 4 9 2 / - * 60 > ! 5 7 * 4 5 3 + / 15 = - ! 4 3 - 1 =
To evaluate this expression, you can use a stack-based algorithm.
1. Start with an empty stack to store the intermediate results.
2. Read the expression from left to right.
3. If the token is a number, push it onto the stack.
4. If the token is an operator, pop the required number of operands from the stack, perform the operation, and push the result back onto the stack.
5. Continue steps 3 and 4 until all tokens in the expression are processed.
6. The final result is the top value on the stack.
Here's the step-by-step evaluation of the given expression:
Input: 5 10 - 4 9 2 / - * 60 > ! 5 7 * 4 5 3 + / 15 = - ! 4 3 - 1 =
1. Push 5 onto the stack.
Stack: 5
2. Push 10 onto the stack.
Stack: 5 10
3. Apply the "-" operator to the top two elements on the stack (10 - 5) and push the result (5) onto the stack.
Stack: 5
4. Push 4 onto the stack.
Stack: 5 4
5. Push 9 onto the stack.
Stack: 5 4 9
6. Push 2 onto the stack.
Stack: 5 4 9 2
7. Apply the "/" operator to the top two elements on the stack (9 / 2) and push the result (4.5) onto the stack.
Stack: 5 4 4.5
8. Apply the "-" operator to the top two elements on the stack (4 - 4.5) and push the result (-0.5) onto the stack.
Stack: 5 -0.5
9. Apply the "*" operator to the top two elements on the stack (-0.5 * 5) and push the result (-2.5) onto the stack.
Stack: -2.5
10. Push 60 onto the stack.
Stack: -2.5 60
11. Apply the ">" operator to the top two elements on the stack (60 > -2.5) and push the result (True) onto the stack.
Stack: True
12. Apply the "!" operator to the top element on the stack (True) and push the result (False) onto the stack.
Stack: False
13. Push 5 onto the stack.
Stack: False 5
14. Push 7 onto the stack.
Stack: False 5 7
15. Apply the "*" operator to the top two elements on the stack (7 * 5) and push the result (35) onto the stack.
Stack: False 35
16. Push 4 onto the stack.
Stack: False 35 4
17. Push 5 onto the stack.
Stack: False 35 4 5
18. Push 3 onto the stack.
Stack: False 35 4 5 3
19. Apply the "+" operator to the top two elements on the stack (5 + 3) and push the result (8) onto the stack.
Stack: False 35 4 8
20. Apply the "/" operator to the top two elements on the stack (4 / 8) and push the result (0.5) onto the stack.
Stack: False 35 0.5
21. Push 15 onto the stack.
Stack: False 35 0.5 15
22. Apply the "=" operator to the top two elements on the stack (0.5 = 15) and push the result (False) onto the stack.
Stack: False 35 False
23. Apply the "-" operator to the top two elements on the stack (False - 35) and push the result (-35) onto the stack.
Stack: -35 False
24. Apply the "!" operator to the top element on the stack (False) and push the result (True) onto the stack.
Stack: -35 True
25. Push 4 onto the stack.
Stack: -35 True 4
26. Push 3 onto the stack.
Stack: -35 True 4 3
27. Apply the "-" operator to the top two elements on the stack (4 - 3) and push the result (1) onto the stack.
Stack: -35 True 1
28. Apply the "=" operator to the top two elements on the stack (1 = 1) and push the result (True) onto the stack.
Stack: -35 True True
The final result on the stack is True, indicating that the given expression is true in postfix notation.