Evaluate a simple string mathematical expression [closed]

Answer 1

This is a simple scan push apply (the twist is the braces).

1. Look for a number:
   • If you see a number push onto stack
   • if you see a '(' push it onto stack and goto 1
   • Otherwise an error.
2. Look for an op:
   • If you see an op push it onto stack
   • Otherwise an error
3. Look for a number:
   • If you see a number push onto stack
   • If you see a '(' push onto stack and goto 1
   • Otherwise an error
4. pop last three items from the stack (should be number op number)
   
   • do the operation and push the result onto the stack.
5. Now the complex bit:
   • Peek to see if the next character is a ')' if it is goto "PopCode" below.
6. If no more input goto 7.
   • Otherewise goto 2
7. If only one item on the stack you have your result.
   • Otherwise an error.

PopCode

1. Pop last two values from the stack. Should be '( Number'
   • If it is not then an error
2. Throw away the '('
3. If the top of the stack is an op push value goto 4 (above)
4. Otherwise push the value onto the stack goto 5 (above)

When finished there should be one number on the stack.

Example:

1+3
Rule 1: push 1             stack = '1'
Rule 2: push +             stack = '1 +'
Rule 3: push 3             stack = '1 + 3'
Rule 4: pop and do:        stack = '4'
Rule 5: Nothing            stack = '4'
Rule 6: goto 7             stack = '4'
Rule 7:                    stack = '4'

(1 + (12 * 2)
Rule 1: push ( goto 1      stack = '('
Rule 1: push 1             stack = '( 1'
Rule 2: push +             stack = '( 1 +'
Rule 3: push ( goto 1      stack = '( 1 + ('
Rule 1: push 12            stack = '( 1 + ( 12'
Rule 2: push *             stack = '( 1 + ( 12 *'
Rule 3: push 2             stack = '( 1 + ( 12 * 2'
Rule 4: Pop and do:        stack = '( 1 + ( 24'
Rule 5: Do 'PopCode'       stack = '( 1 + ( 24'
Pop  1: Pop 2              stack = '( 1 +'
Pop  2: Holding 24         stack = '( 1 +'
Pop  3: push 24 goto 4     stack = '( 1 + 24'
Rule 4: Pop and do         stack = '( 25'
Rule 5: Nothing            stack = '( 25'
Rule 6: goto 7             stacj = '( 25'
Rule 7: More than 1 item error

Re-Doing with correct formula
(1 + (12 * 2))
Rule 1: push ( goto 1      stack = '('
Rule 1: push 1             stack = '( 1'
Rule 2: push +             stack = '( 1 +'
Rule 3: push ( goto 1      stack = '( 1 + ('
Rule 1: push 12            stack = '( 1 + ( 12'
Rule 2: push *             stack = '( 1 + ( 12 *'
Rule 3: push 2             stack = '( 1 + ( 12 * 2'
Rule 4: Pop and do:        stack = '( 1 + ( 24'
Rule 5: Do 'PopCode'       stack = '( 1 + ( 24'
Pop  1: Pop 2              stack = '( 1 +'
Pop  2: Holding 24         stack = '( 1 +'
Pop  3: push 24 goto 4     stack = '( 1 + 24'
Rule 4: Pop and do         stack = '( 25'
Rule 5: Do 'PopCode'       stack = '( 25'
Pop  1: Pop 2              stack = ''
Pop  2: holding 25         stack = ''
Pop  3: Nothing.           stack = ''
Pop  4: push 25 goto 5     stack = '25'
Rule 5: Nothing            stack = '25'
Rule 6: goto 7             stack = '25'
Rule 7: Result = 25