infix to postfix calculator

Guri Bee

3 min read

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19-10-2024

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From Infix to Postfix: Building a Calculator with Stack Magic

Have you ever wondered how calculators understand your mathematical expressions? It's not as simple as just typing in numbers and operators! Under the hood, these expressions undergo a transformation, converting them into a format that's easier for the calculator to process. This format is called postfix notation, and it's achieved through a process called infix to postfix conversion.

Let's break it down:

• Infix notation is the way we usually write mathematical expressions, like "2 + 3 * 4".
• Postfix notation (also known as Reverse Polish Notation or RPN) puts the operators after the operands. For the same expression above, postfix would be "2 3 4 * +".

But why go through this conversion? Well, postfix notation allows for a much simpler and more efficient way to evaluate expressions. With infix, you need to deal with operator precedence and parentheses, which can get complicated. In postfix, the order of operations is clearly defined by the order of the operators themselves.

Here's how infix to postfix conversion works:

1. Initialization: Create an empty stack.
2. Scanning: Process the infix expression from left to right.
3. Operands: When you encounter an operand (number), add it directly to the postfix expression.
4. Operators: When you encounter an operator:
   • If the stack is empty or the top of the stack contains a lower precedence operator than the current operator, push the current operator onto the stack.
   • If the top of the stack contains an operator of equal or higher precedence, pop the operator from the stack and add it to the postfix expression. Repeat this step until the stack is empty or the current operator has a higher precedence than the top of the stack. Then, push the current operator onto the stack.
5. Parentheses:
   • When you encounter an opening parenthesis "(", push it onto the stack.
   • When you encounter a closing parenthesis ")", pop operators from the stack and add them to the postfix expression until an opening parenthesis is encountered. Discard the matching opening parenthesis.
6. Finalization: When you reach the end of the infix expression, pop any remaining operators from the stack and add them to the postfix expression.

Example:

Let's convert the infix expression "(2 + 3) * 4" to postfix.

*The resulting postfix expression is "2 3 + 4 ".

Now, let's evaluate this postfix expression:

1. Scanning: Read the postfix expression from left to right.
2. Operands: When you encounter an operand, push it onto a new stack.
3. Operators: When you encounter an operator, pop the top two operands from the stack, perform the operation, and push the result back onto the stack.

In this case:

• 2 3 + : Pop 3 and 2 from the stack, perform 2 + 3, and push 5 back onto the stack.
• *5 4 : Pop 4 and 5 from the stack, perform 5 * 4, and push 20 back onto the stack.

The final result, 20, is left on the stack.

Benefits of Postfix Notation:

• Simplified evaluation: The order of operations is clear and straightforward.
• Efficiency: Postfix expressions can be evaluated with a single pass, without the need for recursion or complex parsing.
• Ease of implementation: Postfix evaluation is simple to implement using a stack data structure.

Code Example (Python - Inspired by GitHub:)

def infix_to_postfix(expression):
  """Converts an infix expression to postfix."""
  precedence = {'+': 1, '-': 1, '*': 2, '/': 2, '^': 3}
  postfix = ''
  stack = []
  for char in expression:
    if char.isalnum():
      postfix += char
    elif char in precedence:
      while stack and precedence[stack[-1]] >= precedence[char]:
        postfix += stack.pop()
      stack.append(char)
    elif char == '(':
      stack.append(char)
    elif char == ')':
      while stack and stack[-1] != '(':
        postfix += stack.pop()
      stack.pop()
    else:
      raise ValueError("Invalid character in expression")
  while stack:
    postfix += stack.pop()
  return postfix

def evaluate_postfix(expression):
  """Evaluates a postfix expression."""
  stack = []
  for char in expression.split():
    if char.isdigit():
      stack.append(int(char))
    elif char in ['+', '-', '*', '/', '^']:
      op2 = stack.pop()
      op1 = stack.pop()
      if char == '+':
        stack.append(op1 + op2)
      elif char == '-':
        stack.append(op1 - op2)
      elif char == '*':
        stack.append(op1 * op2)
      elif char == '/':
        stack.append(op1 / op2)
      elif char == '^':
        stack.append(op1 ** op2)
    else:
      raise ValueError("Invalid character in expression")
  return stack.pop()

expression = "(2 + 3) * 4"
postfix = infix_to_postfix(expression)
result = evaluate_postfix(postfix)

print(f"Infix: {expression}")
print(f"Postfix: {postfix}")
print(f"Result: {result}")

This code snippet provides a practical example of how to implement infix to postfix conversion and postfix evaluation in Python. You can use this code as a starting point to build your own calculator, or further explore the world of postfix expressions and their applications in programming languages and computer science.