Evaluation of Postfix Expression Example

Evaluating postfix expressions involves processing them from left to right, using a stack to store intermediate results. Here’s a detailed evaluation of each example:

Steps for Postfix Evaluation

  • Start from the leftmost character and move right.
  • Operands: Push onto the stack.
  • Operators: Pop the required number of operands, apply the operation, and push the result back onto the stack.
  • Final Result: The last value remaining on the stack is the result.

Example 1: 21+

Postfix Expression: 21+

  • Push 2: Stack = [2]
  • Push 1: Stack = [2, 1]
  • Operator +: Pop 2 and 1, compute 2 + 1 = 3. Push result: Stack = [3]

Result: 3

Example 2: 321++

Postfix Expression: 321++

  • Push 3: Stack = [3]
  • Push 2: Stack = [3, 2]
  • Push 1: Stack = [3, 2, 1]
  • Operator +: Pop 2 and 1, compute 2 + 1 = 3. Push result: Stack = [3, 3]
  • Operator +: Pop 3 and 3, compute 3 + 3 = 6. Push result: Stack = [6]

Result: 6

Example 3: 43-21++

Postfix Expression: 43-21++

  • Push 4: Stack = [4]
  • Push 3: Stack = [4, 3]
  • Operator -: Pop 4 and 3, compute 4 - 3 = 1. Push result: Stack = [1]
  • Push 2: Stack = [1, 2]
  • Push 1: Stack = [1, 2, 1]
  • Operator +: Pop 2 and 1, compute 2 + 1 = 3. Push result: Stack = [1, 3]
  • Operator +: Pop 1 and 3, compute 1 + 3 = 4. Push result: Stack = [4]

Result: 4

Example 4: 123+4*-

Postfix Expression: 123+4*-

  • Push 1: Stack = [1]
  • Push 2: Stack = [1, 2]
  • Push 3: Stack = [1, 2, 3]
  • Operator +: Pop 2 and 3, compute 2 + 3 = 5. Push result: Stack = [1, 5]
  • Push 4: Stack = [1, 5, 4]
  • Operator *: Pop 5 and 4, compute 5 * 4 = 20. Push result: Stack = [1, 20]
  • Operator -: Pop 1 and 20, compute 1 - 20 = -19. Push result: Stack = [-19]

Result: -19

Example 5: 56/432+*-

Postfix Expression: 56/432+*-

  • Push 5: Stack = [5]
  • Push 6: Stack = [5, 6]
  • Operator /: Pop 5 and 6, compute 5 / 6 ≈ 0.8333 (keep result as a float). Push result: Stack = [0.8333]
  • Push 4: Stack = [0.8333, 4]
  • Push 3: Stack = [0.8333, 4, 3]
  • Push 2: Stack = [0.8333, 4, 3, 2]
  • Operator +: Pop 3 and 2, compute 3 + 2 = 5. Push result: Stack = [0.8333, 4, 5]
  • Operator *: Pop 4 and 5, compute 4 * 5 = 20. Push result: Stack = [0.8333, 20]
  • Operator -: Pop 0.8333 and 20, compute 0.8333 - 20 ≈ -19.1667. Push result: Stack = [-19.1667]

Result: -19.1667