Evaluation of prefix expression with example
- 1. G.SAI NIKHIL 20955A0516(2nd yr. CSE-C) INSTITUTE OF AERONAUTICAL ENGINNERING
- 2. CONTENT 1. EVALUTION OF PREFIX EXPRESSION 2. ALGOIRTHM 3. EXPRESSION 4. EXAMPLE
- 4. The Postfix notation is used to represent algebraic expressions. The expressions written in postfix form are evaluated faster compared to infix notation as parenthesis are not required in postfix. We have discussed infix to postfix conversion. In this post, evaluation of postfix expressions is discussed.
- 5. ALGORITHM
- 6. EVALUATE_PREFIX (STRING) Step 1: Put a pointer P at the end of the end. Step 2: If character at P is an operand push it to Stack Step 3: If the character at P is an operator pop two elements from the Stack. Operate on these elements according to the operator, and push the result back to the Stack. Step 4: Decrement P by 1 and go to Step 2 as long as there are characters left to be scanned in the expression. Step 5: The Result is stored at the top of the Stack, return it, Step 6: End
- 7. EXPRESSION
- 8. EXAMPLE
- 9. Example: Let the given expression be “2 3 1 * + 9 -“. We scan all elements one by one. 1) Scan ‘2’, it’s a number, so push it to stack. Stack contains ‘2’ 2) Scan ‘3’, again a number, push it to stack, stack now contains ‘2 3’ (from bottom to top) 3) Scan ‘1’, again a number, push it to stack, stack now contains ‘2 3 1’ 4) Scan ‘*’, it’s an operator, pop two operands from stack, apply the * operator on operands, we get 3*1 which results in 3. We push the result ‘3’ to stack. Stack now becomes ‘2 3’. 5) Scan ‘+’, it’s an operator, pop two operands from stack, apply the + operator on operands, we get 3 + 2 which results in 5. We push the result ‘5’ to stack. Stack now becomes ‘5’. 6) Scan ‘9’, it’s a number, we push it to the stack. Stack now becomes ‘5 9’. 7) Scan ‘-‘, it’s an operator, pop two operands from stack, apply the – operator on operands, we get 5 – 9 which results in -4. We push the result ‘-4’ to stack. Stack now becomes ‘-4’. 8) There are no more elements to scan, we return the top element from stack (which is the only element left in stack).
- 10. THANK YOU