Stacks are used for converting infix expressions to postfix expressions. What is the postfix form of the infix expression "A + B * C"?
Question
What is the postfix form of the infix expression A + B * C
?
Solution
To convert the infix expression "A + B * C" to postfix, follow these steps:
- Scan the infix expression from left to right.
- If the scanned character is an operand, output it.
- Else,
- If the precedence of the scanned operator is greater than the precedence of the operator in the stack(or the stack is empty), push it.
- Else, Pop the operator from the stack until the precedence of the scanned operator is less-equal to the precedence of the operator residing on the top of the stack. Push the scanned operator to the stack.
- If the scanned infix expression is ended, output the remaining operators from the stack.
Now, let's apply these steps to the given infix expression "A + B * C":
- Scan "A", it's an operand, so output it. Now, the output is "A".
- Scan "+", it's an operator, and the stack is empty, so push it to the stack.
- Scan "B", it's an operand, so output it. Now, the output is "A B".
- Scan "*", it's an operator, and its precedence is greater than the "+" operator in the stack, so push it to the stack.
- Scan "C", it's an operand, so output it. Now, the output is "A B C".
- The infix expression is ended, pop all the operators from the stack and output them. The operators are "" and "+". Since "" has higher precedence, it comes first. Now, the output is "A B C * +".
So, the postfix form of the infix expression "A + B * C" is "A B C * +".
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