a*(b+(c+d)*e+f) find its postfix evaluations
To find the postfix expression of the given infix expression: a*(b+(c+d)*e+f)
First, we convert the infix expression to postfix notation:
Infix Expression: a*(b+(c+d)*e+f
Step 1: Convert the infix expression to postfix notation using the following steps:
1. Start scanning the expression from left to right.
2. If an operand is encountered, add it to the output.
3. If an operator is encountered, then
a. If the operator has higher precedence than the operator at the top of the stack, push it into the stack.
b. If the operator has lower precedence than the operator at the top of the stack, pop from the stack and add to the output until the stack is empty or a lower precedence operator is at the top of the stack. Finally, push the current operator into the stack.
4. If a left parenthesis is encountered, push it into the stack.
5. If a right parenthesis is encountered, pop from the stack and add to the output until a left parenthesis is found. Discard both the parentheses.
6. Repeat steps 2-5 until the expression is scanned completely.
Using the above steps, the postfix expression would be: abcd+e*+f+
Therefore, the postfix expression of a*(b+(c+d)*e+f) is abcd+e*+f+.
Next, to evaluate the postfix expression, we perform the following steps:
1. Start scanning the expression from left to right.
2. If an operand is encountered, push it onto the stack.
3. If an operator is encountered, pop the necessary number of operands from the stack, perform the operation, and push the result back onto the stack.
4. Repeat steps 2-3 until the expression is scanned completely.
Using the above steps, the result of evaluating the postfix expression abcd+e*+f+ is the final result.