Here is an infix expression: 1 + 2*(3*4-5). Suppose that we are using the usual stack algorithm to convert the expression from infix to postfix notation.The maximum number of symbols that will appear on the stack AT ONE TIME during the conversion of this expression?
Question
Here is an infix expression: 1 + 2*(3*4-5). Suppose that we are using the usual stack algorithm to convert the expression from infix to postfix notation.The maximum number of symbols that will appear on the stack AT ONE TIME during the conversion of this expression?
Solution
To convert an infix expression to postfix notation, we use a stack to hold operators and push them onto the stack whenever we encounter them in the expression. We pop them from the stack and add them to the postfix expression when we encounter an operator with lower precedence or a parenthesis that closes a sub-expression.
Let's go through the expression step by step:
- Scan the infix expression from left to right.
1is an operand, so output it.+is an operator, push it onto the stack.2is an operand, so output it.*is an operator, push it onto the stack.(is a special symbol, push it onto the stack.3is an operand, so output it.*is an operator, push it onto the stack.4is an operand, so output it.-is an operator, it has lower precedence than*on top of the stack, so pop*from the stack and output it. Then push-onto the stack.5is an operand, so output it.)is a special symbol, pop everything from the stack until(and output it. Pop(from the stack but do not output it.- Now the stack is not empty, pop everything from the stack and output it.
So, the maximum number of symbols on the stack at one time during the conversion of this expression is 3 (+, *, ().
Similar Questions
Let X be the result when the below postfix expressionis evaluated:X = 4 5 1 + * 2 / 3 1 2 + * +Let Y be the maximum size of the operand stack, thevalue of X-Y is ________
What is the maximum number of symbols that appear on the stack atany point of time during the evaluation of this expression?
Problem StatementTisha wants to learn mathematical expressions and she wants to create a program to accept multiple infix expressions from the user and convert them into postfix expressions using a Stack-based algorithm. The program should prompt the user to enter the number of expressions they wish to convert, and then accept each expression one by one. After converting each infix expression to a postfix, the program should print the corresponding postfix expression to the console. Input format :The first line of input consists of an integer N, denoting the number of infix expressions to be converted.The following N lines of input consist of the infix expressions to be converted.Output format :The N lines of output print "Postfix expression T: " where T is the expression number followed by the corresponding postfix expression for N inputs, in separate lines.Refer to the sample output for the formatting specifications.Code constraints :The maximum length of an infix expression is 100 characters.The program should support multiple infix expressions.The program should use a stack-based algorithm to convert infix expressions to postfix expressions.Sample test cases :Input 1 :1A+B*C-D/E^FOutput 1 :Postfix expression 1: ABC*+DEF^/-Input 2 :2A+B-CD+E/F-GOutput 2 :Postfix expression 1: AB+C-Postfix expression 2: DEF/+G-Input 3 :1a*(b+c)/d-eOutput 3 :Postfix expression 1: abc+*d/e-Note :The program will be evaluated only after the “Submit Code” is clicked.Extra spaces and new line characters in the program output will result in the failure of the test case.
Stacks are used for converting infix expressions to postfix expressions. What is the postfix form of the infix expression "A + B * C"?Group of answer choicesA B + C *B C * A +A B C * +A + B C * PreviousNext
- Evaluate the postfix expression "5 3 * 8 +" using a stack
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.