Infix : An expression is called the Infix expression if the operator appears in between the operands in the expression. Simply of the form (operand1 operator operand2).
Example : (A+B) * (C-D)
Prefix : An expression is called the prefix expression if the operator appears in the expression before the operands. Simply of the form (operator operand1 operand2).
Example : *+AB-CD (Infix : (A+B) * (C-D) )
Given an Infix expression, convert it into a Prefix expression using two stacks.
Input : A * B + C / D Output : + * A B/ C D Input : (A - B/C) * (A/K-L) Output : *-A/BC-/AKL
The idea is to use one stack for storing operators and other to store operands. The stepwise algo is:
- Traverse the infix expression and check if given character is an operator or an operand.
- If it is an operand, then push it into operand stack.
- If it is an operator, then check if priority of current operator is greater than or less than or equal to the operator at top of the stack. If priority is greater, then push operator into operator stack. Otherwise pop two operands from operand stack, pop operator from operator stack and push string operator + operand1 + operand 2 into operand stack. Keep popping from both stacks and pushing result into operand stack until priority of current operator is less than or equal to operator at top of the operator stack.
- If current character is ‘(‘, then push it into operator stack.
- If current character is ‘)’, then check if top of operator stack is opening bracket or not. If not pop two operands from operand stack, pop operator from operator stack and push string operator + operand1 + operand 2 into operand stack. Keep popping from both stacks and pushing result into operand stack until top of operator stack is an opening bracket.
- The final prefix expression is present at top of operand stack.
Below is the implementation of above algorithm:
Time Complexity: O(n)
Auxiliary Space: O(n)
GeeksforGeeks has prepared a complete interview preparation course with premium videos, theory, practice problems, TA support and many more features. Please refer Placement 100 for details
- Prefix to Infix Conversion
- Convert Infix To Prefix Notation
- Postfix to Prefix Conversion
- Prefix to Postfix Conversion
- Postfix to Infix
- Stack | Set 2 (Infix to Postfix)
- Program to convert Infix notation to Expression Tree
- Queue using Stacks
- Check if the two given stacks are same
- Sorting array using Stacks
- Bubble sort using two Stacks
- Implement two stacks in an array
- Iterative Postorder Traversal | Set 1 (Using Two Stacks)
- Sudo Placement[1.3] | Playing with Stacks
- Merging and Sorting Two Unsorted Stacks
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.