Infix converter

Instead, parentheses are used to isolate parts of the infix notation that are to be executed independently of the operators outside of them. Any nested parentheses are evaluated prior to evaluating their encompassing parentheses.

Now that you know what a stack is and have assigned precedence and associativity to each operator, the following are the steps to converting infix to prefix using stack. First, reverse the order of the infix expression. Next, working from left to right on the reversed infix expression, one token at a time, determine whether or not the current token is an operand, an operator, or an opening or closing parenthesis.

If the token is an operand, append it to the output. Operands always appear in the same order in the output as they do in the infix expression. If the token is a closing parenthesis, push it to the stack. This marks the beginning of an expression that should be evaluated separately. If the token is an opening parenthesis, until a closing parenthesis is encountered at the top of the stack, pop each operator from the stack and append to the output. This marks the end of the operands and operators located within the current set of parentheses.

If the token is an operator and it has greater precedence than the operator on the top of the stack, push the token to the stack. If the token is an operator and it has lower precedence than the operator on the top of the stack, until the operator on top of the stack has lower or equal precedence than the token, or until the stack is empty, pop each operator from the stack and append them to the output.

Then push the current token to the stack. If the token is an operator and it has the same precedence as the operator on the top of the stack, and the operator on top of the stack is left-to-right associative, push the token to the stack. If the token is an operator and it has the same precedence as the operator on the top of the stack, but the operator on top of the stack is right-to-left associative, until the operator on top of the stack has lower or equal precedence than the token and is left-to-right associative, or until the stack is empty, pop each operator from the stack and append them to the output.

Once all of the infix tokens have been evaluated, pop any remaining operators from the stack, one at a time, and append each of them to the output expression. The following three infix-to-prefix examples each give a step-by-step illustration of how the rules stated in the previous section are applied on a character-by-character basis. Move the slider to left and right to adjust the calculator width.

Note that the Help and Tools panel will be hidden when the calculator is too wide to fit both on the screen. Moving the slider to the left will bring the instructions and tools panel back into view. Also note that some calculators will reformat to accommodate the screen size as you make the calculator wider or narrower. If the calculator is narrow, columns of entry rows will be converted to a vertical entry form, whereas a wider calculator will display columns of entry rows, and the entry fields will be smaller in size Select Show or Hide to show or hide the popup keypad icons located next to numeric entry fields.

These are generally only needed for mobile devices that don't have decimal points in their numeric keypads. So if you are on a desktop, you may find the calculator to be more user-friendly and less cluttered without them. Select Stick or Unstick to stick or unstick the help and tools panel. Selecting "Stick" will keep the panel in view while scrolling the calculator vertically.

If you find that annoying, select "Unstick" to keep the panel in a stationary position. If the tools panel becomes "Unstuck" on its own, try clicking "Unstick" and then "Stick" to re-stick the panel. Menu Favs. Data Data record Data record Selected data record : None. Selecting "Stick" will keep the panel in view while scrolling the calculator vertically.

If you find that annoying, select "Unstick" to keep the panel in a stationary position. If the tools panel becomes "Unstuck" on its own, try clicking "Unstick" and then "Stick" to re-stick the panel. Menu Favs. Data Data record Data record Selected data record : None. Learn More. Example notations: Example postfix expressions: To see an example of how the Postfix to Infix Converter works, and what types of expressions the calculator is set up to handle, select a postfix expression from the drop-down menu.

Postfix expression: Postfix expression: Enter a postfix expression that fits within the following guidelines: Include a single space between numbers or operators. Numbers, single letters, and operators only no variables or function names. Numbers with a leading decimal point must be preceded by a zero enter. Postfix expression.

Result: Infix: This line will display the result of the postfix to infix conversion. Related Calculators. Other Section Calculators. Show Help and Tools.

Instructions Terms Data PCalc. How to Convert Postfix Notation to Infix Notation Using Stack Working from left to right, scan each character of the postfix expression, and take one of the following two actions.

If the character is an operand, push it to the stack. Posfix to Infix Conversion Examples The following are two examples showing how to apply the conversion process detailed in the previous section. Close Menu. Search Calculator Titles. Repeatedly pop from stack and add it to the postfix expression until a " " is encountered. Discard the " ". That is, remove the from stack and do not add it to the postfix expression IF an operator O is encountered, then a. Repeatedly pop from stack and add each operator popped from the stack to the postfix expression which has the same precedence orahigher precedence than O b.