Flowchart and Algorithm for Converting Infix to Postfix notation

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Infix notation is a type of notation in which arithmetic expressions are normally written.

Postfix notation is a type of notation in which arithmetic expressions are written in a manner such that the operands appear before their operators. Postfix notation is a notation used in the system and is implemented using stacks. There is often a need to convert Infix to Postfix notation, so let's understand how the conversion is done.

Flowchart for converting Infix to Postfix Notation:

Flowchart for converting Infix to Postfix notation

Algorithm for conversion of Infix to Postfix Notation:

Step 1: Start Step 2: Start reading the infix expression from left to right. Step 3: Repeat Step 4 to 7 for each element until the Stack is empty. Step 4: If we scan a operand we output it, print it. Step 5: Else, 5.1: If the scanned operator is greater in precedence than the operator in the stack or if the stack is empty or the stack contains a "(", push it. 5.2: Else, Pop all the operators having greater or equal precedence than that of the scanned operator. After doing that Push the scanned operator to the stack. In case there is a parenthesis while popping then stop and push the scanned operator in the stack. Step 6: If a '(' is encountered, push it onto Stack. Step 7: If a ')' is encountered, repeatedly pop from Stack and output it until a '(' is encountered Step 8: The output is printed in postfix notation Step 9: Stop

Let's take an example to understand a*(b+c),

  1. 'a' being an operand is scanned and printed.
  2. Then * is added to the stack. Again '(' is encountered and pushed in the stack.
  3. 'b' being an operand is scanned and printed.
  4. '+' being an operator is pushed into the stack.
  5. 'c' being an operand is scanned and printed.
  6. An ')' is encountered operator + is popped.
  7. Then, again top is popped and we print * and here, popping ends as the stack is empty.
  8. Stop

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