Convert the following infix  to prefix & prefix expression: (50 - 2 * (2 + 3) - 5 * 4) * 2

Infix to Prefix Conversion:

Converting Infix to prefix using stack, first reverse the infix expression and at last again reverse the output expression to get the prefix expression.

Infix to Prefix Conversion Algorithm:

Traverse given expression from left to right,

Step-1: At the very first step reverse the given expression.

Step 2: If scanned character is an operand then place it into the prefix expression.

Step 3: If scanned character is an operator and operator's stack is empty then push operator into the operators' stack.

Step 4: If operator's stack is not empty, there are many possibilities.

• If precedence of scanned operator is greater than top most operator of operator's stack then push the operator into the operator 's stack.
• If precedence of scanned operator is less than top most operator of operator's stack then pop operators from the operator's stack until we find the low precedence operator than scanned character.
• If precedence of scanned operator is equal then check associativity of operator.
• If associativity is from left to right then put it into the stack.
• If associativity is from right to left then pop operators from the stack until we find the low precedence operator.
• If scanned character is the opening round bracket ( '(' ) then push it into the operator's stack.
• If scanned character is closing the round bracket ( ')' ) then pop out the operators from the operator's stack until we find an opening bracket ('(' ).

Repeat the Step-2,Step-3 and Step-4 till the expression has character.

Step-5: Now, pop out all remaining operators from operator's stack and push it into the postfix expression.