Transcript CSC2100B - Biola University

Infix to postfix conversion
Process the tokens from a vector infixVect of tokens (strings) of an infix expression one by one
When the token is an operand

Add it to the end of the vector postfixVect of token (strings) that is used to store the
corresponding postfix expression
When the token is a left or right parenthesis or an operator

If the token x is “(“


if the token x is “)”



Push the token x onto the stack
Repeatedly pop a token y from the stack and push_back that token y to
postfixVect until “(“ is encountered in the end of the stack. Pop “(“ from the
stack.
If the stack is already empty before finding a “(“, this expression is not a valid
infix expression.
if the token x is a regular operator


Step 1: Check the token y currently on the top of the stack.
Step 2:
If (i) the stack is not empty, (ii) y is not “(“
and (iii) y is an operator of
higher or equal precedence than that of x,


then: pop the token y from the stack and push_back the token y to postfixVect,
and repeat Step 1 again
else: push the token x onto the stack.
When all tokens in infixVect are processed as described above, repeatedly pop a token y from
the stack and push_back that token y to postfixVect until the stack is empty.
Infix to postfix conversion
infixVect
(1+2–3)*4–(5+6)
postfixVect
Infix to postfix conversion
stack
infixVect
(1+2–3)*4–(5+6)
postfixVect
(
Infix to postfix conversion
stack
infixVect
(1+2–3)*4–(5+6)
postfixVect
1
(
Infix to postfix conversion
stack
infixVect
(1+2–3)*4–(5+6)
postfixVect
1
+
(
Infix to postfix conversion
stack
infixVect
(1+2–3)*4–(5+6)
postfixVect
12
+
(
Infix to postfix conversion
stack
infixVect
(1+2–3)*4–(5+6)
postfixVect
12+
-
(
Infix to postfix conversion
stack
infixVect
(1+2–3)*4–(5+6)
postfixVect
12+3
-
(
Infix to postfix conversion
stack
infixVect
(1+2–3)*4–(5+6)
postfixVect
12+3-
Infix to postfix conversion
stack
infixVect
( 1 + 2 – 3 ) *4 – ( 5 + 6 )
postfixVect
12+3-
*
Infix to postfix conversion
stack
infixVect
( 1 + 2 – 3 ) * 4– ( 5 + 6 )
postfixVect
12+3-4
*
Infix to postfix conversion
stack
infixVect
( 1 + 2 – 3 ) * 4 –( 5 + 6 )
postfixVect
12+3–4*
-
Infix to postfix conversion
stack
infixVect
( 1 + 2 – 3 ) * 4 – (5 + 6 )
postfixVect
12+3–4*
(
-
Infix to postfix conversion
stack
infixVect
(1+2–3)*4–(5+6)
postfixVect
12+3–4*5
(
-
Infix to postfix conversion
stack
infixVect
( 1 + 2 – 3 ) * 4 – ( 5 +6 )
postfixVect
+
(
-
12+3–4*5
Infix to postfix conversion
stack
infixVect
( 1 + 2 – 3 ) * 4 – ( 5 + 6)
postfixVect
+
(
-
12+3–4*56
Infix to postfix conversion
stack
infixVect
(1+2–3)*4–(5+6)
postfixVect
12+3–4*56+
-
Infix to postfix conversion
stack
infixVect
(1+2–3)*4–(5+6)
postfixVect
12+3–4*56+–