Operator precedence
Exponentiation has higher precedence than multiplication and division, which have higher precedence than addition and subtraction.
What is Postfix Notation?
In infix notation, an operator appears between its operands, such as A + B.
In postfix notation, the operator appears after its operands: A B +.
Postfix expressions can be evaluated with a stack and do not require parentheses.
TokenizationO(n)
ConversionO(n)
Auxiliary spaceO(n)
AlgorithmShunting Yard
Expression and playback controls
Step-by-step process
Postfix output
—
Enter an expression and click Convert.
Current token—
Operators popped0
Progress0 / 0
ComplexityO(n)
Token table
| # | Token | Type | Status |
|---|
Shunting Yard algorithm
for each token:
if token is an operand:
append token to output
else if token is an operator:
while stack top should be processed first:
append stack.pop() to output
stack.push(token)
else if token is "(":
stack.push(token)
else if token is ")":
pop operators until "("
discard the matching "("
pop remaining operators to output
Important concepts
Associativity
Exponentiation is right-associative. Therefore, A ^ B ^ C becomes
A B C ^ ^, representing A ^ (B ^ C).
Tokenization
Identifiers such as value1, names such as total, and numbers
such as 123 are treated as complete tokens rather than separate characters.
Validation
The converter rejects mismatched parentheses, missing operands, adjacent operands, unsupported characters, and incomplete expressions before playback begins.
Operator rules
| Operator | Precedence | Associativity |
|---|---|---|
| Unary +, unary − | 4 | Right |
| ^ | 3 | Right |
| *, /, % | 2 | Left |
| +, − | 1 | Left |