Operator precedence
Exponentiation has higher precedence than multiplication and division, which have higher precedence than addition and subtraction.
What is Prefix Notation?
In infix notation, an operator appears between its operands, such as A + B.
In prefix notation, the operator appears first: + A B. Prefix expressions do
not require parentheses because the evaluation order is encoded by token order.
TokenizationO(n)
ConversionO(n)
Auxiliary spaceO(n)
SupportedIdentifiers and numbers
Expression and playback controls
Step-by-step process
Postfix output being built
—
Prefix result
—
Enter an expression and click Convert.
Current token—
Operators popped0
Progress0 / 0
ComplexityO(n)
Token table
| # | Token | Type | Status |
|---|
Conversion algorithm
tokens = tokenize(infix)
postfix = shuntingYard(tokens)
prefixStack = empty stack
for token in postfix:
if token is an operand:
prefixStack.push(token)
else:
right = prefixStack.pop()
left = prefixStack.pop()
prefixStack.push(operator + left + right)
prefix = prefixStack.pop()
Important concepts
Associativity
Exponentiation is right-associative, so A ^ B ^ C means
A ^ (B ^ C). The converter preserves this rule.
Tokenization
Multi-character operands such as value1, total, and
123 are treated as single tokens instead of separate characters.
Validation
The converter rejects mismatched parentheses, missing operands, adjacent operands, and unsupported characters before starting the visualization.
Operator rules
| Operator | Precedence | Associativity |
|---|---|---|
| Unary +, unary − | 4 | Right |
| ^ | 3 | Right |
| *, /, % | 2 | Left |
| +, − | 1 | Left |