Final answer:
A postfix evaluation algorithm needs only one stack because it processes operators and operands in direct sequence. Operands are pushed onto the stack, and when an operator is encountered, the needed operands are popped, the operation is performed, and the result is pushed back on the stack. This means only one stack is needed for the whole postfix expression evaluation.
Step-by-step explanation:
The reason a postfix evaluation algorithm needs only one stack is because of the way the operators and operands appear in postfix (also known as Reverse Polish Notation) expressions. In postfix notation, every operator follows all of its operands, which means that when evaluating the expression, you can apply each operation immediately after encountering it, using the most recent operands you've come across.
Here's the typical process:
- Scan the postfix expression from left to right.
- When an operand is encountered, push it onto the stack.
- When an operator is encountered, pop the required number of operands from the top of the stack, perform the operation, and push the result back onto the stack.
- Repeat this process until you reach the end of the expression, and the final result will be the sole element remaining in the stack.
This method does not require storing operators or multiple values that are waiting for further operations, unlike infix expressions where the order of operations must be considered (which might require more complex data structures like multiple stacks or a tree).
Hence, just one stack is sufficient for the entire evaluation process of a postfix expression.