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Postfix Expression Evaluation is a widely used technique in Data Structures and Algorithms (DSA). Unlike infix expressions, postfix expressions do not require parenthesis for operator precedence. The stack is the most efficient data structure for evaluating a postfix expression because it handles the operands and operations in the order they are processed. Steps to Evaluate a Postfix Expression Using a Stack: 1. Traverse the expression from left to right. 2. If the character is an operand, push it onto the stack. 3. If the character is an operator, pop the top two elements from the stack. Perform the operation using the popped operands, then push the result back onto the stack. 4. Continue until the end of the expression. The final value in the stack is the result of the postfix expression. Example: Postfix expression: 5 6 + 3 * • Push 5 → Stack: [5] • Push 6 → Stack: [5, 6] • Encounter +: Pop 6 and 5, compute 5 + 6 = 11, push 11 → Stack: [11] • Push 3 → Stack: [11, 3] • Encounter *: Pop 3 and 11, compute 11 * 3 = 33, push 33 → Stack: [33] Result: 33 Why This Works Efficiently: • A stack ensures O(1)O(1)O(1) insertion and deletion, making it optimal for maintaining intermediate values. • The operations follow the Last-In-First-Out (LIFO) principle, matching the evaluation order of postfix expressions. ________________________________________ Why Other Options Are Incorrect: 1. Recursion with a Stack: While recursion internally uses a stack, explicitly using a single stack for postfix evaluation is more efficient and less error-prone. Recursive evaluation is better suited for tree-based expressions but introduces unnecessary overhead for simple postfix evaluation. 2. Direct Calculation Without Any Data Structure: Postfix expressions do not maintain operator precedence or provide positional cues for evaluation without a stack. Direct calculation is infeasible because operands and operators need to be stored temporarily during evaluation. 3. Using a Queue to Maintain Operands and Operators: Queues follow a First-In-First-Out (FIFO) order, which is unsuitable for postfix evaluation. The LIFO behavior of a stack is crucial for evaluating operators in the correct order. 4. Converting Postfix to Infix for Evaluation: Conversion adds an extra computational overhead and complexity. The purpose of postfix notation is to avoid the ambiguity of infix expressions and eliminate the need for parentheses and precedence rules, making direct stack evaluation more efficient.
