If a stack is used to evaluate an expression in postfix notation, what is the ti
Practice Questions
Q1
If a stack is used to evaluate an expression in postfix notation, what is the time complexity of the evaluation?
O(1)
O(n)
O(log n)
O(n^2)
Questions & Step-by-Step Solutions
If a stack is used to evaluate an expression in postfix notation, what is the time complexity of the evaluation?
Step 1: Understand what postfix notation is. In postfix notation, the operator follows the operands. For example, '3 4 +' means '3 + 4'.
Step 2: Know that a stack is a data structure that follows Last In First Out (LIFO) principle. You can only add or remove items from the top of the stack.
Step 3: When evaluating a postfix expression, you read the expression from left to right.
Step 4: For each token (number or operator) in the expression, do the following: If it's a number, push it onto the stack. If it's an operator, pop the required number of operands from the stack, perform the operation, and push the result back onto the stack.
Step 5: Continue this process until you have processed all tokens in the expression.
Step 6: The final result will be the only item left in the stack after processing all tokens.
Step 7: The time complexity is O(n) because you process each token exactly once, where n is the total number of tokens in the expression.
Postfix Notation Evaluation – Postfix notation (also known as Reverse Polish Notation) is a mathematical notation in which every operator follows all of its operands. Evaluating such expressions using a stack involves pushing operands onto the stack and applying operators to the operands popped from the stack.
Time Complexity Analysis – The time complexity of an algorithm is a computational measure that describes the amount of time it takes to run an algorithm as a function of the length of the input. In this case, the evaluation of a postfix expression involves processing each token exactly once.
