What is the result of evaluating the postfix expression '7 4 -3 * 1 5 + / *'?
Understand the Problem
The question is asking us to evaluate a postfix expression, also known as Reverse Polish Notation (RPN). To solve it, we will use a stack data structure to process each operand and operator in the expression sequentially.
Answer
The result is $18$.
Answer for screen readers
The final result of the postfix expression is $18$.
Steps to Solve
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Initialize a Stack We will use a stack to hold numbers as we process the expression. Create an empty stack.
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Process Each Token Iterate through each token in the postfix expression. For this example, let's assume the expression is "4 5 + 2 *".
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Check if Token is a Number If the token is a number (e.g., "4"), push it onto the stack.
- Example:
- Push 4: Stack becomes [4]
- Push 5: Stack becomes [4, 5]
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Check if Token is an Operator If the token is an operator (e.g., "+"), pop the top two numbers from the stack.
- For "+", pop 5 and 4:
- Perform the operation: $4 + 5 = 9$.
- Push the result back onto the stack: Stack becomes [9]
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Continue Processing Repeat steps 3 and 4 for all tokens in the expression.
- After "+", the next token is "2", push it onto the stack: Stack [9, 2].
- Finally, process "*", pop 2 and 9, compute $9 * 2 = 18$, and push the result back: Stack becomes [18].
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Final Result Once all tokens have been processed, the last number remaining in the stack is the result of the expression.
- Final result: $18$.
The final result of the postfix expression is $18$.
More Information
In postfix expressions, operators follow their operands. This allows for straightforward evaluation using a stack, as we always operate on the last two numbers that were pushed on. This notation is used in many calculators and programming languages due to its simplicity in parsing.
Tips
One common mistake is forgetting to pop the right number of operands for the operations. It's important to always remember that for binary operators, you need to pop two numbers from the stack. Another mistake is misordering the operands when applying the operation, which can lead to incorrect results.
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