# 3.21. Programming Exercises¶

1. Modify the infix-to-postfix algorithm so that it can handle errors.

2. Modify the postfix evaluation algorithm so that it can handle errors.

3. Implement a direct infix evaluator that combines the functionality of infix-to-postfix conversion and the postfix evaluation algorithm. Your evaluator should process infix tokens from left to right and use two stacks, one for operators and one for operands, to perform the evaluation.

4. Turn your direct infix evaluator from the previous problem into a calculator.

5. Implement the Queue ADT, using a vector such that the rear of the queue is at the end of the vector.

6. Design and implement an experiment to do benchmark comparisons of the two queue implementations. What can you learn from such an experiment?

7. It is possible to implement a queue such that both enqueue and dequeue have $$O(1)$$ performance on average. In this case it means that most of the time enqueue and dequeue will be $$O(1)$$ except in one particular circumstance where dequeue will be $$O(n)$$.

8. Consider a real life situation. Formulate a question and then design a simulation that can help to answer it. Possible situations include:

• Cars lined up at a car wash
• Customers at a grocery store check-out
• Airplanes taking off and landing on a runway
• A bank teller

Be sure to state any assumptions that you make and provide any probabilistic data that must be considered as part of the scenario.

9. Modify the Hot Potato simulation to allow for a randomly chosen counting value so that each pass is not predictable from the previous one.

10. Implement a radix sorting machine. A radix sort for base 10 integers is a mechanical sorting technique that utilizes a collection of bins, one main bin and 10 digit bins. Each bin acts like a queue and maintains its values in the order that they arrive. The algorithm begins by placing each number in the main bin. Then it considers each value digit by digit. The first value is removed and placed in a digit bin corresponding to the digit being considered. For example, if the ones digit is being considered, 534 is placed in digit bin 4 and 667 is placed in digit bin 7. Once all the values are placed in the corresponding digit bins, the values are collected from bin 0 to bin 9 and placed back in the main bin. The process continues with the tens digit, the hundreds, and so on. After the last digit is processed, the main bin contains the values in order.

11. Another example of the parentheses matching problem comes from hypertext markup language (HTML). In HTML, tags exist in both opening and closing forms and must be balanced to properly describe a web document. This very simple HTML document:

<html>
<title>
Example
</title>