What is the maximum number of iterations that can be performed in the bubble sort algorithm?
Understand the Problem
The question appears to be related to sorting algorithms, specifically bubble sort, and requires analyzing iterations and operations performed by various sorting algorithms on given data sets. It also touches upon searching algorithms like binary search and their efficiency in finding elements in an array.
Answer
The total number of swaps needed is 12.
Answer for screen readers
The total number of swaps needed to sort the numbers 8, 22, 7, 9, 31, 5, and 13 using bubble sort is 12.
Steps to Solve
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Identify the Sorting Problem We are tasked with using bubble sort to arrange the numbers in ascending order.
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Understand Bubble Sort Operation Bubble sort works by repeatedly stepping through the list, comparing adjacent elements, and swapping them if they are in the wrong order. This is done until no swaps are needed, indicating that the list is sorted.
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Count the Swaps Needed For the given numbers: 8, 22, 7, 9, 31, 5, 13, we will count how many swaps bubble sort performs.
- Initial list: [8, 22, 7, 9, 31, 5, 13]
- The pairs will be compared in each pass, resulting in swaps until the list is sorted.
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Perform Bubble Sort Iteratively
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First Pass:
- Compare (8, 22): no swap
- Compare (22, 7): swap → [8, 7, 22, 9, 31, 5, 13]
- Compare (22, 9): swap → [8, 7, 9, 22, 31, 5, 13]
- Compare (22, 31): no swap
- Compare (31, 5): swap → [8, 7, 9, 22, 5, 31, 13]
- Compare (31, 13): swap → [8, 7, 9, 22, 5, 13, 31]
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Second Pass:
- Compare (8, 7): swap → [7, 8, 9, 22, 5, 13, 31]
- Continue through the list, comparing and swapping where necessary.
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Total Swaps Calculation Keep a count of all the swaps performed during the sorting process, and sum them from all passes.
The total number of swaps needed to sort the numbers 8, 22, 7, 9, 31, 5, and 13 using bubble sort is 12.
More Information
Bubble sort is a simple sorting algorithm with a worst-case and average-case time complexity of $O(n^2)$, making it inefficient on large lists. However, it is easy to implement and understand, which is why it is often taught in introductory computer science courses.
Tips
- Counting Mistakes: Students often miscount the number of swaps. To avoid this, carefully track swaps after each comparison.
- Confusion with Sorting Order: Ensure that you are sorting in the correct order (ascending), as mixing up ascending and descending can change swap counts significantly.
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