Question

Bubble sort places ________ number(s) in place on each pass through the data.

Short answer

#tag_title#Step 4: Example of Bubble Sort#tag_content#Let's take an example with the following list of numbers: 5, 1, 4, 2, 8 Pass 1: - Compare 5 and 1, swap them: 1, 5, 4, 2, 8 - Compare 5 and 4, swap them: 1, 4, 5, 2, 8 - Compare 5 and 2, swap them: 1, 4, 2, 5, 8 - Compare 5 and 8, no swap needed: 1, 4, 2, 5, 8 After Pass 1, the largest number, 8, is in its correct position. Pass 2: - Compare 1 and 4, no swap needed: 1, 4, 2, 5, 8 - Compare 4 and 2, swap them: 1, 2, 4, 5, 8 - Compare 4 and 5, no swap needed: 1, 2, 4, 5, 8 After Pass 2, the second-largest number, 5, is in its correct position. Pass 3: - Compare 1 and 2, no swap needed: 1, 2, 4, 5, 8 - Compare 2 and 4, no swap needed: 1, 2, 4, 5, 8 After Pass 3, the middle number, 4, is in its correct position. Pass 4: - Compare 1 and 2, no swap needed: 1, 2, 4, 5, 8 Now, the entire list is sorted. It took 4 passes to sort the list. By the end of each pass, the algorithm places one number in its correct position. In our example, after Pass 1, one number (8) was placed; after Pass 2, two numbers (8, 5) were placed; after Pass 3, three numbers (8, 5, 4) were placed; after Pass 4, all the numbers were sorted.

Step-by-step solution

Understanding Bubble Sort

Bubble sort is a simple sorting algorithm that works by repeatedly stepping through the list to be sorted, comparing each pair of adjacent items, and swapping them if they are in the wrong order. This process continues until no more swaps are needed, and the list is now sorted.

Working the Algorithm

To sort a list of numbers using Bubble Sort, perform the following procedure: 1. Start at the beginning of the list. 2. Compare the first pair of adjacent numbers in the list. 3. If the first number is greater than the second one, swap their positions. 4. Move to the next pair of adjacent numbers and repeat step 3. 5. Continue this process until you reach the end of the list. 6. After the first pass through the data, the largest number will be in its correct position. 7. Repeat the entire process again, but do not include the previously sorted largest number from step 6. 8. Continue this process, excluding one more sorted number after each pass, until all numbers are sorted.

Number of Elements Sorted After Each Pass

During each pass of the Bubble Sort algorithm, we compare and potentially swap the adjacent elements in the list. By the end of each pass, at least one number (the largest unsorted number) will be in its correct position. Therefore, Bubble Sort places 1 number in place on each pass through the data.

Key concepts

Sorting Algorithms

Sorting algorithms are fundamental procedures used to reorder the elements of a list into a specific order, typically numerical or lexicographical. Among them, the Bubble Sort algorithm stands out for its simplicity and intuitive mechanics. In bubble sort, we sequentially compare adjacent items and swap them if they're in the incorrect order. This process creates a 'bubble effect', where the largest unsorted elements 'float' to the top, or the end, of the list after each pass.

While Bubble Sort is easy to understand and implement, it is less efficient for large datasets compared to more advanced algorithms like Quick Sort or Merge Sort. Despite this, Bubble Sort provides an excellent introduction into the concept of sorting for beginners in computer programming. It emphasizes the importance of iterating over data and the methodical approach required to order elements systematically.

Algorithm Efficiency

Evaluating the efficiency of an algorithm is crucial in computer science. It determines how quickly a task can be completed relative to the size of the input data. Algorithm efficiency is often discussed in terms of time complexity and space complexity. Time complexity refers to the amount of time an algorithm takes to complete as a function of the input size, usually denoted in Big O notation.

For the Bubble Sort algorithm, its time complexity is generally expressed as \(O(n^2)\), meaning that the time to sort the data grows quadratically with the number of elements to sort. This is because each element needs to be compared with each other element. Additionally, Bubble Sort has a space complexity of \(O(1)\), as it requires a constant amount of additional memory space regardless of the input size. Efficiency matters especially as datasets grow larger, and that is why Bubble Sort is often surpassed by more efficient algorithms for large scale data sorting tasks.

Programming Concepts

The Bubble Sort algorithm embodies several key programming concepts that are vital to software development and computer science education. One such concept is the iteration process, where algorithms go through sets of data multiple times to reach a result. This is seen as Bubble Sort repeatedly passes through the list being sorted.

Another concept is conditional statements, which are used to compare elements and determine if a swap is necessary. Control structures, like loops, are also highlighted in Bubble Sort, requiring proper iteration control to halt the process when the sorting is complete. Furthermore, Bubble Sort demonstrates the use of variables to temporarily hold data and the manipulation of data structures, such as arrays, to organize and modify information efficiently. Overall, Bubble Sort serves as a practical example of these fundamental concepts in action, forming a great learning tool for programming students.