Question

Sort the following list using the selection sort algorithm as discussed in this chapter. Show the list after each iteration of the outer for loop. 36, 55, 17, 35, 63, 85, 12, 48, 3, 66

Short answer

Sorted list: \( [3, 12, 17, 35, 36, 48, 55, 63, 66, 85] \).

Step-by-step solution

Initial List

Start with the initial unsorted list: \( [36, 55, 17, 35, 63, 85, 12, 48, 3, 66] \).

First Iteration

Find the smallest element in the list from index 0 to 9, which is \( 3 \) at index 8. Swap it with the element at index 0. The list becomes \( [3, 55, 17, 35, 63, 85, 12, 48, 36, 66] \).

Second Iteration

Find the smallest element from index 1 to 9, which is \( 12 \) at index 6. Swap it with the element at index 1. The list is now \( [3, 12, 17, 35, 63, 85, 55, 48, 36, 66] \).

Third Iteration

Identify the smallest element from index 2 to 9; it's \( 17 \) at index 2. No swap needed as it is already in place. The list remains \( [3, 12, 17, 35, 63, 85, 55, 48, 36, 66] \).

Fourth Iteration

Find the smallest element from index 3 to 9; it's \( 35 \) at index 3. Again, no swap required since it's in place. The list stays \( [3, 12, 17, 35, 63, 85, 55, 48, 36, 66] \).

Fifth Iteration

Select the smallest element from index 4 to 9, which is \( 36 \) at index 8. Swap it with the element at index 4. The list updates to \( [3, 12, 17, 35, 36, 85, 55, 48, 63, 66] \).

Sixth Iteration

Find the smallest element from index 5 to 9, which is \( 48 \) at index 7. Swap it with the element at index 5. The list changes to \( [3, 12, 17, 35, 36, 48, 55, 85, 63, 66] \).

Seventh Iteration

Look for the smallest element from index 6 to 9; it's \( 55 \) at index 6. No swap is needed. The list remains \( [3, 12, 17, 35, 36, 48, 55, 85, 63, 66] \).

Eighth Iteration

Identify the smallest element from index 7 to 9, which is \( 63 \) at index 8. Swap it with the element at index 7. The list updates to \( [3, 12, 17, 35, 36, 48, 55, 63, 85, 66] \).

Ninth Iteration

From index 8 to 9, the smallest is \( 66 \) at index 9. Swap it with the element at index 8. The final sorted list is \( [3, 12, 17, 35, 36, 48, 55, 63, 66, 85] \).

Key concepts

Sorting Algorithms

Sorting algorithms are fundamental concepts in computer science. They are essential for organizing data so that it can be easily searched, accessed, and analyzed. One of the simpler sorting algorithms is the selection sort, which has a straightforward process involving repeated selection and swapping of elements. Its main idea is to divide the list into two parts: a sorted part and an unsorted part. Initially, the sorted part is empty.

Selection sort builds the sorted list by repeatedly finding the smallest (or largest) element from the unsorted section and placing it at the end of the sorted section. Despite its simplicity, selection sort is not the most efficient algorithm for large datasets due to its time complexity of \( O(n^2) \). For small or mostly sorted lists, though, it can be a practical choice.

• Simple to implement and understand
• Suitable for small datasets
• In-place sorting (requires only a small constant amount of extra storage space)

Step-by-Step Programming

Step-by-step programming essentially means breaking down a problem into manageable steps, making it easier to solve. With selection sort, the step-by-step approach involves systematic traversal through the unsorted portion of the list to find the smallest element and performing a swap with the first unsorted element.

A clear step-by-step guide helps to delineate the exact thought processes and steps involved, especially for beginners. They can easily follow along and understand the purpose of each line of code. This method also enables efficient debugging.

• Clear separation of each operation
• Facilitates debugging and error correction
• Provides a structured plan of execution

Data Structures

A data structure is a specialized format for organizing, processing, and storing data. In the context of selection sort, arrays and lists are often used. The data structure dictates how the algorithm manipulates the data.

Selection sort typically operates on arrays in programming, which allows it to use contiguous memory allocation to store the elements. This is crucial because manipulating contiguous blocks of data can be faster and more efficient for the CPU. Understanding the type of data structure involved is essential for implementing an algorithm effectively.

• Arrays provide fixed size and efficient index-based access
• Lists can be more versatile and dynamic
• Choice of data structure affects performance

C++ Programming

When implementing selection sort in C++, you leverage the power of its syntax and performance capabilities. C++ is known for its speed and control over system resources, making it a great choice for implementing algorithms that need efficient processing.

In C++, arrays are used frequently. You access elements using indices, and loops are used to iterate through the array and perform comparisons and swaps. Functions can be used to encapsulate different tasks like swapping or finding the minimum index, making the code cleaner and more modular.

• Use of loops and functions for efficiency
• Array indexing for direct element access
• Ensures that the algorithm runs efficiently with limited overhead