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. 6, 45, 10, 25, 58, 2, 50, 30, 86

Short answer

The sorted list is [2, 6, 10, 25, 30, 45, 50, 58, 86].

Step-by-step solution

Understand Selection Sort

Selection sort is a comparison-based sorting algorithm. It works by repeatedly selecting the smallest (or largest, depending on the order) element from the unsorted portion of the list and swapping it with the first unsorted element, moving the boundary of sorted and unsorted sections forward.

Initialize the Process

Start with the initial list: [6, 45, 10, 25, 58, 2, 50, 30, 86]. Consider the entire list as unsorted initially. At each iteration of the outer loop, we will identify the smallest number in the unsorted portion and swap it with the first unsorted number.

First Iteration

Find the smallest element in the list from index 0 to index 8, which is 2 at index 5. Swap it with the element at index 0. List after this iteration: [2, 45, 10, 25, 58, 6, 50, 30, 86].

Second Iteration

Find the smallest element in the sub-list from index 1 to 8, which is 6 at index 5. Swap it with the element at index 1. List after this iteration: [2, 6, 10, 25, 58, 45, 50, 30, 86].

Third Iteration

Find the smallest element from index 2 to 8, which is 10 at index 2. It is already in place, so no swap is needed. List remains: [2, 6, 10, 25, 58, 45, 50, 30, 86].

Fourth Iteration

Find the smallest element from index 3 to 8, which is 25 at index 3. It is already in place, so no swap is needed. List remains: [2, 6, 10, 25, 58, 45, 50, 30, 86].

Fifth Iteration

Find the smallest element from index 4 to 8, which is 30 at index 7. Swap it with the element at index 4. List after this iteration: [2, 6, 10, 25, 30, 45, 50, 58, 86].

Sixth Iteration

Find the smallest element from index 5 to 8, which is 45 at index 5. It is already in place, so no swap is needed. List remains: [2, 6, 10, 25, 30, 45, 50, 58, 86].

Seventh Iteration

Find the smallest element from index 6 to 8, which is 50 at index 6. It is already in place, so no swap is needed. List remains: [2, 6, 10, 25, 30, 45, 50, 58, 86].

Eighth Iteration

Find the smallest element from index 7 to 8, which is 58 at index 7. It is already in place, so no swap is needed. List remains: [2, 6, 10, 25, 30, 45, 50, 58, 86].

Key concepts

Sorting Algorithms

Sorting algorithms are fundamental techniques used to arrange data in a specific order. They play a crucial role in computer science, particularly in improving the efficiency of other algorithms and in data organization. Each sorting algorithm follows a specific method to reorder the elements of a list or array. Selection sort is one such algorithm.

While there are many sorting algorithms like bubble sort, merge sort, and quicksort, selection sort is known for its simplicity. This algorithm divides the list into a sorted and an unsorted section, progressively shrinks the unsorted portion by selecting the smallest element, and moving it to the end of the sorted section. This process is repeated until the entire list is ordered.

Although selection sort is not the most efficient, especially with large datasets, it serves well for educational purposes. It helps one understand the basic mechanics of sorting and complexity, considering every element at least once to find the minimum or maximum.

Algorithm Step-by-Step

The step-by-step execution of an algorithm is paramount for understanding its functionality and implementation. When discussing selection sort, the process can be broken down into several clear and repeatable steps.

To begin, the algorithm identifies the smallest number in the list. It then swaps this number with the first unsorted element in the list. This process transforms the first element in the unsorted portion into the next element in the sorted portion.

The algorithm then moves to the next element, repeating the same process of identifying the minimum and swapping, marking boundaries between sorted and unsorted.

• Start with the entire list as unsorted.
• Find and select the minimum number from the unsorted portion.
• Swap this minimum with the first unsorted element.
• Mark this element as sorted, then move to the next unsorted element.
• Repeat till the entire list becomes sorted.

By executing each iteration, the list slowly becomes ordered, eventually leading to a fully sorted list.

Data Structures

Data structures are essential to store and manage data efficiently in computer science. They determine how data is organized, accessed, and manipulated. When implementing sorting algorithms, the choice of data structure influences the algorithm's performance and complexity.

For selection sort and many other algorithms, arrays (or lists) are commonly used data structures. Arrays are favored for their simplicity and direct representation of data in memory, allowing easy access by index.

The choice of data structure affects the speed and efficiency of operations such as searching, inserting, and deleting elements. For example:

• Constant time access by index (i.e., O(1) complexity) in an array makes it easy to implement algorithms like selection sort.
• The ability to handle a fixed-size dataset without dynamic expansion requirements.

Understanding the role of data structures aids in selecting the right tool for a specific task, influencing both the design and implementation of algorithms.

C++ Programming

C++ is a powerful programming language commonly used for system/software development and game programming. With its ability to manage both high-level and low-level programming tasks, C++ is ideal for implementing algorithms like selection sort.

When implementing selection sort in C++, one can take advantage of its efficient handling of data structures like arrays and its robust control structures. The syntax is designed to offer precise control over computing resources.

To implement selection sort in C++, you typically declare an array, loop through the elements, and use nested loops to progress through iterations. This repetitive structure is handled efficiently through C++'s loop constructs, including 'for' and 'while' loops.

• Declare a function or method to handle sorting logic.
• Use nested loops to find and swap elements.
• Maintain a clear distinction between sorted and unsorted sections in the array.

By mastering these programming concepts, one can implement robust and efficient algorithms in C++, leveraging the language's powerful features.