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

Identify the first smallest element

In the first iteration, look for the smallest number in the entire list. The smallest number is 3. Swap it with the element in the first position (36). The list becomes: 3,55,17,35,63,85,12,48,36,66.

Find the next smallest element

On the second pass, find the smallest element from the elements starting from the second position. The smallest element is 12. Swap 12 with the second element (55). The list becomes: 3,12,17,35,63,85,55,48,36,66.

Continue finding the smallest

For the third iteration, find the smallest element from the remaining list starting at the third position. The smallest element is already 17, so no swapping is needed. The list remains: 3,12,17,35,63,85,55,48,36,66.

Repeat finding the smallest

In the fourth pass, find the smallest number from the elements starting from the fourth position. The smallest element is 35, which is already in place, so no swapping is required. The list remains: 3,12,17,35,63,85,55,48,36,66.

Select the next smallest piece

For the fifth iteration, look for the smallest value from the remaining unsorted section starting from the fifth position. The smallest is 36. Swap it with 63. The list becomes: 3,12,17,35,36,85,55,48,63,66.

Next smallest search continues

In the sixth pass, find the smallest element from the position directly after the last sorted number (sixth position). The smallest element is 48. Swap it with 85. The list now is: 3,12,17,35,36,48,55,85,63,66.

Proceed with sorting

Continuing with the seventh iteration, find the smallest number starting from the seventh position. The smallest is 55, so no swap is necessary as it is already in position. The list stays: 3,12,17,35,36,48,55,85,63,66.

Finalize the sort

For the eighth pass, look for the smallest element starting from the eighth position. The smallest is 63. Swap it with 85. The list becomes: 3,12,17,35,36,48,55,63,85,66.

Sorted list complete

On the final pass, you only need to ensure the positions of the last two numbers. Swap 85 with 66. The final sorted list is: 3,12,17,35,36,48,55,63,66,85.

Key concepts

Sorting Algorithms

Sorting algorithms are a fundamental part of computer science that deal with arranging a collection of elements in a specified order, usually ascending or descending. These algorithms play a crucial role in optimizing the performance of various software applications by arranging data for better readability and efficiency.
Selection Sort is a simple comparison-based sorting method. It systematically selects the smallest (or largest, depending on order) element from the unsorted portion of the array and moves it to the beginning, incrementing the position by one each time.
Key features of Selection Sort:

• It is in-place, meaning it requires no additional storage space beyond the input array.
• It has a time complexity of \(O(n^2)\), making it less efficient for large lists compared to other algorithms like Quick Sort or Merge Sort.
• This sort is easy to understand and implement, particularly useful for small datasets or educational purposes.

Step-by-Step Algorithm Explanation

Understanding algorithmic steps is essential to grasp how a process works. For Selection Sort, the algorithm repeatedly identifies the smallest element in the unsorted portion of the list and swaps it with the first unsorted element, thereby growing the sorted portion step-by-step.
Here's what the Selection Sort does, in a nutshell:

• Initial Step: Scan the entire list to find the smallest element, and swap it with the first element.
• Repeat: Move the unsorted "pointer" one position right. Again, find the smallest element in this new unsorted section, and swap it with the current first element of this section.
• Finish: Continue this process until the entire list is sorted, which occurs when the unsorted section contains only one element.

You can see the methodical swapping after each outer loop iteration until the last two numbers find their correct order as shown in the provided step-by-step solution.

C++ Programming Concepts

The Selection Sort algorithm can easily be implemented in C++ using loops, swaps, and basic array operations. Let's go over some of the core programming concepts utilized in implementing a Selection Sort in C++:

• For Loops: Employed to iterate over the collection multiple times, one for each pass needed to sort the array.
• Nested Loops: The inner loop finds the smallest element in the remaining unsorted part, while the outer loop runs the process for each position in the list.
• Swapping: A temporary variable is often used to help with swapping two numbers once the smallest one is identified in each iteration.
• Arrays: Selection Sort operates directly on arrays, hence understanding array indices and manipulation is crucial.

These fundamental C++ concepts allow for an effective translation of the Selection Sort logic into a working program.

Data Structure Fundamentals

Understanding data structures is key to implementing sorting algorithms like Selection Sort effectively. Here we focus on the array data structure, which is commonly used in sorting scenarios.
Arrays offer the following advantages in sorting:

• Index-Based Access: Arrays allow elements to be accessed by their indices, making it easy to iterate over the elements both linearly and conditionally.
• Fixed Size: Once an array is created, its size is set, which is efficient for certain performance optimizations during sorting.
• Contiguous Memory Allocation: The elements are stored in contiguous memory locations, leading to improved locality of reference compared to other data structures.

By using arrays, Selection Sort capitalizes on direct index access and efficient memory usage, obtaining functionality in sorting discrete elements.