Lecture 19: SELECTION SORT Algorithm with Theory and Code

Name: Lecture 19: SELECTION SORT Algorithm with Theory and Code
Uploaded: 2023-10-12T00:30:04.000Z
Duration: 1 h 36 min 22 s

What is Sorting and Its Importance?

Introduction to Sorting

The speaker introduces the topic of sorting, explaining it as arranging items in a proper order.

A real-life example is provided: students lining up by height in school, which helps everyone see the stage clearly.

Benefits of Sorting

The speaker discusses how dictionaries are sorted alphabetically, making it easier to find word meanings quickly.

In a hotel with randomly numbered rooms, finding room 34 would be difficult without proper arrangement; sorting makes this process easier.

Application in Programming

The importance of sorting in programming is highlighted. Properly arranged data allows for efficient searching techniques like binary search.

The speaker emphasizes that unsorted data can lead to inefficient searches, while sorted data simplifies the process significantly.

How to Sort Data?

Understanding Array Sorting

An array example is introduced where data needs to be sorted either in ascending or descending order.

The concept of increasing (ascending) and decreasing (descending) order is explained with examples.

Selection Sort Technique

Various sorting algorithms are mentioned, including selection sort, insertion sort, bubble sort, quick sort, and merge sort.

The speaker indicates that today’s focus will be on selection sort while ensuring clarity on what sorting means.

Implementing Sorting Techniques

Problem Statement

A specific problem involving an array with numbers needing to be sorted in increasing order is presented.

Real-Life Analogy for Sorting

Selection Sort Technique Explained

Understanding the Selection Sort Process

The speaker discusses arranging elements by height, starting with the shortest. This method involves identifying the smallest element and placing it in the correct position.

The process continues as the speaker identifies subsequent smallest elements, ensuring that each is placed correctly in relation to others.

The technique being demonstrated is known as "Selection Sort," which operates through multiple rounds of finding and positioning the smallest elements.

In Round One, the smallest number (1) is identified and swapped with another number (9), completing this round of sorting.

As rounds progress, each subsequent round focuses on finding the next smallest element until all are sorted properly.

Rounds of Sorting

In Round Two, the speaker finds 3 as the next smallest element and places it correctly while swapping with 7.

By Round Three, 6 is identified for swapping to maintain order among remaining elements.

The fourth round identifies 7 for placement while confirming that previous numbers are already sorted correctly.

The speaker emphasizes that if an array has 'n' elements, there will be 'n - 1' rounds needed to sort them completely.

Finalizing Sorting Steps

A practical example illustrates how sorting works: after placing four smaller numbers, the fifth automatically falls into its correct position due to prior arrangements.

Another example begins with a new array size of six; again, it follows similar steps to identify and place each element in increasing order.

Each step involves checking for the next smallest number and making necessary swaps until all elements are arranged properly.

Conclusion on Selection Sort

After several rounds of sorting (up to five), all elements are confirmed sorted in their proper positions.

The logic behind selection sort becomes clear: find and swap until fully sorted.

How to Find the Index of the Smallest Element in an Array?

Introduction to the Problem

The speaker poses a question about finding the index of the smallest element in a given array: [3, 4, 1, 2, 6, 0, 1, 2, 3, 4].

Initially assumes that the first element (index 0) is the smallest and sets it as a reference for comparison.

Implementation Logic

The speaker discusses using a loop to iterate through the array starting from index 1 to compare each element with the current smallest.

If an element smaller than the current smallest is found during iteration, its index is stored for later reference.

Step-by-Step Comparison

The process involves checking if each subsequent element is less than the currently identified smallest. For example:

At index 1, checks if 4 < 3 (no change).

At index 2, checks if 1 < 3 (update smallest).

Continues this process until all elements have been checked and confirms which index holds the smallest value.

Selection Sort Implementation Discussion

Transitioning into discussing how this logic applies to implementing selection sort.

Emphasizes indexing elements from 0 to 5 and preparing for sorting by identifying and swapping elements based on their size.

Final Steps in Sorting Process

After identifying indices of smaller elements through multiple iterations:

Swaps are made between identified small elements and their respective positions.

This continues until all rounds of sorting are completed.

Concludes that only specific indices (0, 1, 2, etc.) will change while others remain fixed during sorting operations.

Finding the Index of the Smallest Element

Initial Setup for Finding the Smallest Element

The task involves finding the index of the smallest element in an array, starting from index zero.

A loop is established to iterate through indices from 0 to 4, where i represents the current index being evaluated.

Looping Through Elements

The process includes comparing each element with a stored minimum value and updating it if a smaller element is found.

Once the loop completes, it confirms that the smallest element's index has been identified and prepares for swapping.

Swapping Elements

The identified smallest element will be swapped with its corresponding position in the array based on its index.

A nested loop structure is suggested to handle multiple iterations over different elements as needed.

Understanding Array Length and Indices

Clarification on why loops run until n - 1, explaining that if n equals six, it only goes up to four (indices 0 through 4).

This approach ensures all elements are considered without exceeding array bounds.

Finalizing Logic and Complexity Analysis

The logic behind identifying and swapping elements is reiterated, emphasizing clarity in understanding how exchanges occur during sorting.

Discussion shifts towards analyzing time complexity and space complexity associated with this algorithmic approach.

Complexity Considerations

Time Complexity Insights

An exploration into how time complexity can be assessed based on iterations through arrays.

Space Complexity Evaluation

Explanation of auxiliary space versus total space used by considering only additional variables created during execution.

Total Space Consideration

Understanding Space Complexity and Time Complexity in Arrays

Space Complexity of Arrays

The space taken by constants like integers (A, B, C) is fixed and considered constant space.

When creating an array of a fixed size (e.g., 20), it also occupies constant space since the size is predetermined.

If an array's size is defined beforehand, it remains constant regardless of input changes; this is crucial for understanding space complexity.

The importance of defining arrays with fixed sizes to ensure they are treated as constant space in algorithms.

Regardless of the variable 'n', if the array size is predefined, it does not affect the overall space complexity.

Time Complexity Analysis

To analyze time complexity, consider how many times loops run based on input size; for example, from 1 to n.

Focus on significant operations within loops while ignoring constant-time operations that do not scale with input size.

As loop iterations increase (from 1 to n), the number of operations grows linearly with 'n'.

The total number of loop executions can be calculated using arithmetic series principles leading to a time complexity representation.

Best Case vs. Worst Case Scenarios

The derived time complexity indicates O(n^2), which represents worst-case scenarios where all elements need sorting or processing.

In best-case scenarios (e.g., already sorted arrays), similar processes still apply but may yield different complexities such as Ω(n).

For average cases, if no specific conditions alter performance drastically, expect similar complexities across best and worst cases.

Implementation Insights

Transitioning into code implementation involves setting up an integer array and populating it with values for sorting algorithms like selection sort.

Selection sort operates through nested loops: an outer loop iterates through each element while an inner loop identifies the minimum value for placement.

Selection Sort Algorithm Implementation

Understanding the Selection Sort Process

The discussion begins with determining the number of rounds for sorting, indicating that if there are six elements, five rounds will be needed. This is established by iterating from i = 0 to i < 5.

An integer index is initialized to track the minimum element's position during each round. A nested loop starts from j = i + 1 and continues until j < 6, searching for the smallest element.

If a smaller element is found at index j, it updates the index variable accordingly. After identifying the minimum element, a swap operation occurs between this minimum and the first unsorted element.

Code Execution and Output Verification

The inner part of the code effectively extracts and swaps the minimum element with its corresponding position in an array. The process iterates through all elements, ensuring proper sorting.

Upon executing selection sort, a sorted array output (1, 2, 3, 4, 7, 10) confirms that the algorithm functions correctly as intended.

User Input Integration

To enhance usability, user input for array size is introduced. It’s noted that sizes should not exceed 1000 elements; thus an array of size 1000 is preallocated.

An integer variable n captures user-defined size input for dynamic handling of arrays. Elements are inserted into this array based on user specifications.

Enhancements in User Interaction

Prompts are added to guide users in entering both array size and individual elements clearly. This improves overall interaction quality during execution.

After receiving inputs like "8" for size and several integers (e.g., "2", "1", "4"), outputs reflect successful data processing through selection sort implementation.

Final Adjustments and Testing

The code structure allows flexibility by accommodating varying sizes while maintaining efficiency within defined limits (up to n = 1000).

Testing on online compilers like LeetCode ensures functionality across platforms while confirming time complexity expectations associated with selection sort algorithms.

Transitioning to Vector Usage

Discussion shifts towards using vectors instead of static arrays for better memory management and dynamic sizing capabilities in future lessons.

Vectors provide benefits such as automatic resizing; however, they require additional steps to determine their current size compared to traditional arrays.

Selection Sort Implementation and Homework

Understanding Selection Sort

The speaker discusses the return value of a sorting function, emphasizing clarity in returning sorted arrays. A mistake is noted regarding the naming of an array.

After correcting the naming error, two test cases are run successfully, confirming that the selection sort implementation works as intended.

The execution time exceeds the limit set for running the algorithm, indicating that selection sort has a time complexity of O(n²), while it should ideally be O(n log n). This highlights its inefficiency compared to other algorithms.

The speaker concludes that selection sort is not the most optimized algorithm for sorting but emphasizes its importance for foundational understanding in coding.

Homework Assignment

The homework involves reversing the selection sort process by moving the largest element to the end of an array instead of moving the smallest to the front.

An example is provided where 10 is identified as the largest number and moved to its correct position at the end. This exercise aims to deepen understanding of sorting techniques.

Students are encouraged to implement this reverse logic and consider how they can apply selection sort on character arrays as well, enhancing their coding skills through practical application.