Selection Sort

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Selection Sort is another simple comparison-based sorting algorithm. It works by repeatedly selecting the smallest (or largest) element from an unsorted portion of the list and swapping it with the first unsorted element. Though it is easy to understand and implement, Selection Sort is not the most efficient sorting algorithm, especially for large datasets.

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What is Selection Sort?

Selection Sort is an in-place, comparison-based sorting algorithm. It works by dividing the list into two parts: a sorted part and an unsorted part. Initially, the sorted part is empty, and the unsorted part contains all the elements. The algorithm repeatedly selects the smallest (or largest, depending on the sorting order) element from the unsorted part and swaps it with the first element of the unsorted part.

Key Properties of Selection Sort:

• In-Place: It sorts the list by swapping elements within the list and does not require extra memory.
• Non-Stable: Selection Sort is not a stable algorithm, meaning that the relative order of equal elements may not be preserved.
• Time Complexity: The algorithm has an $O(n^2)$ time complexity, making it inefficient for large lists.
• Simple to Implement: Selection Sort is easy to understand and implement, making it useful for educational purposes.

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How Does Selection Sort Work?

1. Divide the List: The list is divided into two parts: the sorted portion (initially empty) and the unsorted portion (initially the entire list).
2. Select the Minimum Element: The algorithm scans through the unsorted portion of the list and finds the smallest element.
3. Swap: The smallest element is swapped with the first element of the unsorted portion.
4. Repeat: This process is repeated for the remaining unsorted portion of the list until the entire list is sorted.

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Selection Sort: Step-by-Step Process

1. Initialization: Start with the first element of the list as the "current position."
2. Find the Minimum: For the current position, find the smallest element in the unsorted portion of the list.
3. Swap: Swap the smallest element with the element at the current position.
4. Move the Current Position: Move the current position to the next element in the list.
5. Repeat: Repeat the above steps until the entire list is sorted.

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Selection Sort: Python Code Implementation

Here’s how you can implement Selection Sort in Python:

def selection_sort(arr):
    n = len(arr)
    
    # Traverse through all array elements
    for i in range(n):
        # Find the minimum element in the unsorted part of the list
        min_index = i
        for j in range(i+1, n):
            if arr[j] < arr[min_index]:
                min_index = j
                
        # Swap the found minimum element with the first element
        arr[i], arr[min_index] = arr[min_index], arr[i]
    
    return arr

# Example usage:
arr = [64, 25, 12, 22, 11]
print("Unsorted Array:", arr)
sorted_arr = selection_sort(arr)
print("Sorted Array:", sorted_arr)

Output:

Unsorted Array: [64, 25, 12, 22, 11]
Sorted Array: [11, 12, 22, 25, 64]

Explanation of Code:

• Outer loop: The outer loop runs through each element of the list, one by one.
• Inner loop: The inner loop compares each element of the unsorted portion of the list to find the smallest element.
• Swap: Once the smallest element is found, it is swapped with the element at the current position in the list.
• Repeat: The process repeats until the entire list is sorted.

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Time and Space Complexity of Selection Sort

Time Complexity:

• Worst Case: $O(n^2)$ – This happens when the list is sorted in reverse order.
• Best Case: $O(n^2)$ – Even in the best case (already sorted list), Selection Sort still performs the same number of comparisons because it always checks the entire unsorted part of the list.
• Average Case: $O(n^2)$ – On average, the algorithm will need to perform $n(n-1)\mathrm{/}2$ comparisons.

Space Complexity:

• Space Complexity: $O(1)$ – Selection Sort is an in-place sorting algorithm, meaning it does not require extra space apart from the input list.

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Advantages of Selection Sort

1. Simple to Implement: Selection Sort is easy to understand and implement, making it ideal for educational purposes.
2. In-Place Sorting: Since it doesn’t require any additional memory, it’s efficient in terms of space.
3. No Extra Memory: Unlike other algorithms such as Merge Sort or Quick Sort, Selection Sort does not require additional space, making it suitable for scenarios with limited memory resources.

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Disadvantages of Selection Sort

1. Inefficient for Large Lists: With a time complexity of $O(n^2)$, Selection Sort is not efficient for large datasets. More efficient algorithms like Merge Sort and Quick Sort have better average and worst-case performance.
2. Non-Stable Sort: Selection Sort is not stable, meaning that equal elements might not retain their relative order.
3. Too Many Comparisons: Selection Sort makes a large number of comparisons, even when the list is already sorted or nearly sorted.

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When to Use Selection Sort?

1. Small Datasets: For smaller datasets, the overhead of more complex sorting algorithms may not be justified, making Selection Sort an acceptable choice.
2. Educational Purposes: Because of its simplicity, Selection Sort is often used to teach sorting algorithms.
3. When Space Complexity is Critical: Since Selection Sort is an in-place algorithm, it is useful when memory usage needs to be minimized.

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