Teach me about the selection sorting in the C++ in detail
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Selection Sort is a fundamental sorting algorithm that works by repeatedly selecting the minimum element from the unsorted portion of the array and placing it at the beginning. The algorithm divides the array into two parts: a sorted portion on the left and an unsorted portion on the right. In each iteration, we find the smallest element in the unsorted portion and swap it with the first element of the unsorted portion.
Selection sort is a fundamental sorting algorithm that works by dividing the array into two parts: a sorted portion and an unsorted portion. The algorithm repeatedly finds the smallest element from the unsorted portion and moves it to the end of the sorted portion. It has a time complexity of O(n²) and is an in-place sorting algorithm, meaning it requires only a constant amount of additional memory.
The selection sort algorithm uses two nested loops. The outer loop iterates through each position from 0 to n-2, representing the current position to fill. For each position i, we set min_index to i, then use the inner loop to scan from i+1 to n-1 to find the smallest element. When we find an element smaller than the current minimum, we update min_index. After the inner loop completes, we swap the element at position i with the element at min_index.
Here's the complete C++ implementation of selection sort. The function takes a vector of integers by reference. We use two nested for loops - the outer loop runs from 0 to n-2, and for each iteration, we find the minimum element in the remaining unsorted portion using the inner loop. The swap function exchanges the current element with the minimum element found. The main function demonstrates how to use the selection sort with a sample array.
Let's trace through the selection sort algorithm step by step. We start with the unsorted array: 64, 25, 12, 22, 11. In the first iteration, we find the minimum element 11 and swap it with the first element 64. In the second iteration, we find 12 as the minimum and swap it with 25. This process continues until the entire array is sorted. Each iteration places one more element in its correct position.
Selection sort has a time complexity of O(n²) in all cases - best, average, and worst. This is because regardless of the input, the algorithm always performs the same number of comparisons. The space complexity is O(1) as it sorts in-place. While selection sort is simple to implement and memory efficient, its poor time complexity makes it unsuitable for large datasets. It's not stable, meaning it doesn't preserve the relative order of equal elements.