Why is the selection sort more efficient than the bubble sort on large arrays?

Bubble sort is a simple sorting algorithm that repeatedly steps through the array and compares adjacent elements. If a pair of elements is in the wrong order, it swaps them. This process continues until the entire array is sorted. The largest element "bubbles" to the end of the array in each iteration.

Selection sort is another simple sorting algorithm that functions by repeatedly selecting the minimum element from the unsorted part of the array and swapping it with the first element of the unsorted part. This process continues until the entire array is sorted.

Bubble sort has a best-case time complexity of O(n) when the array is already sorted, an average-case time complexity of O(n^2), and a worst-case time complexity of O(n^2). The quadratic complexity of bubble sort is because, in general, it compares every pair of adjacent elements and can potentially swap them for every pass through the array.

Selection sort has a best-case time complexity of O(n^2), an average-case time complexity of O(n^2), and a worst-case time complexity of O(n^2). The quadratic complexity of selection sort is because it searches for the minimum element in the unsorted part of the array during each pass, comparing every remaining element to the minimum found so far.

For large arrays, selection sort is generally more efficient than bubble sort due to the number of swaps performed. Bubble sort can swap elements in every pass of the array, resulting in many exchanges. On the other hand, selection sort only swaps elements once per pass, at the end of each search for the minimum element. In both algorithms, the number of comparisons remains similar, but the reduced number of swaps in selection sort helps to make it more efficient, particularly on large arrays. Additionally, the adaptive behavior of bubble sort (i.e., its ability to detect a sorted array) does not provide significant benefits for large arrays, as it is unlikely that such arrays will be already sorted or require few adjustments. In conclusion, while both bubble sort and selection sort have similar time complexities, selection sort outperforms bubble sort on large arrays due to its reduced number of element swaps.