Implementing the Bubble Sort Algorithm in C++

Bubble Sort is a classic introductory sorting algorithm. Its core idea is similar to bubbles rising: by repeatedly comparing adjacent elements and swapping out-of-order pairs, smaller elements gradually "bubble" to the top of the array. The basic process is as follows: in each round, start from the first element and compare adjacent elements, swapping them if they are out of order. Each round determines the position of one maximum element, and this continues until the array is sorted. In C++ implementation, the `bubbleSort` function uses an outer loop to control the number of rounds (at most n-1 rounds). The inner loop compares adjacent elements and swaps them, with a `swapped` flag for optimization—if no swaps occur in a round, the algorithm exits early. The time complexity is O(n²) in the worst and average cases, O(n) in the best case (after optimization), with a space complexity of O(1). It is a stable sorting algorithm. Despite its low efficiency, Bubble Sort is intuitive and easy to understand. Mastering the "compare and swap" logic is key to learning the basics of sorting, making it suitable for algorithmic introductory practice.