In Algorithm Design Lab, counting the number of comparisons and swaps is an important method for analyzing the performance of algorithms, especially sorting algorithms. Comparisons refer to the number of times an algorithm compares two elements or values to determine their relative order. Swaps refer to the number of times two elements are exchanged or their positions are changed during the execution of an algorithm. These two operations are useful for understanding the time complexity and practical efficiency of an algorithm. Consider a sorting algorithm that arranges an array of elements in ascending order. During sorting, the algorithm generally performs two major types of operations: comparison and rearrangement. For example, if two elements are compared to determine whether the first element is greater than the second, one comparison is counted. If their positions are exchanged because they are in the wrong order, one swap is counted. By keeping separate counts of these operations, we can study how efficiently the algorithm performs. Bubble Sort provides a simple example for counting comparisons and swaps. In Bubble Sort, adjacent elements are repeatedly compared. If the element on the left is greater than the element on the right, the two elements are swapped. For an array containing n elements, the standard version of Bubble Sort performs comparisons in the following manner: (n − 1) + (n − 2) + (n − 3) + ... + 1 The total number of comparisons is therefore: n(n − 1) / 2 For example, suppose the array contains five elements. The number of comparisons in the first pass is four, in the second pass three, in the third pass two, and in the fourth pass one. Therefore: 4 + 3 + 2 + 1 = 10 comparisons. The number of swaps depends on the initial arrangement of the elements. If the array is already sorted, Bubble Sort may perform zero swaps, although it can still perform comparisons. If the array is arranged in reverse order, the maximum number of swaps is: n(n − 1) / 2 For five elements, the maximum number of swaps is: 5(5 − 1) / 2 = 10 swaps. Consider the array [5, 3, 4, 1]. During Bubble Sort, the algorithm compares 5 and 3. Since 5 is greater than 3, they are swapped. The array becomes [3, 5, 4, 1]. This operation contributes one comparison and one swap. Next, 5 and 4 are compared and swapped, producing [3, 4, 5, 1]. Again, one comparison and one swap are counted. Then 5 and 1 are compared and swapped, producing [3, 4, 1, 5]. In this way,