![]() Because the array contains n n n elements, it has an O ( n ) O(n) O ( n ) number of elements. In big O notation, bubble sort performs O ( n ) O(n) O ( n ) comparisons. For each element in the array, bubble sort does n â 1 n-1 n â 1 comparisons. To calculate the complexity of the bubble sort algorithm, it is useful to determine how many comparisons each loop performs. The steps are summarized in the following table:įirst, it goes from j = 1 j=1 j = 1 to j = N â 1 j=N-1 j = N â 1 comparing each element of the list with the next ( \big( (i.e. Show all of the steps that the algorithm takes. Sort the array A = A= A = using the bubble sort algorithm. The animation below illustrates bubble sort: Do this for every pair of elements until the end of the list. If A A A is bigger than A A A, swap the elements. Move to the next element, A A A (which might now contain the result of a swap from the previous step), and compare it with A A A.For each element in the list, the algorithm compares every pair of elements. ![]() The Bubble sort algorithm compares each pair of elements in an array and swaps them if they are out of order until the entire array is sorted. This is a key point for the base case of many sorting algorithms. For example, is sorted alphabetically, is a list of integers sorted in increasing order, and is a list of integers sorted in decreasing order.Ä«y convention, empty arrays and singleton arrays (arrays consisting of only one element) are always sorted. In other words, a sorted array is an array that is in a particular order. Here is what it means for an array to be sorted.Īn array is sorted if and only if for all i < j i< j, a i ⤠a j. Output: A sorted permutation of A A A, called B B B, such that B ⤠B ⤠⯠⤠B. Input: An array, A A A, that contains n n n orderable elements: A A A. An algorithm that maps the following input/output pair is called a sorting algorithm:
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