![]() ![]() 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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