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In this sorting algorithm, multiple swapping occurs in one pass. Smaller elements move or 'bubble' up to the top of the list, so the name given to the algorithm.
In this method, adjacent members of list to be sorted are compared. If item over the top is greater than the item instantly below it, then they are swapped. This procedure is carried on until the list is sorted.
The detailed algorithm is like as:
Algorithm: BUBBLE SORT
1. Begin
2. Read the n elements
3. for i=1 to n
for j=n downto i+1
if a[j] <= a[j-1]
swap(a[j],a[j-1])
4. End // of Bubble Sort
Total number of comparisons in Bubble sort will be:
= (N-1) +(N-2) . . . + 2 + 1
= (N-1)*N / 2 =O(N2)
This inefficiency is because of the fact that an item moves only to the next position in each pass.
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Best Case: If the list is sorted already then A[i] T (n) = c1n + c2 (n -1) + c3(n -1) + c4 (n -1) = O (n), which indicates that the time complexity is linear. Worst Case:
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