Bubble sort is a simple sorting algorithm. It is simple to understand, so it is used as a training algorithm. It is not used in productive programs, since it is not very efficient.
The algorithm's name derives from the fact, that the elements “bubble” up to their designated index, resembling bubbles in a glass of sparkling mineral water.
algorithm[change | change source]
The algorithm compares couples of elements within a vector. The elements constituting pairs are next to each other. Starting at one end of the vector, pairs are sequentially assumed. That means for example, the first and second element are compared, then the second and third element, and then the third and fourth, and so on. If the current pair is out of order, its elements are swapped in place. This process – of comparing two elements – is done over and over again, until the vector is sorted. The vector is sorted, when no pairs had to be swapped.
In the best case, the vector being sorted, the algorithm's complexity is O(n) (Big O notation). In the worst case, the vector being reversely sorted, O(n²).
implementation[change | change source]
In an imperative programming language, bubble sort can be implemented by utilizing a flag variable and looping through the array's elements:
- Set the flag
- Starting at one end, consider every neighbored pair of elements in a vector one after another (in their order).
- If a pair's elements are out of order, swap them, and clear the flag
- Repeat the previous steps until
Alternatively, since the greatest value ascends to the highest index within the first iteration and then has reached its final right position, two for-loops nested into one another sort the vector, too:
for top ≔ high(vector)−1 downto low(vector) do for current ≔ low(vector) to top do if vector[current] > vector[current+1] then exchange(vector, current, current+1)