Bubble sort is a simple sorting algorithm. This sorting algorithm is comparison based algorithm in which each pair of adjacent elements is

compared and elements are swapped if they are not in order. This algorithm does sorting in-place i.e. it does not creates a new array while

carrying out the sorting process.

#### Example

```
array = [5, 1, 4, 2, 8]
First Pass:
( 5 1 4 2 8 ) –> ( 1 5 4 2 8 ), Here, algorithm compares the first two elements, and swaps since 5 > 1.
( 1 5 4 2 8 ) –> ( 1 4 5 2 8 ), Swap since 5 > 4
( 1 4 5 2 8 ) –> ( 1 4 2 5 8 ), Swap since 5 > 2
( 1 4 2 5 8 ) –> ( 1 4 2 5 8 ), Now, since these elements are already in order (8 > 5), algorithm does not swap them.
Second Pass:
( 1 4 2 5 8 ) –> ( 1 4 2 5 8 )
( 1 4 2 5 8 ) –> ( 1 2 4 5 8 ), Swap since 4 > 2
( 1 2 4 5 8 ) –> ( 1 2 4 5 8 )
( 1 2 4 5 8 ) –> ( 1 2 4 5 8 )
Now, the array is already sorted, but our algorithm does not know if it is completed. The algorithm needs one whole pass without any
swap to know it is sorted.
Third Pass:
( 1 2 4 5 8 ) –> ( 1 2 4 5 8 )
( 1 2 4 5 8 ) –> ( 1 2 4 5 8 )
( 1 2 4 5 8 ) –> ( 1 2 4 5 8 )
( 1 2 4 5 8 ) –> ( 1 2 4 5 8 )
```

#### C++ Implementation

```
// Function to implement bubble sort
void bubble_sort(int array[], int n)
{
// Here n is the number of elements in array
int temp;
for(int i = 0; i < n-1; i++)
{
// Last i elements are already in place
for(int j = 0; j < n-i-1; j++)
{
if (array[j] > array[j+1])
{
// swap elements at index j and j+1
temp = array[j];
array[j] = array[j+1];
array[j+1] = temp;
}
}
}
}
```

#### Python Implementation

```
def bubble_sort(arr):
exchanges = True # A check to see if the array is already sorted so that no further steps gets executed
i = len(arr)-1
while i > 0 and exchanges:
exchanges = False
for j in range(i):
if arr[j]>arr[j+1]:
exchanges = True
arr[j], arr[j+1] = arr[j+1], arr[j]
i -= 1
arr = [5,3,23,1,43,2,54]
bubble_sort(arr)
print(arr) # Prints [1, 2, 3, 5, 23, 43, 54]
```

#### Complexity of Algorithm

**Worst and Average Case Time Complexity:** O(n*n). Worst case occurs when array is reverse sorted i.e. the elements are in decreasing order

**Best Case Time Complexity:** O(n). Best case occurs when array is already sorted.