Bubble_sort.md

Bubble Sort - O[n²] (worst case)

Bubble Sort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in wrong order.
Example:

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 )

cpp

#include <stdio.h> 
  
void swap(int *xp, int *yp) 
{ 
    int temp = *xp; 
    *xp = *yp; 
    *yp = temp; 
} 
  
// An optimized version of Bubble Sort 
void bubbleSort(int arr[], int n) 
{ 
   int i, j; 
   bool swapped; 
   for (i = 0; i < n-1; i++) 
   { 
     swapped = false; 
     for (j = 0; j < n-i-1; j++) 
     { 
        if (arr[j] > arr[j+1]) 
        { 
           swap(&arr[j], &arr[j+1]); 
           swapped = true; 
        } 
     } 
  
     // IF no two elements were swapped by inner loop, then break 
     if (swapped == false) 
        break; 
   } 
} 
  
/* Function to print an array */
void printArray(int arr[], int size) 
{ 
    int i; 
    for (i=0; i < size; i++) 
        printf("%d ", arr[i]); 
    printf("n"); 
} 
  
// Driver program to test above functions 
int main() 
{ 
    int arr[] = {64, 34, 25, 12, 22, 11, 90}; 
    int n = sizeof(arr)/sizeof(arr[0]); 
    bubbleSort(arr, n); 
    printf("Sorted array: \n"); 
    printArray(arr, n); 
    return 0; 
} 

Python

def bubbleSort(arr): 
    n = len(arr) 
   
    # Traverse through all array elements 
    for i in range(n): 
        swapped = False
  
        # Last i elements are already 
        #  in place 
        for j in range(0, n-i-1): 
   
            # traverse the array from 0 to 
            # n-i-1. Swap if the element  
            # found is greater than the 
            # next element 
            if arr[j] > arr[j+1] : 
                arr[j], arr[j+1] = arr[j+1], arr[j] 
                swapped = True
  
        # IF no two elements were swapped 
        # by inner loop, then break 
        if swapped == False: 
            break
           
# Driver code to test above 
arr = [64, 34, 25, 12, 22, 11, 90] 
   
bubbleSort(arr) 
   
print ("Sorted array :") 
for i in range(len(arr)): 
    print ("%d" %arr[i],end=" ")