Background: Bubble Sort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in the wrong order. Following is the iterative Bubble sort algorithm :
// Iterative Bubble Sort bubbleSort(arr[], n) { for (i = 0; i n-1; i++) // Last i elements are already in place for (j = 0; j < n-i-1; j++) swap(arr[j], arr[j+1]); }
Recursion Idea
- Base Case: If array size is 1, return.
- Do One Pass of normal Bubble Sort? This pass fixes the last element of the current subarray.
- Recur for all elements except the last of the current subarray.
Recursive Bubble Sort Implementation in C++
C++
// C/C++ program for recursive implementation // of Bubble sort #include <bits/stdc++.h> using namespace std;
// A function to implement bubble sort void bubbleSort( int arr[], int n)
{ // Base case
if (n == 1)
return ;
// One pass of bubble sort. After
// this pass, the largest element
// is moved (or bubbled) to end.
for ( int i = 0; i < n - 1; i++)
if (arr[i] > arr[i + 1])
swap(arr[i], arr[i + 1]);
// Largest element is fixed,
// recur for remaining array
bubbleSort(arr, n - 1);
} /* Function to print an array */ void printArray( int arr[], int n)
{ for ( int i = 0; i < n; 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;
} |
Output
Sorted array : 11 12 22 25 34 64 90
Time Complexity: O(n*n)
Auxiliary Space: O(1)
Please refer complete article on Recursive Bubble Sort for more details!