bubble sort algorithm java code

sure! bubble sort is a simple sorting algorithm that repeatedly steps through the list, compares adjacent elements, and swaps them if they are in the wrong order. the pass through the list is repeated until the list is sorted. the algorithm gets its name because smaller elements "bubble" to the top of the list.

characteristics of bubble sort:
- **time complexity**:
- worst-case: o(n²)
- average-case: o(n²)
- best-case: o(n) (when the array is already sorted)
- **space complexity**: o(1) (in-place sorting)
- **stable**: yes (maintains the relative order of records with equal keys)
- **adaptive**: yes (can be optimized to stop early if the array is sorted)

bubble sort algorithm:
1. start from the beginning of the array.
2. compare the current element with the next element.
3. if the current element is greater than the next element, swap them.
4. move to the next element and repeat steps 2-3 until the end of the array is reached.
5. repeat the process for the entire array until no swaps are needed (the array is sorted).

java code example:
here’s a simple implementation of the bubble sort algorithm in java:

explanation of the code:
1. **bubblesort method**:
- takes an integer array as input.
- the outer loop iterates through each element of the array.
- the inner loop compares each element to its adjacent element and swaps them if they are out of order.
- the `swapped` flag is used to optimize the algorithm; if no elements were swapped during a pass, the array is already sorted, and we can exit early.

2. **printarray method**:
- a utility method to print the elements of the array.

3. **main method**:
- initializes an unsorted array.
- calls the `bubblesort` method to sort the array.
- prints the unsorted and sorted arrays.

conclusion:
bubble sort is not the most efficient sorting algorithm for large datasets, but it is easy to understand and implement. it is mainly used for educational purposes to illustrate the concept of so ...

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