1. Bubble Sort

public void bubbleSort(int[] arr) {
  boolean swapped = true;
  int j = 0;
  int tmp;
  while (swapped) {
    swapped = false;
    j++;
    for (int i = 0; i < arr.length - j; i++) {
      if (arr[i] > arr[i + 1]) {
      tmp = arr[i];
      arr[i] = arr[i + 1];
      arr[i + 1] = tmp;
      swapped = true;
      }
    }
 }
}

Performance

Worst case performance O(n^2)
Best case performance O(n)
Average case performance O(n^2)
Worst case space complexity O(1) auxiliary

2. Selection Sort

  public void doSelectionSort(int[] arr){ 
    for (int i = 0; i < arr.length - 1; i++){
      int index = i;
      for (int j = i + 1; j < arr.length; j++){
         if (arr[j] < arr[index]){
            index = j;
         }
      }
      int smallerNumber = arr[index]; 
      arr[index] = arr[i];
      arr[i] = smallerNumber;
   }
  }

Performance

Worst case performance О(n2)
Best case performance О(n2)
Average case performance О(n2)
Worst case space complexity О(n) total, O(1) auxiliary

3. Insertion Sort

public static void insertionSort(int array[]) {
  int n = array.length;
  for (int j = 1; j < n; j++) {
    int key = array[j];
    int i = j-1;
    while ( (i > -1) && ( array [i] > key ) ) {
      array [i+1] = array [i];
      i--;
    }
    array[i+1] = key;
  }
}

Performance

Worst case performance О(n2) comparisons, swaps
Best case performance O(n) comparisons, O(1) swaps
Average case performance О(n2) comparisons, swaps
Worst case space complexity О(n) total, O(1) auxiliary

Comparison:

There’s probably no point in using the bubble sort, unless you don’t have your algorithm book handy. The bubble sort is so simple that you can write it from memory. Even so, it’s practical only if the amount of data is small.

The selection sort minimizes the number of swaps, but the number of comparisons is still high. This sort might be useful when the amount of data is small and swapping data items is very time-consuming compared with comparing them. The insertion sort is the most versatile of the three and is the best bet in most situa- tions, assuming the amount of data is small or the data is almost sorted. For larger amounts of data, quicksort is generally considered the fastest approach.

It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort. However, insertion sort provides several advantages:

We’ve compared the sorting algorithms in terms of speed. Another consideration for any algorithm is how much memory space it needs. All three of the algorithms in this chapter carry out their sort in place, meaning that, besides the initial array, very little extra memory is required. All the sorts require an extra variable to store an item temporarily while it’s being swapped.

Basic Sort Algorithms