Common sorting algorithm (V): insertion sort

Insertion sort ( English: Insertion the Sort) is a simple and intuitive sorting algorithm . It works by constructing an ordered sequence , for unsorted data in sorted sequence in the forward and backward scans to find the corresponding position and insert . Insertion sort in the realization, usually sorted in-place (i.e., use only O (1) ordering the extra space), thus forwardly from the scanning process, the need to repeatedly sorted elements gradually move rearward position , the latest element inserted into the space provided.

 

Generally, insertion sort are implemented using in-place on the array. The algorithm is described as follows:

1. From the first element beginning, the element can be considered has been sorted

2. Remove the next element in the sorted elements in sequence from the forward scan

3. If the element (sorted) is greater than the new element , will the element to the next position

4. Repeat step 3 until it finds the sorted elements less than or equal to the new position of the element

5. The new element is inserted into the discharge position

6. Repeat steps 2 to 5

Insertion sort code is as follows:

. 1      public  static  void insertSort ( int [] ARR) {
 2          for ( int I =. 1; I <arr.length; I ++ ) {
 . 3              int Key = ARR [I];
 . 4              int J = I -. 1 ;
 . 5              the while (J > = 0 && ARR [J]> Key) { // if the current element is greater than the new element is moved back element
 . 6                  ARR [J +. 1] = ARR [J];
 . 7                  J, ;
 . 8              }
 . 9              ARR [ . 1 + J] = Key;
 10          }
 . 11      }

The algorithm for each element a movement, from the back scan, a forward scan until the last array that the average time complexity is O (N²) , the best case is O (n) (already sorted case), the worst case is O (n²). Algorithm utilizes a temporary variable to exchange elements, the space complexity is O (. 1) . 

 

Test code:

1     public static void main(String[] args) {
2         int[] arr = {1, 1, 2, 0, 9, 3, 12, 7, 8, 3, 4, 65, 22};
3 
4         insertSort(arr);
5 
6         for (int i : arr) {
7             System.out.print(i + " ");
8         }
9     }