Algorithm backup ---- Insertion Sort(插入排序算法)

　　Insertion sort is a simple sorting algorithm, a comparison sort in which the sorted array (or list) is built one entry at a time. 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:

  1. simple implementation

  2. efficient for (quite) small data sets

  3. adaptive, i.e. efficient for data sets that are already substantially sorted: the time compexity is O(n + d), where d is the number of inversions

  4. more efficient in practice than most other simple quadratic (i.e. O(n²)) algorithms such as selection sort or  bubble sort: the average running time is n²/4, and the running time is linear in the best case

  5. stable, i.e. does not change the relative order of elements with equal keys

  6. in-place, i.e. only requires a constant amount O(1) of additional memory space

  7. online, i.e. can sort a list as it receives it.

　　Below is the implementation using C#:

/// <summary>
/// Insertion sort algorithm
/// </summary>
/// <param name="numbers">numbers array to be sorted</param>
public static void InsertionSort(int[] numbers)
{
    for (int i = 1; i < numbers.Length; ++i)
    {
        int temp = numbers[i];
        int j = i;
        //Find its place and insert.
        while (j > 0 && numbers[j - 1] >= temp)
        {
            numbers[j] = numbers[j - 1];
            j--;
        }
        numbers[j] = temp;
    }
}

 

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