问题 c: 插入排序

Insertion sort is a simple sorting algorithm for a small number of elements.

插入排序是一种针对少量元素的简单排序算法。

例： (Example:)

In Insertion sort, you compare the key element with the previous elements. If the previous elements are greater than the key element, then you move the previous element to the next position.

在插入排序中，您将key元素与之前的元素进行比较。 如果先前的元素大于key元素，则将先前的元素移动到下一个位置。

Start from index 1 to size of the input array.

从索引1开始到输入数组的大小。

[ 8 3 5 1 4 2 ]

[8 3 5 1 4 2]

Step 1 :

第1步 ：

key = 3 //starting from 1st index.Here `key` will be compared with the previous elements.In this case, `key` is compared with 8. since 8 > 3, move the element 8to the next position and insert `key` to the previous position.Result: [ 3 8 5 1 4 2 ]

Step 2 :

第2步 ：

key = 5 //2nd index8 > 5 //move 8 to 2nd index and insert 5 to the 1st index.Result: [ 3 5 8 1 4 2 ]

Step 3 :

第三步：

key = 1 //3rd index8 > 1     => [ 3 5 1 8 4 2 ]  5 > 1     => [ 3 1 5 8 4 2 ]3 > 1     => [ 1 3 5 8 4 2 ]Result: [ 1 3 5 8 4 2 ]

Step 4 :

第4步 ：

key = 4 //4th index8 > 4   => [ 1 3 5 4 8 2 ]5 > 4   => [ 1 3 4 5 8 2 ]3 > 4   ≠>  stopResult: [ 1 3 4 5 8 2 ]

Step 5 :

步骤5：

key = 2 //5th index8 > 2   => [ 1 3 4 5 2 8 ]5 > 2   => [ 1 3 4 2 5 8 ]4 > 2   => [ 1 3 2 4 5 8 ]3 > 2   => [ 1 2 3 4 5 8 ]1 > 2   ≠> stopResult: [1 2 3 4 5 8]

The algorithm shown below is a slightly optimized version to avoid swapping the key element in every iteration. Here, the key element will be swapped at the end of the iteration (step).

下面显示的算法是经过稍微优化的版本，可避免在每次迭代中交换key元素。 此处， key元素将在迭代(步骤)结束时交换。

InsertionSort(arr[])for j = 1 to arr.lengthkey = arr[j]i = j - 1while i > 0 and arr[i] > keyarr[i+1] = arr[i]i = i - 1arr[i+1] = key

Here is a detailed implementation in JavaScript:

这是JavaScript的详细实现：

function insertion_sort(A) {var len = array_length(A);var i = 1;while (i < len) {var x = A[i];var j = i - 1;while (j >= 0 && A[j] > x) {A[j + 1] = A[j];j = j - 1;}A[j+1] = x;i = i + 1;}
}

A quick implementation in Swift is shown below :

Swift中的快速实现如下所示：

var array = [8, 3, 5, 1, 4, 2]func insertionSort(array:inout Array<Int>) -> Array<Int>{for j in 0..<array.count {let key = array[j]var i = j-1while (i > 0 && array[i] > key){array[i+1] = array[i]i = i-1}array[i+1] = key}return array}

The Java example is shown below:

Java示例如下所示：

public int[] insertionSort(int[] arr)for (j = 1; j < arr.length; j++) {int key = arr[j]int i = j - 1while (i > 0 and arr[i] > key) {arr[i+1] = arr[i]i -= 1}arr[i+1] = key}return arr;

插入排序在... (insertion sort in c....)

void insertionSort(int arr[], int n)
{ int i, key, j; for (i = 1; i < n; i++) { key = arr[i]; j = i-1;while (j >= 0 && arr[j] > key) { arr[j+1] = arr[j]; j = j-1; } arr[j+1] = key; }
}

特性： (Properties:)

• Space Complexity: O(1)空间复杂度：O(1)

Time Complexity: O(n), O(n* n), O(n* n) for Best, Average, Worst cases respectively.

时间复杂度：分别为最佳，平均和最差情况下的O(n)，O(n * n)，O(n * n)。

• Best Case: array is already sorted最佳情况：数组已排序
• Average Case: array is randomly sorted平均情况：数组随机排序
• Worst Case: array is reversely sorted.最坏的情况：数组被反向排序。
• Sorting In Place: Yes就地排序：是
• Stable: Yes稳定：是的

其他资源： (Other Resources:)

• Wikipedia

  维基百科

• CS50 - YouTube

  CS50-YouTube

• SortInsertion - GeeksforGeeks, YouTube

  SortInsertion-GeeksforGeeks，YouTube

• Insertion Sort Visualization

  插入排序可视化

• Insertion Sort - MyCodeSchool

  插入排序-MyCodeSchool

• Insertion Sort - VisuAlgo

  插入排序-VisuAlgo

翻译自: https://www.freecodecamp.org/news/insertion-sort-what-it-is-and-how-it-works/

问题 c: 插入排序