In-depth understanding of the insertion sort algorithm and its implementation principles in Java

In-depth understanding of the insertion sort algorithm and its implementation principle in Java

Insertion sort is a simple but commonly used sorting algorithm, and its implementation principle is relatively simple. This article will delve into the insertion sort algorithm and its implementation principles in Java, and attach specific code examples.

1. The idea of ​​insertion sort algorithm
The idea of ​​insertion sort is to insert an element to be sorted into an appropriate position in an already ordered partial sequence, thereby dividing the sequence into sorted and unsorted Two parts. During the sorting process, by constantly comparing and moving the positions of elements, a completely ordered sequence is finally obtained.

2. Specific steps of the insertion sort algorithm
The specific steps of the insertion sort algorithm can be divided into the following steps:

1. Start from the first element and treat it as Sorted sequence.
2. Take out the next element, traverse from back to front in the sorted sequence, and find the appropriate insertion position.
3. Insert the element into the appropriate position in the sorted sequence.
4. Repeat steps 2 and 3 until all elements are inserted into their appropriate positions.

3. Implementation code of insertion sort algorithm
The following is an example of implementation code of insertion sort algorithm in Java:

public class InsertionSort {
    public static void insertionSort(int[] arr) {
        int n = arr.length;
        for (int i = 1; i < n; i++) {
            int key = arr[i];
            int j = i - 1;
            while (j >= 0 && arr[j] > key) {
                arr[j + 1] = arr[j];
                j--;
            }
            arr[j + 1] = key;
        }
    }

    public static void main(String[] args) {
        int[] arr = {9, 5, 1, 3, 8, 4, 7, 2, 6};
        insertionSort(arr);
        System.out.println("排序结果：");
        for (int num : arr) {
            System.out.print(num + " ");
        }
    }
}

In the above code, insertionSort Method sorts the array using the insertion sort algorithm. In each traversal, the current element is stored as key, and then key is compared with the elements in the sorted sequence one by one and moved until a suitable insertion position is found. Finally, insert key into the correct location.

4. Time complexity and space complexity of insertion sort
The time complexity of insertion sort is O(n^2), where n is the length of the sequence to be sorted. In the worst case, where the sequence is in reverse order, n(n-1)/2 comparison and move operations are required. But under average circumstances, insertion sort performs well.

The space complexity of insertion sort is O(1) because it only requires a constant level of extra space to store temporary variables.

5. Summary
Insertion sort is a simple but commonly used sorting algorithm. Sorting is achieved by inserting an element to be sorted into an appropriate position in the sorted sequence. Its implementation principle is relatively simple and suitable for small-scale data sorting. An in-depth understanding and practice of insertion sort can help us better grasp the core concepts of algorithms and data structures.

The above is an in-depth understanding of the insertion sort algorithm and its implementation principles in Java and an introduction to specific code examples. Hope this helps!

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