Merge sort

归并排序适合处理大规模数据排序，尤其是当需要稳定排序时非常有用

归并排序原理

1. 分治Divide，将数组从中间分成两半
2. 解决conquer，递归地对左右两半分别进行归并排序
3. 合并combine，将两个已排序的子数组合并成一个有序数组

• 时间复杂度：O(n logn)
• 空间复杂度：O(n)，需要额外数组用于合并
• 稳定排序，相同元素的相对顺序保持不变

代码实现

package main

import "fmt"

func mergeSort(arr []int) []int {
    if len(arr) <= 1 {
        return arr
    }

    mid := len(arr) / 2
    left := mergeSort(arr[:mid])
    right := mergeSort(arr[mid:])

    return merge(left, right)
}

func merge(left, right []int) []int {
    result := []int{}
    i, j := 0, 0
    for i < len(left) && j < len(right) {
        if left[i] <= right[j] {
            result = append(result, left[i])
            i++
        } else {
            result = append(result, right[j])
            j++
        }
    }
    result = append(result, left[i:]...)
    result = append(result, right[j:]...)
    return result
}

func main() {
    arr := []int{5, 2, 4, 6, 1, 3}
    sorted := mergeSort(arr)
    fmt.Println(sorted) // [1 2 3 4 5 6]
}

import java.util.Arrays;

public class MergeSort {
    public static void mergeSort(int[] arr) {
        if (arr.length <= 1) return;
        mergeSortHelper(arr, 0, arr.length - 1);
    }

    private static void mergeSortHelper(int[] arr, int left, int right) {
        if (left >= right) return;
        int mid = left + (right - left) / 2;
        mergeSortHelper(arr, left, mid);
        mergeSortHelper(arr, mid + 1, right);
        merge(arr, left, mid, right);
    }

    private static void merge(int[] arr, int left, int mid, int right) {
        int[] temp = new int[right - left + 1];
        int i = left, j = mid + 1, k = 0;

        while (i <= mid && j <= right) {
            if (arr[i] <= arr[j]) temp[k++] = arr[i++];
            else temp[k++] = arr[j++];
        }

        while (i <= mid) temp[k++] = arr[i++];
        while (j <= right) temp[k++] = arr[j++];

        for (int p = 0; p < temp.length; p++) arr[left + p] = temp[p];
    }

    public static void main(String[] args) {
        int[] arr = {5, 2, 4, 6, 1, 3};
        mergeSort(arr);
        System.out.println(Arrays.toString(arr)); // [1, 2, 3, 4, 5, 6]
    }
}