常用排序：快速排序 与 归并排序

快排

思路：
第一步 确定分界点 x=q[l] q[r] q[l+r >>1] 任意数都可以
第二步 左右双指针调整数组，使x 所在位置右值皆大于x 左值皆小于x
第三步 递归处理左右两段数组

快排模板

import java.util.*;
import java.lang.*;


public class Main {
    
    
    public static void main(String[] args) {
    
    
        Scanner mc = new Scanner(System.in);
        int n = mc.nextInt();
        int[] q = new int[n];
        
        for (int i = 0; i < n; i++) {
    
    
            q[i] = mc.nextInt();
        }
        
        quick_sort(q, 0, n - 1);
        
        for (int i = 0; i < n; i++) {
    
    
            System.out.print(q[i]+" ");
        }
    }

    static void quick_sort(int q[], int l, int r) {
    
    
        if (l >= r) return;

        int x = q[l + r >> 1], i = l - 1, j = r + 1;
        while (i < j) {
    
    
            do i++; while (q[i] < x);
            do j--; while (q[j] > x);
            if (i < j) {
    
     //两指针交换
                int temp = 0;
                temp = q[i];
                q[i] = q[j];
                q[j] = temp;
            }
        }
        quick_sort(q, l, j); //递归
        quick_sort(q, j + 1, r);
    }
}

归并排序——分治

思路：
第一步 确定分界点 mid = l + r >> 1
第二步 对左右进行递归排序
第三步 归并 合二为一

动态图解：

import java.util.*;
import java.lang.*;

public class Main {
    
    
    public static void main(String[] args) {
    
    
        Scanner mc = new Scanner(System.in);
        int n = mc.nextInt();

        int[] q = new int[n];

        for (int i = 0; i < n; i++) {
    
    
            q[i] = mc.nextInt();
        }

        merge_sort(q, 0, n - 1);

        for (int i = 0; i < n; i++) {
    
    
            System.out.print(q[i] + " ");
        }
    }

    static void merge_sort(int q[], int l, int r) {
    
    
        if (l >= r) return;

        int mid = l + r >> 1;
        merge_sort(q, l, mid);
        merge_sort(q, mid + 1, r);
        int[] tmp = new int[r+1];
        int k = 0, i = l, j = mid + 1;
        while (i <= mid && j <= r)
            if (q[i] <= q[j]) tmp[k++] = q[i++]; //取最小值
            else tmp[k++] = q[j++];

        while (i <= mid) tmp[k++] = q[i++]; //判界 指针后移
        while (j <= r) tmp[k++] = q[j++];

        for (i = l, j = 0; i <= r; i++, j++) q[i] = tmp[j];
    }
}

小练：逆序对的数量

import java.util.*;
import java.lang.*;

public class Main {
    
    
    public static void main(String[] args) {
    
    
        Scanner mc = new Scanner(System.in);
        int n = mc.nextInt();

        int[] q = new int[n + 1];

        for (int i = 0; i < n; i++) {
    
    
            q[i] = mc.nextInt();
        }

        System.out.print(merge_sort(q, 0, n - 1));

    }

    static long merge_sort(int[] q, int l, int r) {
    
    
        if (l >= r) return 0;

        int mid = l + r >> 1;
        long sum = merge_sort(q, l, mid) + merge_sort(q, mid + 1, r);

        int[] tmp = new int[r + 1];
        int k = 0, i = l, j = mid + 1;
        while (i <= mid && j <= r)

            if (q[i] <= q[j]) tmp[k++] = q[i++];
            else {
    
    
                sum += mid - i + 1; //
                tmp[k++] = q[j++];
            }
        while (i <= mid) tmp[k++] = q[i++];
        while (j <= r) tmp[k++] = q[j++];

        for (i = l, j = 0; i <= r; i++, j++) q[i] = tmp[j];
        return sum;
    }
}

来源：Acwing算法基础课