概念

归并排序是建立在归并操作上的一种有效的排序算法。该算法是采用分治法（Divide and Conquer）的一个非常典型的应用，归并排序将两个已排序的表合并成一个表。

归并排序基本原理

通过对若干个有序结点序列的归并来实现排序。
所谓归并是指将若干个已排好序的部分合并成一个有序的部分。

单链表实现归并排序

找到中间点拆分链表

//找到中间点，然后分割
    public ListNode getMiddle(ListNode head) {
        if (head == null) {
            return head;
        }
        //快慢指针
        ListNode slow, fast;
        slow = fast = head;
        while (fast.next != null && fast.next.next != null) {
            slow = slow.next;
            fast = fast.next.next;
        }
        return slow;
    }

合并排好序的链表

// 合并排好序的链表
    public ListNode merge(ListNode a, ListNode b) {
        ListNode dummyHead, curr;
        dummyHead = new ListNode(0);
        curr = dummyHead;
        while (a != null && b != null) {
            if (a.val <= b.val) {
                curr.next = a;
                a = a.next;
            } else {
                curr.next = b;
                b = b.next;
            }
            curr = curr.next;
        }
        curr.next = (a == null) ? b : a;
        return dummyHead.next;
    }

单链表的归并排序

//单链表的归并排序
    public ListNode merge_sort(ListNode head) {
        if (head == null || head.next == null) {
            return head;
        }
        //得到链表中间的数
        ListNode middle = getMiddle(head);
        ListNode sHalf = middle.next;
        //拆分链表
        middle.next = null;
        //递归调用
        return merge(merge_sort(head), merge_sort(sHalf));
    }

Application.java

public static void main(String[] args) {
        ListNode head = new ListNode(0);
        ListNode l1 = new ListNode(2);
        ListNode l2 = new ListNode(5);
        ListNode l3 = new ListNode(3);
        ListNode l4 = new ListNode(8);
        ListNode l5 = new ListNode(4);
        ListNode l6 = new ListNode(2);
        ListNode l7 = new ListNode(1);

        head.next = l1;
        l1.next = l2;
        l2.next = l3;
        l3.next = l4;
        l4.next = l5;
        l5.next = l6;
        l6.next = l7;
        l7.next = null;

        ListNode p = head;
        while (p.next != null) {
            System.out.print(p.val);
            p = p.next;
        }
        System.out.print(p.val);
        System.out.println();

        new MergeSort().merge_sort(head);

        p = head;
        while (p != null) {
            System.out.print(p.val);
            p = p.next;
        }
    }

执行效果图