排序链表

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快慢指针拆半,递归归并排序,O(n log n) 时间 O(log n) 递归空间。

OJ: leetcodecn

题目 ID: sort-list

难度:普及+/提高

标签:链表排序归并排序cpppython

日期: 2026-07-28 22:05

题意

对链表排序,要求 O(n log n) 时间、O(1) 额外空间。

思路

数组排序 O(n) 辅助空间。归并排序满足要求:快慢指针找中点分割,递归排序两半,合并两个有序链表。递归深度 O(log n)。

代码

cpp
/**
 * Author by Rainboy
 */
// main.cpp:快慢指针拆半,递归归并 O(n log n) O(log n)。
#include <bits/stdc++.h>
using namespace std;

struct ListNode {
    int val;
    ListNode *next;

    ListNode(int x) : val(x), next(nullptr) {}
};

class Solution {
public:
    ListNode *sortList(ListNode *head) {
        if (!head || !head->next)
            return head;
        auto slow = head, fast = head->next;
        while (fast && fast->next) {
            slow = slow->next;
            fast = fast->next->next;
        }
        auto mid = slow->next;
        slow->next = nullptr;
        auto l = sortList(head), r = sortList(mid);
        ListNode dummy(0), *cur = &dummy;
        while (l && r) {
            if (l->val < r->val) {
                cur->next = l;
                l = l->next;
            } else {
                cur->next = r;
                r = r->next;
            }
            cur = cur->next;
        }
        cur->next = l ? l : r;
        return dummy.next;
    }
};

ListNode *build(istream &in, int n) {
    if (!n)
        return nullptr;
    auto head = new ListNode(0), cur = head;
    for (int i = 0, v; i < n; i++) {
        in >> v;
        cur->next = new ListNode(v);
        cur = cur->next;
    }
    return head->next;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int n;
    cin >> n;
    auto head = build(cin, n);
    head = Solution().sortList(head);
    for (auto p = head; p; p = p->next)
        cout << p->val << ' ';
    return 0;
}
python
#!/usr/bin/env python3
class ListNode:
    def __init__(self, x):
        self.val = x
        self.next = None


class Solution:
    def sortList(self, head: ListNode) -> ListNode:
        if not head or not head.next:
            return head
        slow, fast = head, head.next
        while fast and fast.next:
            slow = slow.next
            fast = fast.next.next
        mid = slow.next
        slow.next = None
        l = self.sortList(head)
        r = self.sortList(mid)
        dummy = cur = ListNode(0)
        while l and r:
            if l.val < r.val:
                cur.next = l
                l = l.next
            else:
                cur.next = r
                r = r.next
            cur = cur.next
        cur.next = l or r
        return dummy.next


def build(arr):
    dummy = cur = ListNode(0)
    for v in arr:
        cur.next = ListNode(v)
        cur = cur.next
    return dummy.next


def main() -> None:
    n = int(input())
    a = list(map(int, input().split()))
    head = build(a)
    head = Solution().sortList(head)
    while head:
        print(head.val, end=" ")
        head = head.next


if __name__ == "__main__":
    main()

复杂度

  • 时间复杂度:O(n log n)。
  • 空间复杂度:O(log n) 递归栈。

总结

链表归并排序是"寻中-递归-合并"三步曲,核心是利用链表 O(1) 拆分和 O(n) 合并的特性。