148. Sort List

题目：

Sort a linked list in O(n log n) time using constant space complexity.

链接： http://leetcode.com/problems/sort-list/

题解：

Sort List，链表排序，一看到O(nlogn)就想到使用merge sort。对于merge sort，还要研究一下bottom-up和top-down的区别，优劣点，如何继续优化等等，比如n较小时使用insertion sort，了解Python的Tim-sort之类。也要研究一下链表的Quicksort，以及3-way Quicksort。当时电面Amazon的时候写排序作死选择Quicksort，还尝试写了一个3-way Quicksort，由于理解不深同时当天也头昏脑胀没解释清楚，被面试官白大姐秒拒，如此浪费一年机会，甚是可惜。对于各种排序的stalability也要好好复习。熟能生巧，多练吧。另外，external sorting，B tree，A* tree，indexing，paging之类的也要复习。聊远了...

这题使用Merge Sort的话，还是按照Divide-and-Conquer分治。两个辅助方法是findMid找中点，以及merge合并。 merge的话完全可以使用"Merge Sorted List"的代码，找中点我们也使用过，所以可以直接写。

Time Complexity - O(nlogn)， Space Complexity - O(logn)。

/*** Definition for singly-linked list.* public class ListNode {*     int val;*     ListNode next;*     ListNode(int x) { val = x; }* }*/
public class Solution {public ListNode sortList(ListNode head) {if(head == null || head.next == null)return head;ListNode mid = findMid(head);ListNode right = sortList(mid.next);mid.next = null;ListNode left = sortList(head);return merge(left, right);}private ListNode findMid(ListNode head) {　　　　　　　　if(head == null || head.next == null)return head;ListNode fast = head, slow = head;while(fast.next != null && fast.next.next != null) {fast = fast.next.next;slow = slow.next;}return slow;}private ListNode merge(ListNode left, ListNode right) {ListNode dummy = new ListNode(-1);ListNode node = dummy;while(left != null && right != null) {if(left.val < right.val) {node.next = left;left = left.next;} else {node.next = right;right = right.next;}node = node.next;}if(left != null)node.next = left;elsenode.next = right;return dummy.next;}
}

到这里其实还没结束。仔细看题目要求constant space complexity。这样的话我们就不能使用递归了。

二刷:

O(1) space并不好写，此刷没有完成，也并没有尝试quicksort，很忧伤... 最后还是使用的merge sort recrusive的方法。代码大都参考了Discuss区里zwangbo同学的。

Java:

Time Complexity - O(nlogn)， Space Complexity - O(logn)。

/*** Definition for singly-linked list.* public class ListNode {*     int val;*     ListNode next;*     ListNode(int x) { val = x; }* }*/
public class Solution {public ListNode sortList(ListNode head) {if (head == null || head.next == null) return head; ListNode fast = head, slow = head, preMid = head;while (fast != null && fast.next != null) {preMid = slow;fast = fast.next.next;slow = slow.next;}preMid.next = null;return merge(sortList(head), sortList(slow));}private ListNode merge(ListNode l1, ListNode l2) {if (l1 == null) return l2;if (l2 == null) return l1;if (l1.val < l2.val) {l1.next = merge(l1.next, l2);return l1;} else {l2.next = merge(l1, l2.next);return l2;}}
}

三刷:

依然是使用之前的方法，找中点，再递归进行mergesort。

Java:

Time Complexity - O(nlogn)， Space Complexity - O(logn)。

/*** Definition for singly-linked list.* public class ListNode {*     int val;*     ListNode next;*     ListNode(int x) { val = x; }* }*/
public class Solution {public ListNode sortList(ListNode head) {if (head == null || head.next == null) return head;ListNode fast = head, slow = head, prev = head;while (fast != null && fast.next != null) {prev = slow;fast = fast.next.next;slow = slow.next;}prev.next = null;return mergeTwoSortedList(sortList(head), sortList(slow));}private ListNode mergeTwoSortedList(ListNode l1, ListNode l2) {if (l1 == null) return l2;if (l2 == null) return l1;ListNode dummy = new ListNode(-1);ListNode curNode = dummy, p1 = l1, p2 = l2;while (p1 != null && p2 != null) {if (p1.val < p2.val) {curNode.next = p1;p1 = p1.next;} else {curNode.next = p2;p2 = p2.next;}curNode = curNode.next;}curNode.next = (p1 != null) ? p1 : p2;return dummy.next;} }

Reference：

http://www.mathcs.emory.edu/~cheung/Courses/171/Syllabus/7-Sort/merge-sort5.html

https://en.wikipedia.org/wiki/Merge_sort#Bottom-up_implementation

https://leetcode.com/discuss/10264/my-o-n-log-n-time-o-1-space-solution

https://leetcode.com/discuss/12014/my-iterative-merge-sort

https://leetcode.com/discuss/15420/java-solution-with-strict-o-1-auxiliary-space-complexity

https://leetcode.com/discuss/18210/i-think-my-java-solution-is-o-1-space

https://leetcode.com/discuss/19119/java-merge-sort-solution-with-o-1-memory

https://leetcode.com/discuss/24917/my-java-code-with-constant-space

https://leetcode.com/discuss/28594/bottom-recurring-with-space-complextity-time-complextity

https://leetcode.com/discuss/39867/java-solution-bottom-iterative-merge-with-detailed-comments

https://leetcode.com/discuss/1709/have-pretty-mergesort-method-anyone-speed-reduce-memory-usage

https://leetcode.com/discuss/92701/java-solution-using-merge-sort

https://leetcode.com/discuss/44369/java-merge-sort-solution

https://leetcode.com/discuss/29921/basically-seems-merge-sort-problem-really-easy-understand

https://leetcode.com/discuss/81455/java-quick-sort-fast-beats-98%25-also-includes-merge-sort-code

https://leetcode.com/discuss/81263/super-easy-understand-java-iterative-merge-sort-using-space

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