From b60b313305d3633391afb2d6a406006753035fcd Mon Sep 17 00:00:00 2001
From: ShusenTang <tangshusen@pku.edu.cn>
Date: Tue, 30 Jun 2020 20:29:36 +0800
Subject: [PATCH] add mergeSort

---
 algorithm/array/sort.md | 51 ++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 50 insertions(+), 1 deletion(-)

diff --git a/algorithm/array/sort.md b/algorithm/array/sort.md
index c98f08f..aae1187 100644
--- a/algorithm/array/sort.md
+++ b/algorithm/array/sort.md
@@ -48,4 +48,53 @@ void quick_sort(vector<int> &arr, int left, int right){
 ```
 
 ## 2. 归并排序
-TODO
\ No newline at end of file
+### 2.1 算法描述
+归并排序采用的是分治法（Divide and Conquer）思想。基本步骤是：
+1. 拆分：将原序列划分成子序列，然后假设子序列已经有序；
+2. 合并：将有序的子序列合并，得到完全有序的序列；
+
+归并排序具体有两种思路：一种是自上而下递归地归并，另一种是自下而上迭代地归并。
+
+时间复杂度：最坏、平均时间复杂度均为O(nlogn)。
+
+### 2.2 代码
+这里给出归并排序的典型应用：链表排序的代码，采用的是自上而下归并。
+``` C++
+ListNode* mergeSort(ListNode *head){
+    if(!head || !head -> next) return head;
+
+    ListNode *pre_slow = NULL, *slow = head, *fast = head;
+    while(fast && fast -> next){
+        pre_slow = slow;
+        slow = slow -> next;
+        fast = fast -> next -> next;
+    }
+    pre_slow -> next = NULL; // 1.1 divide into sublists
+    ListNode *l1 = mergeSort(head); 1.2 mergeSort sublists
+    ListNode *l2 = mergeSort(slow);
+
+    return merge2SortedLists(l1, l2); // 2. merge
+}
+
+ListNode* merge2SortedLists(ListNode *l1, ListNode *l2){
+    ListNode *head = new ListNode(0), *p = head;
+
+    while(l1 && l2){
+        if(l1 -> val <= l2 -> val){
+            p -> next = l1;
+            p = p -> next;
+            l1 = l1 -> next;
+        }
+        else{
+            p -> next = l2;
+            p = p -> next;
+            l2 = l2 -> next;
+        }
+    }
+
+    if(l1) p -> next = l1;
+    if(l2) p -> next = l2;
+    p = head -> next; delete head;
+    return p;
+}
+```