Problem 876 (#20)

* add solution and resources

* update readme

Author: curtisbarnard

README.md

@@ -27,7 +27,7 @@ As I work through this list I figure I would make a GitHub repo with my solution
 19. [Majority Element #169](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/easy/majority-element-169.md)
 20. [Add Binary #67](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/easy/add-binary-67.md)
 21. [Diameter of Binary Tree #543](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/easy/diameter-binary-tree-543.md)
-22. Middle of the Linked List #876
+22. [Middle of the Linked List #876](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/easy/middle-linked-list-876.md)
 23. Maximum Depth of Binary Tree #104
 24. Contains Duplicate #217
 
@@ -120,6 +120,7 @@ In order to practice with similar data structures I'll be placing each problem i
 - [Convert Binary Number in a Linked List to Integer #1290](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/easy/binary-linked-list-1290.md)
 - [Linked List Cycle #141](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/easy/linked-list-cycle-141.md)
 - [Reverse Linked List #206](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/easy/reverse-linked-list-206.md)
+- [Middle of the Linked List #876](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/easy/middle-linked-list-876.md)
 
 ### Hash Table
 
@@ -149,6 +150,7 @@ Within the problems above there are several patterns that often occur. I plan to
 - [Valid Palindrome #125](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/easy/valid-palindrome-125.md)
 - [Linked List Cycle #141](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/easy/linked-list-cycle-141.md)
 - [Reverse Linked List #206](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/easy/reverse-linked-list-206.md)
+- [Middle of the Linked List #876](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/easy/middle-linked-list-876.md)
 
 ### Binary Search
 

easy/middle-linked-list-876.md

@@ -0,0 +1,71 @@
+# Middle of the Linked List
+
+Page on leetcode:https://leetcode.com/problems/middle-of-the-linked-list/
+
+## Problem Statement
+
+Given the head of a singly linked list, return the middle node of the linked list. If there are two middle nodes, return the second middle node.
+
+### Constraints
+
+- The number of nodes in the list is in the range [1, 100].
+- 1 <= Node.val <= 100
+
+### Example
+
+```
+Input: head = [1,2,3,4,5]
+Output: [3,4,5]
+Explanation: The middle node of the list is node 3.
+```
+
+## Solution
+
+### Pseudocode
+
+1. Find the length of the linked list.
+2. Find the middle floor(length/2) + 1
+3. Run a second loop and update head to middle
+4. Return head
+
+### Initial Solution
+
+This solution has a time complexity of O(n) as we have to touch every node and a space complexity of O(1) as we only stored the mid point.
+
+```javascript
+const middleNode = function (head) {
+  let newHead = head;
+  let length = 0;
+  while (newHead) {
+    length++;
+    newHead = newHead.next;
+  }
+
+  let midpoint = Math.floor(length / 2) + 1;
+
+  while (midpoint > 1) {
+    head = head.next;
+    midpoint--;
+  }
+
+  return head;
+};
+```
+
+### Optimized Solution
+
+While the below solution has the same time and space complexity of above it is more efficient. You can see and explanation here: https://www.youtube.com/watch?v=wmpivqMlClI
+
+```javascript
+const middleNode = function (head) {
+  let slow = head;
+  let fast = head;
+
+  while (fast && fast.next) {
+    slow = slow.next;
+    fast = fast.next.next;
+  }
+
+  return slow;
+};
+```