diff --git a/problems/0015.三数之和.md b/problems/0015.三数之和.md
index da319866..a4b6b84d 100644
--- a/problems/0015.三数之和.md
+++ b/problems/0015.三数之和.md
@@ -493,6 +493,9 @@ function threeSum(nums: number[]): number[][] {
         right: number = length - 1;
     let resArr: number[][] = [];
     for (let i = 0; i < length; i++) {
+    	if (nums[i]>0) {
+            return resArr; //nums经过排序后，只要nums[i]>0, 此后的nums[i] + nums[left] + nums[right]均大于0,可以提前终止循环。	
+	}
         if (i > 0 && nums[i] === nums[i - 1]) {
             continue;
         }
diff --git a/problems/0019.删除链表的倒数第N个节点.md b/problems/0019.删除链表的倒数第N个节点.md
index 65a4e383..00caeea0 100644
--- a/problems/0019.删除链表的倒数第N个节点.md
+++ b/problems/0019.删除链表的倒数第N个节点.md
@@ -191,18 +191,20 @@ TypeScript:
 ```typescript
 function removeNthFromEnd(head: ListNode | null, n: number): ListNode | null {
     let newHead: ListNode | null = new ListNode(0, head);
-    let slowNode: ListNode | null = newHead,
-        fastNode: ListNode | null = newHead;
-    for (let i = 0; i < n; i++) {
-        fastNode = fastNode.next;
+    //根据leetcode题目的定义可推断这里快慢指针均不需要定义为ListNode | null。
+    let slowNode: ListNode = newHead;
+    let fastNode: ListNode = newHead;
+
+    while(n--) {
+        fastNode = fastNode.next!; //由虚拟头节点前进n个节点时,fastNode.next可推断不为null。
     }
-    while (fastNode.next) {
+    while(fastNode.next) {  //遍历直至fastNode.next = null， 即尾部节点。 此时slowNode指向倒数第n个节点。
         fastNode = fastNode.next;
-        slowNode = slowNode.next;
+        slowNode = slowNode.next!;
     }
-    slowNode.next = slowNode.next.next;
-    return newHead.next;
-};
+    slowNode.next = slowNode.next!.next; //倒数第n个节点可推断其next节点不为空。 
+    return newHead.next; 
+}
 ```
 
 版本二（计算节点总数法）：
diff --git a/problems/0203.移除链表元素.md b/problems/0203.移除链表元素.md
index 6fd9b66f..5622fd1c 100644
--- a/problems/0203.移除链表元素.md
+++ b/problems/0203.移除链表元素.md
@@ -385,7 +385,8 @@ function removeElements(head: ListNode | null, val: number): ListNode | null {
         if (cur.val === val) {
             pre.next = cur.next;
         } else {
-            pre = pre.next;
+            //此处不加类型断言时：编译器会认为pre类型为ListNode, pre.next类型为ListNode | null
+            pre = pre.next as ListNode;
         }
         cur = cur.next;
     }
diff --git a/problems/链表理论基础.md b/problems/链表理论基础.md
index 1a29c32a..8378f7f2 100644
--- a/problems/链表理论基础.md
+++ b/problems/链表理论基础.md
@@ -186,7 +186,7 @@ TypeScript:
 ```typescript
 class ListNode {
   public val: number;
-  public next: ListNode = null;
+  public next: ListNode|null = null;
   constructor(value: number) {
     this.val = value;
     this.next = null;