Merge pull request #171 from kestory/master

fix typo

C13-Red-Black-Trees/13.1.md

@@ -1,6 +1,6 @@
 ### Exercises 13.1-1
 ***
-In the style of Figure 13.1(a), draw the complete binary search tree of height 3 on the keys {1, 2, ..., 15}. Add the NIL leaves and color the nodes in three different ways such that the black- heights of the resulting red-black trees are 2, 3, and 4.
+In the style of Figure 13.1(a), draw the complete binary search tree of height 3 on the keys {1, 2, ..., 15}. Add the NIL leaves and color the nodes in three different ways such that the black-heights of the resulting red-black trees are 2, 3, and 4.
 
 ### `Answer`
 因为是一颗完全二叉树，超级平衡，所以填色很容易. 感谢[psu](http://test.scripts.psu.edu/users/d/j/djh300/cmpsc465/notes-4985903869437/solutions-to-some-homework-exercises-as-shared-with-students/3-solutions-clrs-13.pdf)提供的图片
@@ -12,10 +12,10 @@ In the style of Figure 13.1(a), draw the complete binary search tree of height 3
 Draw the red-black tree that results after TREE-INSERT is called on the tree in Figure 13.1 with key 36. If the inserted node is colored red, is the resulting tree a red-black tree? What if it is colored black?
 
 ### `Answer`
-插入后如何上红色，那么违反了红节点的儿子节点是黑色这个规则.
+插入后如果上红色，那么违反了红节点的儿子节点是黑色这个规则.
 ![image](./repo/s1/2.png)
 
-插入后如何上黑色，那么违反了路径上包含相同黑节点数这个规则.
+插入后如果上黑色，那么违反了路径上包含相同黑节点数这个规则.
 ![image](./repo/s1/3.png)
 
 
@@ -48,6 +48,7 @@ length at most twice that of the shortest simple path from node x to a descendan
 What is the largest possible number of internal nodes in a red-black tree with black-height *k*? What is the smallest possible number?
 
 ### `Answer`
+
 假如有一颗完美二叉树，如果每个节点都是黑的. 这种情况下, 节点数最小, 是 ![](http://latex.codecogs.com/gif.latex?2^k-1)
 
 The smallest possible number of internal nodes is ![](http://latex.codecogs.com/gif.latex?2^k-1). When it's a complete binary tree with k levels with all nodes black.