diff --git a/.gitignore b/.gitignore
index 259148f..5adf70a 100644
--- a/.gitignore
+++ b/.gitignore
@@ -30,3 +30,6 @@
 *.exe
 *.out
 *.app
+
+# vscode
+.vscode/
diff --git a/README.md b/README.md
index 8fe8653..ad31902 100644
--- a/README.md
+++ b/README.md
@@ -282,10 +282,10 @@ $$
     - [二叉树的存储结构](ch5/binary-tree-storage/README.md#二叉树的存储结构)
   - [二叉树的遍历](ch5/binary-tree-traversal/README.md#二叉树的遍历)
   - [线索二叉树](ch5/binary-tree-traversal/README.md#7-线索二叉树)
-  - [二叉树的应用]()
-    - [二叉排序树]()
-    - [平衡二叉树]()
-    - [哈夫曼树和哈夫曼编码]()
+  - [二叉树的应用](ch5/binary-tree-applications/README.md#二叉树的应用)
+    - [二叉排序树](ch5/binary-tree-applications/README.md#1-二叉排序树)
+    - [平衡二叉树](ch5/binary-tree-applications/README.md#2-平衡二叉树)
+    - [哈夫曼树和哈夫曼编码](ch5/binary-tree-applications/README.md#3-哈夫曼树)
 - [树和森林](ch5/README.md#树与二叉树)
   - [树的基本概念](ch5/README.md#1-树的基本概念)
   - [树的存储结构](ch5/tree-storage/README.md#树的存储结构)
diff --git a/ch5/README.md b/ch5/README.md
index dff0f4c..0e5c717 100644
--- a/ch5/README.md
+++ b/ch5/README.md
@@ -120,3 +120,6 @@ $n$ 个结点的树中只有 $n-1$ 条边。
 ## 7. [树的应用](tree-applications/README.md)
 
 - [并查集](tree-applications/README.md#1-并查集)
+- [二叉排序树](binary-tree-applications/README.md#1-二叉排序树)
+- [平衡二叉树](binary-tree-applications/README.md#2-平衡二叉树)
+- [哈夫曼树和哈夫曼编码](binary-tree-applications/README.md#3-哈夫曼树)
diff --git a/ch5/binary-tree-applications/README.md b/ch5/binary-tree-applications/README.md
new file mode 100644
index 0000000..40acdf4
--- /dev/null
+++ b/ch5/binary-tree-applications/README.md
@@ -0,0 +1,271 @@
+# 二叉树的应用
+
+## 1. 二叉排序树
+
+BST，也称二叉查找树。
+
+二叉排序树或者为空树，或者为非空树，当为非空树时有如下特点：
+
+- 若左子树非空，则左子树上所有结点关键字值均**小于**根结点的关键字。
+- 若右子树非空，则右子树上所有结点关键字值均**大于**根结点的关键字。
+- 左、右子树本身也分别是一棵二叉排序树。
+
+$$
+左子树结点值 < 根结点值 < 右子树结点值
+$$
+
+二叉排序树的**中序遍历序列**是一个递增有序序列。
+
+### 1.1. 查找
+
+1. 二叉树非空时，查找根结点，若相等则查找成功；
+2. 若不等，则当小于根结点值时，查找左子树；当大于根结点的值时，查找右子树。
+3. 当查找到叶结点仍没查找到相应的值，则查找失败。
+
+```cpp
+// T 为二叉排序树
+// key 为查找的值
+BSTNode *BST_Search(BiTree T, ElemType key, BSTNode *&p)
+{
+    p = NULL;
+    while (T != NULL && key != T->data)
+    {
+        p = T;
+        if (key < T->data)
+        {
+            T = T->lchild;
+        }
+        else
+        {
+            T = T->rchild;
+        }
+    }
+    return T;
+}
+```
+
+时间复杂度：$O(h)$。（$h$ 为二叉排序树的高度）
+
+### 1.2. 插入
+
+1. 若二叉排序树为空，则直接插入结点；
+2. 若二叉排序树非空，
+   1. 当值小于根结点时，插入左子树；
+   2. 当值大于根结点时，插入右子树；
+   3. 当值等于根结点时，不进行插入。
+
+```cpp
+int BST_Insert(BiTree &T, keyType k)
+{
+    if (T == NULL)
+    {
+        T = (BiTree)malloc(sizeof(BSTNode));
+        T->key = k;
+        T.lchild = T.rchild = NULL;
+        return 1;
+    }
+    else if (k == T->key)
+    {
+        return 0;
+    }
+    else if (k < T->key)
+    {
+        BST_Insert(T.lchild, k);
+    }
+    else
+    {
+        BST_Insert(T.rchild, k);
+    }
+}
+```
+
+### 1.3. 构造二叉排序树
+
+1. 读入一个元素并建立结点，若二叉树为空将其作为根结点；
+2. 若二叉排序树非空，
+   1. 当值小于根结点时，插入左子树；
+   2. 当值大于根结点时，插入右子树；
+   3. 当值等于根结点时，不进行插入。
+
+```cpp
+void Create_BST(BiTree &T, KetType str[], int n)
+{
+    T = NULL;
+    int i = 0;
+    while (i < n)
+    {
+        BST_Insert(T, str[i]);
+        i++;
+    }
+}
+```
+
+### 1.4. 删除
+
+- 若被删除结点 $z$ 是叶子结点，则直接删除；
+- 若被删除结点 $z$ 只有一棵子树，则让 $z$ 的子树成为 $z$ 父结点的子树，代替 $z$ 结点。
+- 若被删除结点 $z$ 有两棵子树，则让 $z$ 的中序序列直接后继代替 $z$，并删去直接后继结点。
+
+![删除二叉排序树上的结点](delete-node-from-binary-sort-tree.png)
+
+在二叉排序树中删除并插入某结点，得到的二叉排序树是否与原来相同？（可能相同，也可能不同）
+
+### 1.5. 查找效率
+
+平均查找长度（ASL）取决于树的高度。
+
+![二叉排序树的查找效率](search-efficiency-of-binary-sort-tree.png)
+
+## 2. 平衡二叉树
+
+AVL，任意结点的**平衡因子**的绝对值不超过 $1$。
+
+$$
+平衡因子=左子树高度-右子树高度
+$$
+
+![平衡二叉树1](balanced-binary-tree1.png)
+
+![平衡二叉树2](balanced-binary-tree2.png)
+
+高度为 $h$ 的最小平衡二叉树的结点数 $N_h$。
+
+$$
+N_h=N_{h-1}+N_{h-2}+1
+$$
+
+$$
+N_0=0
+$$
+
+$$
+N_1=1
+$$
+
+### 2.1. 平衡二叉树的判断
+
+利用递归的后序遍历过程：
+
+1. 判断左子树是一棵平衡二叉树；
+2. 判断右子树是一棵平衡二叉树；
+3. 判断以该结点为根的二叉树为平衡二叉树。
+
+判断条件：
+
+- 若左子树和右子树均为平衡二叉树；
+- 且左子树与右子树高度差的绝对值小于等于 $1$；
+- 则平衡。
+
+![平衡二叉树3](balanced-binary-tree3.png)
+
+- $b$ 表示该结点的平衡性。
+- $h$ 表示该结点的高度。
+
+```cpp
+void Judge_AVL(BiTree bt, int &balance, int &h)
+{
+    int bl = 0, br = 0, hl = 0, hr = 0;
+    if (bt == NULL)
+    {
+        h = 0;
+        balance = 1;
+    }
+    else if (bt->lchild == NULL && bt->rchild == NULL)
+    {
+        h = 1;
+        balance = 1;
+    }
+    else
+    {
+        Judge_AVL(bt->lchild, bl, hl);
+        Judge_AVL(bt->rchild, br, hr);
+        if (hl > hr)
+        {
+            h = hl + 1;
+        }
+        else
+        {
+            h = hr + 1;
+        }
+        if (abs(hl - hr) < 2 && bl == 1 && br == 1)
+        {
+            balance = 1;
+        }
+        else
+        {
+            balance = 0;
+        }
+    }
+}
+```
+
+### 2.2. 平衡二叉树的插入
+
+先插入，后调整。**每次调整最小不平衡子树。**
+
+![平衡二叉树4](balanced-binary-tree4.png)
+
+#### 2.2.1. LL 平衡旋转
+
+![平衡二叉树5](balanced-binary-tree5.png)
+
+![平衡二叉树6](balanced-binary-tree6.png)
+
+#### 2.2.2. RR 平衡旋转
+
+![平衡二叉树7](balanced-binary-tree7.png)
+
+![平衡二叉树8](balanced-binary-tree8.png)
+
+#### 2.2.3. LR 平衡旋转
+
+![平衡二叉树9](balanced-binary-tree9.png)
+
+![平衡二叉树10](balanced-binary-tree10.png)
+
+#### 2.2.4. RL 平衡旋转
+
+![平衡二叉树11](balanced-binary-tree11.png)
+
+![平衡二叉树12](balanced-binary-tree12.png)
+
+## 3. 哈夫曼树
+
+带权路径长度。
+
+- 路径长度：路径上所经理**边**的个数。
+- 结点的权：结点被赋予的数值。
+
+树的带权路径长度，WPL，树中所有**叶结点**的带权路径长度之和，记为：
+
+$$
+WPL=\sum_{i=0}^nw_il_i
+$$
+
+![哈夫曼树1](huffman-tree1.png)
+
+哈夫曼树，也称最优二叉树，含有 $n$ 个带权叶子结点带权路径长度最小的二叉树。
+
+### 3.1. 构造算法
+
+1. 将 $n$ 个结点作为 $n$ 棵仅含有一个根结点的二叉树，构成森林 $F$；
+2. 生成一个新结点，并从 $F$ 中找出根结点权值最小的两棵树作为它的左右子树，且新结点的权值为两棵子树根结点的权值之和；
+3. 从 $F$ 中删除这两个树，并将新生成的树加入到 $F$ 中；
+4. 重复 2、3 步骤，直到 $F$ 中只有一棵树为止。
+
+![哈夫曼树2](huffman-tree2.png)
+
+### 3.2. 性质
+
+- 每个初始结点都会成为叶结点，双支结点都为新生成的结点。
+- 权值越大离根结点越近，反之权值越小离根结点越远。
+- 哈夫曼树中没有结点的度为 $1$。
+- $n$ 个叶子结点的哈夫曼树的结点总数为 $2n-1$，其中度为 $2$ 的结点数为 $n-1$。
+
+### 3.3. 编码问题
+
+![哈夫曼树3](huffman-tree3.png)
+
+![哈夫曼树4](huffman-tree4.png)
+
+![哈夫曼树5](huffman-tree5.png)
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