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en/docs/chapter_tree/exercises.md

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+<!-- Generated by utils/exercises/publish_exercises.py; do not edit directly. -->
+
+# 7.7 &nbsp; Exercises
+
+## 7.7.1 &nbsp; Concept Review
+
+### 1. &nbsp; Complete, Full, and Perfect Binary Trees
+
+The following two arrays represent binary trees in level order, where `None` marks an empty position:
+
+- Tree A: `[1, 2, 3, 4, 5, 6]`
+- Tree B: `[1, 2, 3, None, None, 6, 7]`
+
+<!-- numbered-subquestions -->
+
+1. Which tree is a complete binary tree?
+2. Which tree is a full binary tree, meaning every non-leaf node has two children?
+3. Is either tree a perfect binary tree? Explain the reason for each tree.
+
+??? success "Answer"
+
+    1. Tree A is a complete binary tree. Only its lowest level is not full, and the nodes on that level occupy consecutive positions from left to right.
+        Tree B is not complete because there are empty positions on the left of the lowest level while nodes still appear on the right.
+
+    2. Tree B is a full binary tree: nodes 1 and 3 each have two children, and all other nodes are leaves.
+        Tree A is not full because node 3 has only one child, its left child 6.
+
+    3. Neither tree is perfect because the lowest level of each tree is not completely filled.
+
+### 2. &nbsp; Three Traversal Orders for the Same Tree
+
+Store the array `[1, 2, 3, 4, 5, 6, 7]` in level order in a complete binary tree.
+
+<!-- numbered-subquestions -->
+
+1. Draw the tree.
+2. Write its preorder, inorder, and postorder traversal sequences.
+3. In the inorder sequence, which parts of the tree correspond to the subsequences to the left and right of root node 1?
+
+??? success "Answer"
+
+    1. The tree is:
+
+        ```text
+              1
+            /   \
+           2     3
+          / \   / \
+         4   5 6   7
+        ```
+
+    2. The preorder traversal is `1, 2, 4, 5, 3, 6, 7`;
+        the inorder traversal is `4, 2, 5, 1, 6, 3, 7`;
+        the postorder traversal is `4, 5, 2, 6, 7, 3, 1`.
+
+    3. The sequence `4, 2, 5` to the left of root node 1 is the inorder traversal of the left subtree;
+        the sequence `6, 3, 7` to its right is the inorder traversal of the right subtree.
+
+### 3. &nbsp; Compare Two Binary Search Trees
+
+Insert each of the following sequences from left to right into an empty binary search tree:
+
+- Sequence A: `[4, 2, 6, 1, 3, 5, 7]`
+- Sequence B: `[1, 2, 3, 4, 5, 6, 7]`
+
+<!-- numbered-subquestions -->
+
+1. For each tree, write the nodes visited when searching for 7.
+2. If height is measured by the number of edges from the root node to the farthest leaf node, what is the height of each tree?
+3. Based on the first two questions, is searching for 7 equally efficient in the two trees? Explain using the trees' shapes and search paths.
+
+??? success "Answer"
+
+    1. In the tree built from Sequence A, the search path is `4 → 6 → 7`.
+        In the tree built from Sequence B, the search path is `1 → 2 → 3 → 4 → 5 → 6 → 7`.
+
+    2. Every level of the first tree is full, and its height is 2. The second tree has only right children, and its height is 6.
+
+    3. Searching for 7 is not equally efficient in the two trees. The insertion order changes the shape and height of a binary search tree. The search visits only 3 nodes in the first tree
+        but all 7 nodes in the second. The taller the tree, the more nodes may need to be compared along a path in the worst case.
+
+## 7.7.2 &nbsp; Programming Exercises
+
+### 1. &nbsp; Maximum Depth of a Binary Tree
+
+You are given the root node `root` of a binary tree. Each node contains an integer value and references to its left and right children.
+
+The maximum depth is the **number of nodes** on the path from the root node to the farthest leaf node. Return the maximum depth of the tree; the maximum depth of an empty tree is 0.
+Use recursion.
+
+??? tip "Hints"
+
+    1. Depth is measured by the number of nodes in this exercise, so a tree containing only a root node has a maximum depth of 1
+    2. Let the recursive function return the maximum depth of the subtree rooted at the current node
+    3. Return 0 for an empty node; for a nonempty node, return max(depth(left), depth(right)) + 1
+
+[LeetCode](https://leetcode.com/problems/maximum-depth-of-binary-tree/){ .rounded-button .exercise-button target="_blank" rel="noopener noreferrer" }
+
+### 2. &nbsp; Traverse a Binary Tree Level by Level
+
+Given the root node `root` of a binary tree, use a queue to visit all nodes level by level from top to bottom and from left to right within each level.
+
+Return a two-dimensional array: the first subarray stores the values at the root's level, the second stores the values at the next level, and so on.
+If the tree is empty, return an empty array.
+
+??? tip "Hints"
+
+    1. Level-order traversal visits earlier enqueued nodes first, so use a queue
+    2. At the beginning of each round, all nodes currently in the queue belong to the same level
+    3. First record the queue's length, then remove exactly that many nodes and enqueue their children
+
+[LeetCode](https://leetcode.com/problems/binary-tree-level-order-traversal/){ .rounded-button .exercise-button target="_blank" rel="noopener noreferrer" }
+
+### 3. &nbsp; Kth Smallest Element in a Binary Search Tree
+
+A binary search tree contains `n` nodes with distinct values.
+If all node values are arranged from smallest to largest, their positions are numbered starting from 1.
+
+Given the root node `root` and an integer `k` satisfying `1 <= k <= n`, return the value at position `k`.
+Find the answer directly during an inorder traversal rather than collecting all node values first.
+
+??? tip "Hints"
+
+    1. An inorder traversal of a binary search tree visits node values from smallest to largest
+    2. Inorder traversal processes the left subtree, the current node, and then the right subtree; increment the count when visiting the current node
+    3. When the count first equals k, the current node's value is the answer, so no further traversal is needed
+
+[LeetCode](https://leetcode.com/problems/kth-smallest-element-in-a-bst/){ .rounded-button .exercise-button target="_blank" rel="noopener noreferrer" }

en/docs/chapter_tree/index.md

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 - [7.4   Binary Search Tree](binary_search_tree.md)
 - [7.5   AVL Tree *](avl_tree.md)
 - [7.6   Summary](summary.md)
+- [7.7   Exercises](exercises.md)