From ff8e7ceec50bc4198c90287e23b384e75d9f6c7f Mon Sep 17 00:00:00 2001
From: krahets <krahets@163.com>
Date: Sun, 24 Sep 2023 20:38:21 +0800
Subject: [PATCH] Several bug fixes.

---
 codes/c/chapter_hashing/hash_map_chaining.c                     | 2 +-
 codes/cpp/chapter_hashing/hash_map_chaining.cpp                 | 2 +-
 codes/cpp/chapter_hashing/hash_map_open_addressing.cpp          | 2 +-
 codes/csharp/chapter_hashing/hash_map_chaining.cs               | 2 +-
 codes/csharp/chapter_hashing/hash_map_open_addressing.cs        | 2 +-
 codes/dart/chapter_hashing/hash_map_chaining.dart               | 2 +-
 codes/go/chapter_hashing/hash_map_chaining.go                   | 2 +-
 codes/go/chapter_hashing/hash_map_open_addressing.go            | 2 +-
 codes/java/chapter_hashing/hash_map_chaining.java               | 2 +-
 codes/java/chapter_hashing/hash_map_open_addressing.java        | 2 +-
 codes/javascript/chapter_hashing/hash_map_chaining.js           | 2 +-
 codes/python/chapter_hashing/hash_map_chaining.py               | 2 +-
 codes/python/chapter_hashing/hash_map_open_addressing.py        | 2 +-
 codes/swift/chapter_hashing/hash_map_chaining.swift             | 2 +-
 codes/swift/chapter_hashing/hash_map_open_addressing.swift      | 2 +-
 codes/typescript/chapter_hashing/hash_map_chaining.ts           | 2 +-
 .../chapter_computational_complexity/iteration_and_recursion.md | 2 +-
 docs/chapter_hashing/hash_collision.md                          | 2 +-
 docs/chapter_preface/about_the_book.md                          | 2 +-
 19 files changed, 19 insertions(+), 19 deletions(-)

diff --git a/codes/c/chapter_hashing/hash_map_chaining.c b/codes/c/chapter_hashing/hash_map_chaining.c
index de8cb11fb..94e7202e0 100644
--- a/codes/c/chapter_hashing/hash_map_chaining.c
+++ b/codes/c/chapter_hashing/hash_map_chaining.c
@@ -48,7 +48,7 @@ hashMapChaining *newHashMapChaining() {
     hashmap->capacity = tableSize;
     hashmap->size = 0;
     hashmap->extendRatio = 2;
-    hashmap->loadThres = 2.0 / 3;
+    hashmap->loadThres = 2.0 / 3.0;
 
     return hashmap;
 }
diff --git a/codes/cpp/chapter_hashing/hash_map_chaining.cpp b/codes/cpp/chapter_hashing/hash_map_chaining.cpp
index a61703724..2302f0c0d 100644
--- a/codes/cpp/chapter_hashing/hash_map_chaining.cpp
+++ b/codes/cpp/chapter_hashing/hash_map_chaining.cpp
@@ -17,7 +17,7 @@ class HashMapChaining {
 
   public:
     /* 构造方法 */
-    HashMapChaining() : size(0), capacity(4), loadThres(2.0 / 3), extendRatio(2) {
+    HashMapChaining() : size(0), capacity(4), loadThres(2.0 / 3.0), extendRatio(2) {
         buckets.resize(capacity);
     }
 
diff --git a/codes/cpp/chapter_hashing/hash_map_open_addressing.cpp b/codes/cpp/chapter_hashing/hash_map_open_addressing.cpp
index ef39aecf9..4c411fb48 100644
--- a/codes/cpp/chapter_hashing/hash_map_open_addressing.cpp
+++ b/codes/cpp/chapter_hashing/hash_map_open_addressing.cpp
@@ -11,7 +11,7 @@ class HashMapOpenAddressing {
   private:
     int size;                             // 键值对数量
     int capacity = 4;                     // 哈希表容量
-    const double loadThres = 2.0 / 3;     // 触发扩容的负载因子阈值
+    const double loadThres = 2.0 / 3.0;     // 触发扩容的负载因子阈值
     const int extendRatio = 2;            // 扩容倍数
     vector<Pair *> buckets;               // 桶数组
     Pair *TOMBSTONE = new Pair(-1, "-1"); // 删除标记
diff --git a/codes/csharp/chapter_hashing/hash_map_chaining.cs b/codes/csharp/chapter_hashing/hash_map_chaining.cs
index a05edf574..39270333a 100644
--- a/codes/csharp/chapter_hashing/hash_map_chaining.cs
+++ b/codes/csharp/chapter_hashing/hash_map_chaining.cs
@@ -18,7 +18,7 @@ class HashMapChaining {
     public HashMapChaining() {
         size = 0;
         capacity = 4;
-        loadThres = 2 / 3.0;
+        loadThres = 2.0 / 3.0;
         extendRatio = 2;
         buckets = new List<List<Pair>>(capacity);
         for (int i = 0; i < capacity; i++) {
diff --git a/codes/csharp/chapter_hashing/hash_map_open_addressing.cs b/codes/csharp/chapter_hashing/hash_map_open_addressing.cs
index e9f062d75..b41a2621d 100644
--- a/codes/csharp/chapter_hashing/hash_map_open_addressing.cs
+++ b/codes/csharp/chapter_hashing/hash_map_open_addressing.cs
@@ -10,7 +10,7 @@ namespace hello_algo.chapter_hashing;
 class HashMapOpenAddressing {
     private int size; // 键值对数量
     private int capacity = 4; // 哈希表容量
-    private double loadThres = 2.0 / 3; // 触发扩容的负载因子阈值
+    private double loadThres = 2.0 / 3.0; // 触发扩容的负载因子阈值
     private int extendRatio = 2; // 扩容倍数
     private Pair[] buckets; // 桶数组
     private Pair TOMBSTONE = new Pair(-1, "-1"); // 删除标记
diff --git a/codes/dart/chapter_hashing/hash_map_chaining.dart b/codes/dart/chapter_hashing/hash_map_chaining.dart
index 1804ab7e8..fcf3ab0d2 100644
--- a/codes/dart/chapter_hashing/hash_map_chaining.dart
+++ b/codes/dart/chapter_hashing/hash_map_chaining.dart
@@ -23,7 +23,7 @@ class HashMapChaining {
   HashMapChaining() {
     size = 0;
     capacity = 4;
-    loadThres = 2 / 3.0;
+    loadThres = 2.0 / 3.0;
     extendRatio = 2;
     buckets = List.generate(capacity, (_) => []);
   }
diff --git a/codes/go/chapter_hashing/hash_map_chaining.go b/codes/go/chapter_hashing/hash_map_chaining.go
index c0b59ea73..201674090 100644
--- a/codes/go/chapter_hashing/hash_map_chaining.go
+++ b/codes/go/chapter_hashing/hash_map_chaining.go
@@ -28,7 +28,7 @@ func newHashMapChaining() *hashMapChaining {
 	return &hashMapChaining{
 		size:        0,
 		capacity:    4,
-		loadThres:   2 / 3.0,
+		loadThres:   2.0 / 3.0,
 		extendRatio: 2,
 		buckets:     buckets,
 	}
diff --git a/codes/go/chapter_hashing/hash_map_open_addressing.go b/codes/go/chapter_hashing/hash_map_open_addressing.go
index a03017993..4db637e6c 100644
--- a/codes/go/chapter_hashing/hash_map_open_addressing.go
+++ b/codes/go/chapter_hashing/hash_map_open_addressing.go
@@ -25,7 +25,7 @@ func newHashMapOpenAddressing() *hashMapOpenAddressing {
 	return &hashMapOpenAddressing{
 		size:        0,
 		capacity:    4,
-		loadThres:   2 / 3.0,
+		loadThres:   2.0 / 3.0,
 		extendRatio: 2,
 		buckets:     buckets,
 		removed: pair{
diff --git a/codes/java/chapter_hashing/hash_map_chaining.java b/codes/java/chapter_hashing/hash_map_chaining.java
index 9f77421af..9133ef02b 100644
--- a/codes/java/chapter_hashing/hash_map_chaining.java
+++ b/codes/java/chapter_hashing/hash_map_chaining.java
@@ -21,7 +21,7 @@ class HashMapChaining {
     public HashMapChaining() {
         size = 0;
         capacity = 4;
-        loadThres = 2 / 3.0;
+        loadThres = 2.0 / 3.0;
         extendRatio = 2;
         buckets = new ArrayList<>(capacity);
         for (int i = 0; i < capacity; i++) {
diff --git a/codes/java/chapter_hashing/hash_map_open_addressing.java b/codes/java/chapter_hashing/hash_map_open_addressing.java
index b8176bf5f..4e1534b58 100644
--- a/codes/java/chapter_hashing/hash_map_open_addressing.java
+++ b/codes/java/chapter_hashing/hash_map_open_addressing.java
@@ -10,7 +10,7 @@ package chapter_hashing;
 class HashMapOpenAddressing {
     private int size; // 键值对数量
     private int capacity = 4; // 哈希表容量
-    private final double loadThres = 2.0 / 3; // 触发扩容的负载因子阈值
+    private final double loadThres = 2.0 / 3.0; // 触发扩容的负载因子阈值
     private final int extendRatio = 2; // 扩容倍数
     private Pair[] buckets; // 桶数组
     private final Pair TOMBSTONE = new Pair(-1, "-1"); // 删除标记
diff --git a/codes/javascript/chapter_hashing/hash_map_chaining.js b/codes/javascript/chapter_hashing/hash_map_chaining.js
index 151cb5a57..6f1276f15 100644
--- a/codes/javascript/chapter_hashing/hash_map_chaining.js
+++ b/codes/javascript/chapter_hashing/hash_map_chaining.js
@@ -24,7 +24,7 @@ class HashMapChaining {
     constructor() {
         this.#size = 0;
         this.#capacity = 4;
-        this.#loadThres = 2 / 3.0;
+        this.#loadThres = 2.0 / 3.0;
         this.#extendRatio = 2;
         this.#buckets = new Array(this.#capacity).fill(null).map((x) => []);
     }
diff --git a/codes/python/chapter_hashing/hash_map_chaining.py b/codes/python/chapter_hashing/hash_map_chaining.py
index 96769eb5e..069d43a53 100644
--- a/codes/python/chapter_hashing/hash_map_chaining.py
+++ b/codes/python/chapter_hashing/hash_map_chaining.py
@@ -17,7 +17,7 @@ class HashMapChaining:
         """构造方法"""
         self.size = 0  # 键值对数量
         self.capacity = 4  # 哈希表容量
-        self.load_thres = 2 / 3  # 触发扩容的负载因子阈值
+        self.load_thres = 2.0 / 3.0  # 触发扩容的负载因子阈值
         self.extend_ratio = 2  # 扩容倍数
         self.buckets = [[] for _ in range(self.capacity)]  # 桶数组
 
diff --git a/codes/python/chapter_hashing/hash_map_open_addressing.py b/codes/python/chapter_hashing/hash_map_open_addressing.py
index 9ecefe863..475859038 100644
--- a/codes/python/chapter_hashing/hash_map_open_addressing.py
+++ b/codes/python/chapter_hashing/hash_map_open_addressing.py
@@ -17,7 +17,7 @@ class HashMapOpenAddressing:
         """构造方法"""
         self.size = 0  # 键值对数量
         self.capacity = 4  # 哈希表容量
-        self.load_thres = 2 / 3  # 触发扩容的负载因子阈值
+        self.load_thres = 2.0 / 3.0  # 触发扩容的负载因子阈值
         self.extend_ratio = 2  # 扩容倍数
         self.buckets: list[Pair | None] = [None] * self.capacity  # 桶数组
         self.TOMBSTONE = Pair(-1, "-1")  # 删除标记
diff --git a/codes/swift/chapter_hashing/hash_map_chaining.swift b/codes/swift/chapter_hashing/hash_map_chaining.swift
index abeebd1ee..7d88f78be 100644
--- a/codes/swift/chapter_hashing/hash_map_chaining.swift
+++ b/codes/swift/chapter_hashing/hash_map_chaining.swift
@@ -18,7 +18,7 @@ class HashMapChaining {
     init() {
         size = 0
         capacity = 4
-        loadThres = 2 / 3
+        loadThres = 2.0 / 3.0
         extendRatio = 2
         buckets = Array(repeating: [], count: capacity)
     }
diff --git a/codes/swift/chapter_hashing/hash_map_open_addressing.swift b/codes/swift/chapter_hashing/hash_map_open_addressing.swift
index 9b26128d8..53e01da24 100644
--- a/codes/swift/chapter_hashing/hash_map_open_addressing.swift
+++ b/codes/swift/chapter_hashing/hash_map_open_addressing.swift
@@ -19,7 +19,7 @@ class HashMapOpenAddressing {
     init() {
         size = 0
         capacity = 4
-        loadThres = 2 / 3
+        loadThres = 2.0 / 3.0
         extendRatio = 2
         buckets = Array(repeating: nil, count: capacity)
         removed = Pair(key: -1, val: "-1")
diff --git a/codes/typescript/chapter_hashing/hash_map_chaining.ts b/codes/typescript/chapter_hashing/hash_map_chaining.ts
index 3da27403e..51a59b636 100644
--- a/codes/typescript/chapter_hashing/hash_map_chaining.ts
+++ b/codes/typescript/chapter_hashing/hash_map_chaining.ts
@@ -26,7 +26,7 @@ class HashMapChaining {
     constructor() {
         this.#size = 0;
         this.#capacity = 4;
-        this.#loadThres = 2 / 3.0;
+        this.#loadThres = 2.0 / 3.0;
         this.#extendRatio = 2;
         this.#buckets = new Array(this.#capacity).fill(null).map((x) => []);
     }
diff --git a/docs/chapter_computational_complexity/iteration_and_recursion.md b/docs/chapter_computational_complexity/iteration_and_recursion.md
index 7a4e2393a..62767d8a8 100644
--- a/docs/chapter_computational_complexity/iteration_and_recursion.md
+++ b/docs/chapter_computational_complexity/iteration_and_recursion.md
@@ -429,7 +429,7 @@
 以上述的求和函数为例，设问题 $f(n) = 1 + 2 + \dots + n$ 。
 
 - **迭代**：在循环中模拟求和过程，从 $1$ 遍历到 $n$ ，每轮执行求和操作，即可求得 $f(n)$ 。
-- **递归**：将问题分解为子问题 $f(n) = n + f(n-1)$ ，不断（递归地）分解下去，直至基本情况 $f(0) = 0$ 时终止。
+- **递归**：将问题分解为子问题 $f(n) = n + f(n-1)$ ，不断（递归地）分解下去，直至基本情况 $f(1) = 1$ 时终止。
 
 ### 调用栈
 
diff --git a/docs/chapter_hashing/hash_collision.md b/docs/chapter_hashing/hash_collision.md
index 3d076926f..90124c450 100644
--- a/docs/chapter_hashing/hash_collision.md
+++ b/docs/chapter_hashing/hash_collision.md
@@ -29,7 +29,7 @@
 以下代码给出了链式地址哈希表的简单实现，需要注意两点。
 
 - 使用列表（动态数组）代替链表，从而简化代码。在这种设定下，哈希表（数组）包含多个桶，每个桶都是一个列表。
-- 以下实现包含哈希表扩容方法。当负载因子超过 $0.75$ 时，我们将哈希表扩容至 $2$ 倍。
+- 以下实现包含哈希表扩容方法。当负载因子超过 $\frac{2}{3}$ 时，我们将哈希表扩容至 $2$ 倍。
 
 === "Python"
 
diff --git a/docs/chapter_preface/about_the_book.md b/docs/chapter_preface/about_the_book.md
index 147cd0818..3d4880574 100644
--- a/docs/chapter_preface/about_the_book.md
+++ b/docs/chapter_preface/about_the_book.md
@@ -26,7 +26,7 @@
 - **数据结构**：基本数据类型，数据结构的分类方法。数组、链表、栈、队列、哈希表、树、堆、图等数据结构的定义、优缺点、常用操作、常见类型、典型应用、实现方法等。
 - **算法**：搜索、排序、分治、回溯、动态规划、贪心等算法的定义、优缺点、效率、应用场景、解题步骤、示例题目等。
 
-![Hello 算法内容结构](about_the_book.assets/hello_algo_mindmap.png)
+![Hello 算法内容结构](about_the_book.assets/hello_algo_mindmap.jpg)
 
 ## 致谢