From f2ef38c6184960affa56c5be12939514aff9f0bd Mon Sep 17 00:00:00 2001
From: Cathay <cathaycchen@gmail.com>
Date: Tue, 13 Dec 2022 17:15:22 +0800
Subject: [PATCH 1/2] feat(time-complexity): add code implemented by go

---
 .../time_complexity_types.go                  | 134 +++++++++++
 .../time_complexity_types_test.go             |  49 ++++
 .../worst_best_time_complexity.go             |  31 +++
 .../worst_best_time_complexity_test.go        |  20 ++
 .../time_complexity.md                        | 214 ++++++++++++++++--
 5 files changed, 433 insertions(+), 15 deletions(-)
 create mode 100644 codes/go/chapter_computational_complexity/time_complexity_types.go
 create mode 100644 codes/go/chapter_computational_complexity/time_complexity_types_test.go
 create mode 100644 codes/go/chapter_computational_complexity/worst_best_time_complexity.go
 create mode 100644 codes/go/chapter_computational_complexity/worst_best_time_complexity_test.go

diff --git a/codes/go/chapter_computational_complexity/time_complexity_types.go b/codes/go/chapter_computational_complexity/time_complexity_types.go
new file mode 100644
index 000000000..69b87a118
--- /dev/null
+++ b/codes/go/chapter_computational_complexity/time_complexity_types.go
@@ -0,0 +1,134 @@
+// File: time_complexity_types.go
+// Created Time: 2022-12-13
+// Author: cathay (cathaycchen@gmail.com)
+
+package chapter_computational_complexity
+
+// constant 常数阶
+func constant(n int) int {
+	count := 0
+	var size = 100000
+	for i := 0; i < size; i++ {
+		count++
+	}
+	return count
+}
+
+// linear 线性阶
+func linear(n int) int {
+	count := 0
+	for i := 0; i < n; i++ {
+		count++
+	}
+	return count
+}
+
+// arrayTraversal 线性阶（遍历数组）
+func arrayTraversal(nums []int) int {
+	count := 0
+	// 循环次数与数组长度成正比
+	for range nums {
+		count++
+	}
+	return count
+}
+
+// quadratic 平方阶
+func quadratic(n int) int {
+	count := 0
+	// 循环次数与数组长度成平方关系
+	for i := 0; i < n; i++ {
+		for j := 0; j < n; j++ {
+			count++
+		}
+	}
+	return count
+}
+
+// bubbleSort 平方阶（冒泡排序）
+func bubbleSort(nums []int) int {
+	count := 0  // 计数器
+	// 外循环：待排序元素数量为 n-1, n-2, ..., 1
+	for i := len(nums) - 1; i > 0; i-- {
+		// 内循环：冒泡操作
+		for j := 0; j < i; j++ {
+			if nums[j] > nums[j + 1] {
+				// 交换 nums[j] 与 nums[j + 1]
+				tmp := nums[j]
+				nums[j] = nums[j + 1]
+				nums[j + 1] = tmp
+				count += 3 	// 元素交换包含 3 个单元操作
+			}
+		}
+	}
+	return count
+}
+
+// exponential 指数阶（循环实现）
+func exponential(n int) int {
+	count := 0
+	base := 1
+	// cell 每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)
+	for i := 0; i < n; i++ {
+		for j := 0; j < base; j++ {
+			count++
+		}
+		base *= 2
+	}
+	// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1
+	return count
+}
+
+// expRecur 指数阶（递归实现）
+func expRecur(n int) int {
+	if n == 1 {
+		return 1
+	}
+	return expRecur(n - 1) + expRecur(n - 1) + 1
+}
+
+// logarithmic 对数阶（循环实现）
+func logarithmic(n float32) int {
+	count := 0
+	for n > 1 {
+		n = n / 2
+		count++
+	}
+	return count
+}
+
+// logRecur 对数阶（递归实现）
+func logRecur(n float32) int {
+	if n <= 1 {
+		return 0
+	}
+	return logRecur(n / 2) + 1
+}
+
+// 线性对数阶
+func linearLogRecur(n float32) int {
+	if n <= 1 {
+		return 1
+	}
+	count := linearLogRecur(n / 2) + linearLogRecur(n / 2)
+	for i := 0; float32(i) < n; i++ {
+		count++
+	}
+	return count
+}
+
+/* 阶乘阶（递归实现） */
+func factorialRecur(n int) int {
+	if n == 0 {
+		return 1
+	}
+	count := 0
+	// 从 1 个分裂出 n 个
+	for i := 0; i < n; i++ {
+		count += factorialRecur(n - 1)
+	}
+	return count
+}
+
+
+
diff --git a/codes/go/chapter_computational_complexity/time_complexity_types_test.go b/codes/go/chapter_computational_complexity/time_complexity_types_test.go
new file mode 100644
index 000000000..e410c2c23
--- /dev/null
+++ b/codes/go/chapter_computational_complexity/time_complexity_types_test.go
@@ -0,0 +1,49 @@
+// File: time_complexity_types_test.go
+// Created Time: 2022-12-13
+// Author: cathay (cathaycchen@gmail.com)
+
+package chapter_computational_complexity
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestRunCount(t *testing.T) {
+	// ======= Test Case =======
+	n := 8
+	fmt.Println("输入数据大小 n =", n)
+
+	// ====== Driver Code ======
+	count := constant(n)
+	fmt.Println("常数阶的计算操作数量 =", count)
+
+	count = linear(n)
+	fmt.Println("线性阶的计算操作数量 =", count)
+	count = arrayTraversal(make([]int, n))
+	fmt.Println("线性阶（遍历数组）的计算操作数量 =", count)
+
+	count = quadratic(n)
+	fmt.Println("平方阶的计算操作数量 =", count)
+	nums := make([]int, n)
+	for i := 0; i < n; i++ {
+		nums[i] = n - i  // [n,n-1,...,2,1]
+	}
+	count = bubbleSort(nums)
+	fmt.Println("平方阶（冒泡排序）的计算操作数量 =", count)
+
+	count = exponential(n)
+	fmt.Println("指数阶（循环实现）的计算操作数量 =", count)
+	count = expRecur(n)
+	fmt.Println("指数阶（递归实现）的计算操作数量 =", count)
+
+	count = logarithmic(float32(n))
+	fmt.Println("对数阶（循环实现）的计算操作数量 =", count)
+	count = logRecur(float32(n))
+	fmt.Println("对数阶（递归实现）的计算操作数量 =", count)
+	count = linearLogRecur(float32(n))
+	fmt.Println("线性对数阶（递归实现）的计算操作数量 =", count)
+
+	count = factorialRecur(n)
+	fmt.Println("阶乘阶（递归实现）的计算操作数量 =", count)
+}
\ No newline at end of file
diff --git a/codes/go/chapter_computational_complexity/worst_best_time_complexity.go b/codes/go/chapter_computational_complexity/worst_best_time_complexity.go
new file mode 100644
index 000000000..a91fd4938
--- /dev/null
+++ b/codes/go/chapter_computational_complexity/worst_best_time_complexity.go
@@ -0,0 +1,31 @@
+// File: worst_best_time_complexity.go
+// Created Time: 2022-12-13
+// Author: cathay (cathaycchen@gmail.com)
+
+package chapter_computational_complexity
+
+import "math/rand"
+
+// randomNumbers 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱
+func randomNumbers(n int) []int {
+	nums := make([]int, n)
+	// 生成数组 nums = { 1, 2, 3, ..., n }
+	for i := 0; i < n; i++ {
+		nums[i] = i + 1
+	}
+	// 随机打乱数组元素
+	rand.Shuffle(len(nums), func(i, j int) {
+		nums[i], nums[j] = nums[j], nums[i]
+	})
+	return nums
+}
+
+// findOne 查找数组 nums 中数字 1 所在索引
+func findOne(nums []int) int {
+	for i := 0; i < len(nums); i++ {
+		if nums[i] == 1 {
+			return i
+		}
+	}
+	return -1
+}
\ No newline at end of file
diff --git a/codes/go/chapter_computational_complexity/worst_best_time_complexity_test.go b/codes/go/chapter_computational_complexity/worst_best_time_complexity_test.go
new file mode 100644
index 000000000..33767f781
--- /dev/null
+++ b/codes/go/chapter_computational_complexity/worst_best_time_complexity_test.go
@@ -0,0 +1,20 @@
+// Copyright 2022 Cathay.  All rights reserved.
+// Use of this source code is governed by a MIT style
+// license that can be found in the LICENSE file.
+
+package chapter_computational_complexity
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestWorstBestTimeComplexity(t *testing.T) {
+	for i := 0; i < 10; i++ {
+		n := 100
+		nums := randomNumbers(n)
+		index := findOne(nums)
+		fmt.Println("打乱后的数组为", nums)
+		fmt.Println("数字 1 的索引为", index)
+	}
+}
diff --git a/docs/chapter_computational_complexity/time_complexity.md b/docs/chapter_computational_complexity/time_complexity.md
index ab55268c5..34315f5d9 100644
--- a/docs/chapter_computational_complexity/time_complexity.md
+++ b/docs/chapter_computational_complexity/time_complexity.md
@@ -64,7 +64,16 @@ $$
 === "Go"
 
     ```go title=""
-
+    // 在某运行平台下
+    func algorithm(n int) {
+        var a int = 2  // 1 ns
+        a = a + 1      // 1 ns
+        a = a * 2      // 10 ns
+        // 循环 n 次
+        for i := 0; i < n; i++ {  // 1 ns ，每轮都要执行 i++
+            println(0)            // 5 ns
+        }
+    }
     ```
 
 === "JavaScript"
@@ -107,7 +116,7 @@ $$
 
     ```java title=""
     // 算法 A 时间复杂度：常数阶
-    void algorithm_A(int n) {
+    void algorithm_A(n int) {
         System.out.println(0);
     }
     // 算法 B 时间复杂度：线性阶
@@ -164,7 +173,24 @@ $$
 === "Go"
 
     ```go title=""
+    // 算法 A 时间复杂度：常数阶
+    func algorithm_A(n int) {
+        println(0)
+    }
 
+    // 算法 B 时间复杂度：线性阶
+    func algorithm_B(n int) {
+        for i := 0; i < n; i++ {
+            println(0)
+        }
+    }
+
+    // 算法 C 时间复杂度：常数阶
+    func algorithm_C(n int) {
+        for i := 0; i < 1000000; i++ {
+            println(0)
+        }
+    }
     ```
 
 === "JavaScript"
@@ -255,7 +281,15 @@ $$
 === "Go"
 
     ```go title=""
-
+    func algorithm(n int) {
+        var a int = 1  // +1
+        a = a + 1      // +1
+        a = a * 2      // +1
+        // 循环 n 次
+        for i := 0; i < n; i++ {  // +1（每轮都执行 i ++）
+            println(0)            // +1
+        }
+    }
     ```
 
 === "JavaScript"
@@ -389,7 +423,20 @@ $$
 === "Go"
 
     ```go title=""
-
+    func algorithm(n int) {
+        var a int = 1 // +0（技巧 1）
+        a = a + n     // +0（技巧 1）
+        // +n（技巧 2）
+        for i := 0; i < 5 * n + 1; i++ {
+            println(0)
+        }
+        // +n*n（技巧 3）
+        for i := 0; i < 2 * n; i++ {
+            for j := 0; j < n + 1; j++ {
+                println(0)
+            }
+        }
+    }
     ```
 
 === "JavaScript"
@@ -500,7 +547,15 @@ $$
 === "Go"
 
     ```go title="time_complexity_types.go"
-
+    // constant 常数阶
+    func constant(n int) int {
+        count := 0
+        var size = 100000
+        for i := 0; i < size; i++ {
+            count++
+        }
+        return count
+    }
     ```
 
 === "JavaScript"
@@ -569,7 +624,14 @@ $$
 === "Go"
 
     ```go title="time_complexity_types.go"
-
+    // linear 线性阶
+    func linear(n int) int {
+        count := 0
+        for i := 0; i < n; i++ {
+            count++
+        }
+        return count
+    }
     ```
 
 === "JavaScript"
@@ -645,7 +707,15 @@ $$
 === "Go"
 
     ```go title="time_complexity_types.go"
-
+    // arrayTraversal 线性阶（遍历数组）
+    func arrayTraversal(nums []int) int {
+        count := 0
+        // 循环次数与数组长度成正比
+        for range nums {
+            count++
+        }
+        return count
+    }
     ```
 
 === "JavaScript"
@@ -724,7 +794,17 @@ $$
 === "Go"
 
     ```go title="time_complexity_types.go"
-
+    // quadratic 平方阶
+    func quadratic(n int) int {
+        count := 0
+        // 循环次数与数组长度成平方关系
+        for i := 0; i < n; i++ {
+            for j := 0; j < n; j++ {
+                count++
+            }
+        }
+        return count
+    }
     ```
 
 === "JavaScript"
@@ -829,7 +909,24 @@ $$
 === "Go"
 
     ```go title="time_complexity_types.go"
-
+    // bubbleSort 平方阶（冒泡排序）
+    func bubbleSort(nums []int) int {
+        count := 0  // 计数器
+        // 外循环：待排序元素数量为 n-1, n-2, ..., 1
+        for i := len(nums) - 1; i > 0; i-- {
+            // 内循环：冒泡操作
+            for j := 0; j < i; j++ {
+                if nums[j] > nums[j + 1] {
+                    // 交换 nums[j] 与 nums[j + 1]
+                    tmp := nums[j]
+                    nums[j] = nums[j + 1]
+                    nums[j + 1] = tmp
+                    count += 3 	// 元素交换包含 3 个单元操作
+                }
+            }
+        }
+        return count
+    }
     ```
 
 === "JavaScript"
@@ -918,7 +1015,20 @@ $$
 === "Go"
 
     ```go title="time_complexity_types.go"
-
+    // exponential 指数阶（循环实现）
+    func exponential(n int) int {
+        count := 0
+        base := 1
+        // cell 每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)
+        for i := 0; i < n; i++ {
+            for j := 0; j < base; j++ {
+                count++
+            }
+            base *= 2
+        }
+        // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1
+        return count
+    }
     ```
 
 === "JavaScript"
@@ -983,7 +1093,13 @@ $$
 === "Go"
 
     ```go title="time_complexity_types.go"
-
+    // expRecur 指数阶（递归实现）
+    func expRecur(n int) int {
+        if n == 1 {
+            return 1
+        }
+        return expRecur(n - 1) + expRecur(n - 1) + 1
+    }
     ```
 
 === "JavaScript"
@@ -1061,7 +1177,15 @@ $$
 === "Go"
 
     ```go title="time_complexity_types.go"
-
+    // logarithmic 对数阶（循环实现）
+    func logarithmic(n float32) int {
+        count := 0
+        for n > 1 {
+            n = n / 2
+            count++
+        }
+        return count
+    }
     ```
 
 === "JavaScript"
@@ -1126,7 +1250,13 @@ $$
 === "Go"
 
     ```go title="time_complexity_types.go"
-
+    // logRecur 对数阶（递归实现）
+    func logRecur(n float32) int {
+        if n <= 1 {
+            return 0
+        }
+        return logRecur(n / 2) + 1
+    }
     ```
 
 === "JavaScript"
@@ -1205,7 +1335,17 @@ $$
 === "Go"
 
     ```go title="time_complexity_types.go"
-
+    // 线性对数阶
+    func linearLogRecur(n float32) int {
+        if n <= 1 {
+            return 1
+        }
+        count := linearLogRecur(n / 2) + linearLogRecur(n / 2)
+        for i := 0; float32(i) < n; i++ {
+            count++
+        }
+        return count
+    }
     ```
 
 === "JavaScript"
@@ -1292,7 +1432,18 @@ $$
 === "Go"
 
     ```go title="time_complexity_types.go"
-
+    /* 阶乘阶（递归实现） */
+    func factorialRecur(n int) int {
+        if n == 0 {
+            return 1
+        }
+        count := 0
+        // 从 1 个分裂出 n 个
+        for i := 0; i < n; i++ {
+            count += factorialRecur(n - 1)
+        }
+        return count
+    }
     ```
 
 === "JavaScript"
@@ -1447,7 +1598,40 @@ $$
 === "Go"
 
     ```go title="worst_best_time_complexity.go"
+    // randomNumbers 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱
+    func randomNumbers(n int) []int {
+        nums := make([]int, n)
+        // 生成数组 nums = { 1, 2, 3, ..., n }
+        for i := 0; i < n; i++ {
+            nums[i] = i + 1
+        }
+        // 随机打乱数组元素
+        rand.Shuffle(len(nums), func(i, j int) {
+            nums[i], nums[j] = nums[j], nums[i]
+        })
+        return nums
+    }
 
+    // findOne 查找数组 nums 中数字 1 所在索引
+    func findOne(nums []int) int {
+        for i := 0; i < len(nums); i++ {
+            if nums[i] == 1 {
+                return i
+            }
+        }
+        return -1
+    }
+
+    // TestWorstBestTimeComplexity Driver Code
+    func TestWorstBestTimeComplexity(t *testing.T) {
+        for i := 0; i < 10; i++ {
+            n := 100
+            nums := randomNumbers(n)
+            index := findOne(nums)
+            fmt.Println("打乱后的数组为", nums)
+            fmt.Println("数字 1 的索引为", index)
+        }
+    }
     ```
 
 === "JavaScript"

From fd4a519c6f22139b65af3860e5c208bb74847416 Mon Sep 17 00:00:00 2001
From: Cathay <cathaycchen@gmail.com>
Date: Tue, 13 Dec 2022 17:44:25 +0800
Subject: [PATCH 2/2] fix(time-complexity): fixed some careless mistakes

---
 .../chapter_computational_complexity/time_complexity_types.go | 2 +-
 docs/chapter_computational_complexity/time_complexity.md      | 4 ++--
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/codes/go/chapter_computational_complexity/time_complexity_types.go b/codes/go/chapter_computational_complexity/time_complexity_types.go
index 69b87a118..8488cacb7 100644
--- a/codes/go/chapter_computational_complexity/time_complexity_types.go
+++ b/codes/go/chapter_computational_complexity/time_complexity_types.go
@@ -117,7 +117,7 @@ func linearLogRecur(n float32) int {
 	return count
 }
 
-/* 阶乘阶（递归实现） */
+// factorialRecur 阶乘阶（递归实现）
 func factorialRecur(n int) int {
 	if n == 0 {
 		return 1
diff --git a/docs/chapter_computational_complexity/time_complexity.md b/docs/chapter_computational_complexity/time_complexity.md
index 34315f5d9..13a52f154 100644
--- a/docs/chapter_computational_complexity/time_complexity.md
+++ b/docs/chapter_computational_complexity/time_complexity.md
@@ -116,7 +116,7 @@ $$
 
     ```java title=""
     // 算法 A 时间复杂度：常数阶
-    void algorithm_A(n int) {
+    void algorithm_A(int n) {
         System.out.println(0);
     }
     // 算法 B 时间复杂度：线性阶
@@ -1432,7 +1432,7 @@ $$
 === "Go"
 
     ```go title="time_complexity_types.go"
-    /* 阶乘阶（递归实现） */
+    // factorialRecur 阶乘阶（递归实现）
     func factorialRecur(n int) int {
         if n == 0 {
             return 1