From 1b356ba0a2b0c67b549cee72fe9ea5dd191d24cd Mon Sep 17 00:00:00 2001
From: sjinzh <99076655+sjinzh@users.noreply.github.com>
Date: Tue, 3 Jan 2023 21:19:11 +0800
Subject: [PATCH 1/2] add c code for chapter_computational_complexity

---
 .../time_complexity.c                         | 192 ++++++++++++++++++
 .../worst_best_time_complexity.c              |  65 ++++++
 2 files changed, 257 insertions(+)
 create mode 100644 codes/c/chapter_computational_complexity/time_complexity.c
 create mode 100644 codes/c/chapter_computational_complexity/worst_best_time_complexity.c

diff --git a/codes/c/chapter_computational_complexity/time_complexity.c b/codes/c/chapter_computational_complexity/time_complexity.c
new file mode 100644
index 000000000..b7e6cef9c
--- /dev/null
+++ b/codes/c/chapter_computational_complexity/time_complexity.c
@@ -0,0 +1,192 @@
+// File: time_complexity.c
+// Created Time: 2023-01-03
+// Author: sjinzh (sjinzh@gmail.com)
+
+#include "stdio.h"
+#include "stdlib.h"
+
+// 常数阶
+int constant(int n) 
+{
+    int count = 0;
+    int size = 100000;
+    int i = 0;
+    for(int i = 0; i < size; i++){
+        count ++;
+    }
+    return count;
+}
+
+// 线性阶
+int linear(int n) 
+{
+    int count = 0;
+    for(int i = 0; i < n; i++){
+        count ++;
+    }
+    return count;
+}
+
+// 线性阶（遍历数组）
+int arrayTraversal(int *nums, int n)
+{
+    int count = 0;
+    // 循环次数与数组长度成正比
+    for(int i = 0; i < n; i++){
+        count ++;
+    }
+    return count;
+}
+
+// 平方阶
+int quadratic(int n) 
+{
+    int count = 0;
+    // 循环次数与数组长度成平方关系
+    for(int i = 0; i < n; i++){
+        for(int j = 0; j < n; j++){
+            count ++;
+        }
+    }
+    return count;
+}
+
+// 平方阶（冒泡排序）
+int bubbleSort(int *nums, int n)
+{
+    int count = 0;  // 计数器 
+    // 外循环：待排序元素数量为 n-1, n-2, ..., 1
+    for(int i = n - 1; i > 0; i--){
+        // 内循环：冒泡操作
+        for (int j = 0; j < i; j++)
+        {
+            // 交换 nums[j] 与 nums[j + 1]
+            int 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;
+}
+
+// 指数阶（循环实现）
+int exponential(int n) 
+{
+    int count = 0;
+    int bas = 1;
+    // cell 每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)
+    for (int i = 0; i < n; i++)
+    {
+        for (int j = 0; j < bas; j++)
+        {
+            count++;
+        }
+        bas *= 2;
+    }
+    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1
+    return count;
+}
+
+// 指数阶（递归实现）
+int expRecur(int n) 
+{
+    if (n == 1) return 1;
+    return expRecur(n - 1) + expRecur(n - 1) + 1;
+}
+
+// 对数阶（循环实现）
+int logarithmic(float n)
+{
+    int count = 0;
+    while (n > 1)
+    {
+        n = n / 2;
+        count++;
+    }
+    return count;
+}
+
+// 对数阶（递归实现）
+int logRecur(float n)
+{
+    if (n <= 1) return 0;
+    return logRecur(n / 2) + 1;
+}
+
+// 线性对数阶
+int linearLogRecur(float n)
+{
+    if (n <= 1) return 1;
+    int count = linearLogRecur(n / 2) +
+                linearLogRecur(n / 2);
+    for (int i = 0; i < n; i++)
+    {
+        count ++;
+    }
+    return count;
+}
+
+// 阶乘阶（递归实现）
+int factorialRecur(int n) 
+{
+    if (n == 0) return 1;
+    int count = 0;
+    for (int i = 0; i < n; i++)
+    {
+        count += factorialRecur(n - 1);
+    }
+    return count;
+}
+
+// Driver Code
+int main(int argc, char *argv[])
+ {
+    // 可以修改 n 运行，体会一下各种复杂度的操作数量变化趋势
+    int n = 8;
+    printf("输入数据大小 n = %d\n", n);
+
+    int count = constant(n);
+    printf("常数阶的计算操作数量 = %d\n", count);
+
+    count = linear(n);
+    printf("线性阶的计算操作数量 = %d\n", count);
+    // 分配堆区内存（创建一维可变长数组：数组中元素数量为n，元素类型为int）
+    int *nums = (int *)malloc(n * sizeof(int));
+    count = arrayTraversal(nums, n);
+    printf("线性阶（遍历数组）的计算操作数量 = %d\n", count);
+
+    count = quadratic(n);
+    printf("平方阶的计算操作数量 = %d\n", count);
+    for(int i = 0; i < n; i++){
+        nums[i] = n - i;    // [n,n-1,...,2,1]
+    }
+    count = bubbleSort(nums, n);
+    printf("平方阶（冒泡排序）的计算操作数量 = %d\n", count);
+
+    count = exponential(n);
+    printf("指数阶（循环实现）的计算操作数量 = %d\n", count);
+    count = expRecur(n);
+    printf("指数阶（递归实现）的计算操作数量 = %d\n", count);
+
+    count = logarithmic(n);
+    printf("对数阶（循环实现）的计算操作数量 = %d\n", count);
+    count = logRecur(n);
+    printf("对数阶（递归实现）的计算操作数量 = %d\n", count);
+
+    count = linearLogRecur(n);
+    printf("线性对数阶（递归实现）的计算操作数量 = %d\n", count);
+
+    count = factorialRecur(n);
+    printf("阶乘阶（递归实现）的计算操作数量 = %d\n", count);
+
+    // 释放堆区内存
+    if(nums != NULL){
+        free(nums);
+        nums = NULL;
+    }
+    getchar();
+    return 0;
+}
+
diff --git a/codes/c/chapter_computational_complexity/worst_best_time_complexity.c b/codes/c/chapter_computational_complexity/worst_best_time_complexity.c
new file mode 100644
index 000000000..11139630f
--- /dev/null
+++ b/codes/c/chapter_computational_complexity/worst_best_time_complexity.c
@@ -0,0 +1,65 @@
+// File: worst_best_time_complexity.c
+// Created Time: 2023-01-03
+// Author: sjinzh (sjinzh@gmail.com)
+
+#include "stdio.h"
+#include "stdlib.h"
+#include "time.h"
+
+// 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱
+int *randomNumbers(int n)  
+{
+    // 分配堆区内存（创建一维可变长数组：数组中元素数量为n，元素类型为int）
+    int *nums = (int *)malloc(n * sizeof(int));
+    // 生成数组 nums = { 1, 2, 3, ..., n }
+    for (int i = 0; i < n; i++)
+    {
+        nums[i] = i + 1;
+    }
+    // 随机打乱数组元素 
+	for (int i = n - 1; i > 0; i--)
+	{
+		int j = rand() % (i + 1);
+		int temp = nums[i];
+		nums[i] = nums[j];
+		nums[j] = temp; 
+	}
+    return nums;
+}
+
+// 查找数组 nums 中数字 1 所在索引
+int findOne(int *nums, int n) 
+{
+    for (int i = 0; i < n; i++)
+    {
+        if (nums[i] == 1) return i;
+    }
+    return -1;
+}
+
+// Driver Code
+int main(int argc, char *argv[])
+{
+    // 初始化随机数种子
+    srand((unsigned int)time(NULL));
+    for (int i = 0; i < 10; i++)
+    {
+        int n = 100;
+        int *nums = randomNumbers(n);
+        int index = findOne(nums, n);
+        printf("\n数组 [ 1, 2, ..., n ] 被打乱后 = ");
+        for (int j = 0; j < n; j++)
+        {
+            printf("%d%s", nums[j], (j == n-1)? "" : "," );
+        }
+        printf("\n数字 1 的索引为 %d\n", index);
+        // 释放堆区内存
+        if(nums != NULL){
+            free(nums);
+            nums = NULL;
+        }
+    }
+    getchar();
+    return 0;
+}
+

From 9e4a5fd6d897bb70e049758ef3ccb975e96c30a8 Mon Sep 17 00:00:00 2001
From: sjinzh <99076655+sjinzh@users.noreply.github.com>
Date: Wed, 4 Jan 2023 08:09:22 +0800
Subject: [PATCH 2/2] update c code for chapter_computational_complexity, add c
 code to  time_complexity.md

---
 .../time_complexity.c                         |  35 +--
 .../worst_best_time_complexity.c              |  18 +-
 codes/c/include/include.h                     |   4 +-
 .../time_complexity.md                        | 249 ++++++++++++++++--
 4 files changed, 264 insertions(+), 42 deletions(-)

diff --git a/codes/c/chapter_computational_complexity/time_complexity.c b/codes/c/chapter_computational_complexity/time_complexity.c
index b7e6cef9c..4355ea3ad 100644
--- a/codes/c/chapter_computational_complexity/time_complexity.c
+++ b/codes/c/chapter_computational_complexity/time_complexity.c
@@ -1,11 +1,12 @@
-// File: time_complexity.c
-// Created Time: 2023-01-03
-// Author: sjinzh (sjinzh@gmail.com)
+/*
+ * File: time_complexity.c
+ * Created Time: 2023-01-03
+ * Author: sjinzh (sjinzh@gmail.com)
+ */
 
-#include "stdio.h"
-#include "stdlib.h"
+#include "../include/include.h"
 
-// 常数阶
+/* 常数阶 */
 int constant(int n) 
 {
     int count = 0;
@@ -17,7 +18,7 @@ int constant(int n)
     return count;
 }
 
-// 线性阶
+/* 线性阶 */
 int linear(int n) 
 {
     int count = 0;
@@ -27,7 +28,7 @@ int linear(int n)
     return count;
 }
 
-// 线性阶（遍历数组）
+/* 线性阶（遍历数组） */
 int arrayTraversal(int *nums, int n)
 {
     int count = 0;
@@ -38,7 +39,7 @@ int arrayTraversal(int *nums, int n)
     return count;
 }
 
-// 平方阶
+/* 平方阶 */
 int quadratic(int n) 
 {
     int count = 0;
@@ -51,7 +52,7 @@ int quadratic(int n)
     return count;
 }
 
-// 平方阶（冒泡排序）
+/* 平方阶（冒泡排序） */
 int bubbleSort(int *nums, int n)
 {
     int count = 0;  // 计数器 
@@ -71,7 +72,7 @@ int bubbleSort(int *nums, int n)
     return count;
 }
 
-// 指数阶（循环实现）
+/* 指数阶（循环实现） */
 int exponential(int n) 
 {
     int count = 0;
@@ -89,14 +90,14 @@ int exponential(int n)
     return count;
 }
 
-// 指数阶（递归实现）
+/* 指数阶（递归实现） */
 int expRecur(int n) 
 {
     if (n == 1) return 1;
     return expRecur(n - 1) + expRecur(n - 1) + 1;
 }
 
-// 对数阶（循环实现）
+/* 对数阶（循环实现） */
 int logarithmic(float n)
 {
     int count = 0;
@@ -108,14 +109,14 @@ int logarithmic(float n)
     return count;
 }
 
-// 对数阶（递归实现）
+/* 对数阶（递归实现） */
 int logRecur(float n)
 {
     if (n <= 1) return 0;
     return logRecur(n / 2) + 1;
 }
 
-// 线性对数阶
+/* 线性对数阶 */
 int linearLogRecur(float n)
 {
     if (n <= 1) return 1;
@@ -128,7 +129,7 @@ int linearLogRecur(float n)
     return count;
 }
 
-// 阶乘阶（递归实现）
+/* 阶乘阶（递归实现） */
 int factorialRecur(int n) 
 {
     if (n == 0) return 1;
@@ -140,7 +141,7 @@ int factorialRecur(int n)
     return count;
 }
 
-// Driver Code
+/* Driver Code */
 int main(int argc, char *argv[])
  {
     // 可以修改 n 运行，体会一下各种复杂度的操作数量变化趋势
diff --git a/codes/c/chapter_computational_complexity/worst_best_time_complexity.c b/codes/c/chapter_computational_complexity/worst_best_time_complexity.c
index 11139630f..fc37ae0f0 100644
--- a/codes/c/chapter_computational_complexity/worst_best_time_complexity.c
+++ b/codes/c/chapter_computational_complexity/worst_best_time_complexity.c
@@ -1,12 +1,12 @@
-// File: worst_best_time_complexity.c
-// Created Time: 2023-01-03
-// Author: sjinzh (sjinzh@gmail.com)
+/*
+ * File: worst_best_time_complexity.c
+ * Created Time: 2023-01-03
+ * Author: sjinzh (sjinzh@gmail.com)
+ */
 
-#include "stdio.h"
-#include "stdlib.h"
-#include "time.h"
+#include "../include/include.h"
 
-// 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱
+/* 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱 */
 int *randomNumbers(int n)  
 {
     // 分配堆区内存（创建一维可变长数组：数组中元素数量为n，元素类型为int）
@@ -27,7 +27,7 @@ int *randomNumbers(int n)
     return nums;
 }
 
-// 查找数组 nums 中数字 1 所在索引
+/* 查找数组 nums 中数字 1 所在索引 */
 int findOne(int *nums, int n) 
 {
     for (int i = 0; i < n; i++)
@@ -37,7 +37,7 @@ int findOne(int *nums, int n)
     return -1;
 }
 
-// Driver Code
+/* Driver Code */
 int main(int argc, char *argv[])
 {
     // 初始化随机数种子
diff --git a/codes/c/include/include.h b/codes/c/include/include.h
index 44843254e..8ce104cd2 100644
--- a/codes/c/include/include.h
+++ b/codes/c/include/include.h
@@ -1,2 +1,4 @@
 #include <stdio.h>
-#include <stdbool.h>
\ No newline at end of file
+#include <stdbool.h>
+#include <stdlib.h>
+#include <time.h>
\ No newline at end of file
diff --git a/docs/chapter_computational_complexity/time_complexity.md b/docs/chapter_computational_complexity/time_complexity.md
index 539c9b5cb..5d61dc005 100644
--- a/docs/chapter_computational_complexity/time_complexity.md
+++ b/docs/chapter_computational_complexity/time_complexity.md
@@ -91,7 +91,17 @@ $$
 === "C"
 
     ```c title=""
-
+    // 在某运行平台下
+    void algorithm(int n) 
+    {
+        int a = 2;  // 1 ns
+        a = a + 1;  // 1 ns
+        a = a * 2;  // 10 ns
+        // 循环 n 次
+        for (int i = 0; i < n; i++) {   // 1 ns ，每轮都要执行 i++
+            printf("%d", 0);            // 5 ns
+        }
+    }
     ```
 
 === "C#"
@@ -232,7 +242,25 @@ $$
 === "C"
 
     ```c title=""
-
+    // 算法 A 时间复杂度：常数阶
+    void algorithm_A(int n) 
+    {
+        printf("%d", 0);
+    }
+    // 算法 B 时间复杂度：线性阶
+    void algorithm_B(int n) 
+    {
+        for (int i = 0; i < n; i++) {
+            printf("%d", 0);
+        }
+    }
+    // 算法 C 时间复杂度：常数阶
+    void algorithm_C(int n) 
+    {
+        for (int i = 0; i < 1000000; i++) {
+            printf("%d", 0);
+        }
+    }
     ```
 
 === "C#"
@@ -373,7 +401,16 @@ $$
 === "C"
 
     ```c title=""
-
+    void algorithm(int n) 
+    {
+        int a = 1;  // +1
+        a = a + 1;  // +1
+        a = a * 2;  // +1
+        // 循环 n 次
+        for (int i = 0; i < n; i++) {   // +1（每轮都执行 i ++）
+            printf("%d", 0);            // +1
+        }
+    }  
     ```
 
 === "C#"
@@ -542,7 +579,21 @@ $$
 === "C"
 
     ```c title=""
-
+    void algorithm(int n) 
+    {
+        int a = 1;  // +0（技巧 1）
+        a = a + n;  // +0（技巧 1）
+        // +n（技巧 2）
+        for (int i = 0; i < 5 * n + 1; i++) {
+            printf("%d", 0);
+        }
+        // +n*n（技巧 3）
+        for (int i = 0; i < 2 * n; i++) {
+            for (int j = 0; j < n + 1; j++) {
+                printf("%d", 0);
+            }
+        }
+    }
     ```
 
 === "C#"
@@ -697,7 +748,17 @@ $$
 === "C"
 
     ```c title="time_complexity.c"
-
+    /* 常数阶 */
+    int constant(int n) 
+    {
+        int count = 0;
+        int size = 100000;
+        int i = 0;
+        for(int i = 0; i < size; i++){
+            count ++;
+        }
+        return count;
+    }
     ```
 
 === "C#"
@@ -795,7 +856,15 @@ $$
 === "C"
 
     ```c title="time_complexity.c"
-
+    /* 线性阶 */
+    int linear(int n) 
+    {
+        int count = 0;
+        for(int i = 0; i < n; i++){
+            count ++;
+        }
+        return count;
+    }
     ```
 
 === "C#"
@@ -899,7 +968,16 @@ $$
 === "C"
 
     ```c title="time_complexity.c"
-
+    /* 线性阶（遍历数组） */
+    int arrayTraversal(int *nums, int n)
+    {
+        int count = 0;
+        // 循环次数与数组长度成正比
+        for(int i = 0; i < n; i++){
+            count ++;
+        }
+        return count;
+    }
     ```
 
 === "C#"
@@ -1012,7 +1090,18 @@ $$
 === "C"
 
     ```c title="time_complexity.c"
-
+    /* 平方阶 */
+    int quadratic(int n) 
+    {
+        int count = 0;
+        // 循环次数与数组长度成平方关系
+        for(int i = 0; i < n; i++){
+            for(int j = 0; j < n; j++){
+                count ++;
+            }
+        }
+        return count;
+    }
     ```
 
 === "C#"
@@ -1163,7 +1252,25 @@ $$
 === "C"
 
     ```c title="time_complexity.c"
-
+    /* 平方阶（冒泡排序） */
+    int bubbleSort(int *nums, int n)
+    {
+        int count = 0;  // 计数器 
+        // 外循环：待排序元素数量为 n-1, n-2, ..., 1
+        for(int i = n - 1; i > 0; i--){
+            // 内循环：冒泡操作
+            for (int j = 0; j < i; j++)
+            {
+                // 交换 nums[j] 与 nums[j + 1]
+                int 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;
+    }
     ```
 
 === "C#"
@@ -1309,7 +1416,23 @@ $$
 === "C"
 
     ```c title="time_complexity.c"
-
+    /* 指数阶（循环实现） */
+    int exponential(int n) 
+    {
+        int count = 0;
+        int bas = 1;
+        // cell 每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)
+        for (int i = 0; i < n; i++)
+        {
+            for (int j = 0; j < bas; j++)
+            {
+                count++;
+            }
+            bas *= 2;
+        }
+        // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1
+        return count;
+    }
     ```
 
 === "C#"
@@ -1414,7 +1537,12 @@ $$
 === "C"
 
     ```c title="time_complexity.c"
-
+    /* 指数阶（递归实现） */
+    int expRecur(int n) 
+    {
+        if (n == 1) return 1;
+        return expRecur(n - 1) + expRecur(n - 1) + 1;
+    }
     ```
 
 === "C#"
@@ -1517,7 +1645,17 @@ $$
 === "C"
 
     ```c title="time_complexity.c"
-
+    /* 对数阶（循环实现） */
+    int logarithmic(float n)
+    {
+        int count = 0;
+        while (n > 1)
+        {
+            n = n / 2;
+            count++;
+        }
+        return count;
+    }
     ```
 
 === "C#"
@@ -1613,7 +1751,12 @@ $$
 === "C"
 
     ```c title="time_complexity.c"
-
+    /* 对数阶（递归实现） */
+    int logRecur(float n)
+    {
+        if (n <= 1) return 0;
+        return logRecur(n / 2) + 1;
+    }
     ```
 
 === "C#"
@@ -1720,7 +1863,18 @@ $$
 === "C"
 
     ```c title="time_complexity.c"
-
+    /* 线性对数阶 */
+    int linearLogRecur(float n)
+    {
+        if (n <= 1) return 1;
+        int count = linearLogRecur(n / 2) +
+                    linearLogRecur(n / 2);
+        for (int i = 0; i < n; i++)
+        {
+            count ++;
+        }
+        return count;
+    }
     ```
 
 === "C#"
@@ -1845,7 +1999,17 @@ $$
 === "C"
 
     ```c title="time_complexity.c"
-
+    /* 阶乘阶（递归实现） */
+    int factorialRecur(int n) 
+    {
+        if (n == 0) return 1;
+        int count = 0;
+        for (int i = 0; i < n; i++)
+        {
+            count += factorialRecur(n - 1);
+        }
+        return count;
+    }
     ```
 
 === "C#"
@@ -2061,7 +2225,62 @@ $$
 === "C"
 
     ```c title="worst_best_time_complexity.c"
+    /* 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱 */
+    int *randomNumbers(int n)  
+    {
+        // 分配堆区内存（创建一维可变长数组：数组中元素数量为n，元素类型为int）
+        int *nums = (int *)malloc(n * sizeof(int));
+        // 生成数组 nums = { 1, 2, 3, ..., n }
+        for (int i = 0; i < n; i++)
+        {
+            nums[i] = i + 1;
+        }
+        // 随机打乱数组元素 
+        for (int i = n - 1; i > 0; i--)
+        {
+            int j = rand() % (i + 1);
+            int temp = nums[i];
+            nums[i] = nums[j];
+            nums[j] = temp; 
+        }
+        return nums;
+    }
 
+    /* 查找数组 nums 中数字 1 所在索引 */
+    int findOne(int *nums, int n) 
+    {
+        for (int i = 0; i < n; i++)
+        {
+            if (nums[i] == 1) return i;
+        }
+        return -1;
+    }
+
+    /* Driver Code */
+    int main(int argc, char *argv[])
+    {
+        // 初始化随机数种子
+        srand((unsigned int)time(NULL));
+        for (int i = 0; i < 10; i++)
+        {
+            int n = 100;
+            int *nums = randomNumbers(n);
+            int index = findOne(nums, n);
+            printf("\n数组 [ 1, 2, ..., n ] 被打乱后 = ");
+            for (int j = 0; j < n; j++)
+            {
+                printf("%d%s", nums[j], (j == n-1)? "" : "," );
+            }
+            printf("\n数字 1 的索引为 %d\n", index);
+            // 释放堆区内存
+            if(nums != NULL){
+                free(nums);
+                nums = NULL;
+            }
+        }
+        getchar();
+        return 0;
+    }
     ```
 
 === "C#"