update c code for chapter_computational_complexity, add c code to time_complexity.md

This commit is contained in:
sjinzh 2023-01-04 08:09:22 +08:00
parent 07827ae298
commit 9e4a5fd6d8
4 changed files with 264 additions and 42 deletions

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@ -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

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@ -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

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@ -1,2 +1,4 @@
#include <stdio.h>
#include <stdbool.h>
#include <stdlib.h>
#include <time.h>

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@ -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#"