yetao
/
hello-algo
mirror of https://github.com/krahets/hello-algo.git
1
0
Fork 0
Code Issues Packages Projects Releases Wiki Activity

Merge pull request #208 from sjinzh/master

Browse Source 
(PR #204) update c code and doc for time_complexity
pull/212/head
Yudong Jin 2 years ago committed by GitHub
parent 75217d5e8b ea867eadac
commit fdb102eb16
No known key found for this signature in database
GPG Key ID: 4AEE18F83AFDEB23
4 changed files with 446 additions and 27 deletions
Show Stats Download Patch File Download Diff File

175
codes/c/chapter_computational_complexity/time_complexity.c
Unescape View File

@ -0,0 +1,175 @@
/*
* File: time_complexity.c
* Created Time: 2023-01-03
* Author: sjinzh (sjinzh@gmail.com)
*/
#include "../include/include.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;
}

55
codes/c/chapter_computational_complexity/worst_best_time_complexity.c
Unescape View File

@ -0,0 +1,55 @@
/*
* File: worst_best_time_complexity.c
* Created Time: 2023-01-03
* Author: sjinzh (sjinzh@gmail.com)
*/
#include "../include/include.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 = ");
printArray(nums, n);
printf("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;
}

27
codes/c/include/include.h
Unescape View File

@ -1,12 +1,15 @@
/*
* File: include.h
* Created Time: 2022-12-20
* Author: MolDuM (moldum@163.com)
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include "PrintUtil.h"
/*
* File: include.h
* Created Time: 2022-12-20
* Author: MolDuM (moldum@163.com)
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <time.h>
#include "PrintUtil.h"

216
docs/chapter_computational_complexity/time_complexity.md
Unescape View File

@ -91,7 +91,16 @@ $$
=== "C"
```c title=""
// 在某运行平台下
void algorithm(int n) {
int a = 2; // 1 ns
a = a + 1; // 1 ns
a = a * 2; // 10 ns
// 循环 n 次
for (int i = 0; i < n; i++) { // 1 ns ，每轮都要执行 i++
printf("%d", 0); // 5 ns
}
}
```
=== "C#"
@ -232,7 +241,22 @@ $$
=== "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 +397,15 @@ $$
=== "C"
```c title=""
void algorithm(int n) {
int a = 1; // +1
a = a + 1; // +1
a = a * 2; // +1
// 循环 n 次
for (int i = 0; i < n; i++) { // +1（每轮都执行 i ++）
printf("%d", 0); // +1
}
}
```
=== "C#"
@ -542,7 +574,20 @@ $$
=== "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 +742,16 @@ $$
=== "C"
```c title="time_complexity.c"
/* 常数阶 */
int constant(int n) {
int count = 0;
int size = 100000;
int i = 0;
for (int i = 0; i < size; i++) {
count ++;
}
return count;
}
```
=== "C#"
@ -795,7 +849,14 @@ $$
=== "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 +960,15 @@ $$
=== "C"
```c title="time_complexity.c"
/* 线性阶（遍历数组） */
int arrayTraversal(int *nums, int n) {
int count = 0;
// 循环次数与数组长度成正比
for (int i = 0; i < n; i++) {
count ++;
}
return count;
}
```
=== "C#"
@ -1012,7 +1081,17 @@ $$
=== "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 +1242,23 @@ $$
=== "C"
```c title="time_complexity.c"
/* 平方阶（冒泡排序） */
int bubbleSort(int *nums, int n) {
int count = 0; // 计数器
// 外循环：待排序元素数量为 n-1, n-2, ..., 1
for (int i = n - 1; i > 0; i--) {
// 内循环：冒泡操作
for (int j = 0; j < i; j++) {
// 交换 nums[j] 与 nums[j + 1]
int tmp = nums[j];
nums[j] = nums[j + 1];
nums[j + 1] = tmp;
count += 3; // 元素交换包含 3 个单元操作
}
}
return count;
}
```
=== "C#"
@ -1309,7 +1404,20 @@ $$
=== "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 +1522,11 @@ $$
=== "C"
```c title="time_complexity.c"
/* 指数阶（递归实现） */
int expRecur(int n) {
if (n == 1) return 1;
return expRecur(n - 1) + expRecur(n - 1) + 1;
}
```
=== "C#"
@ -1517,7 +1629,15 @@ $$
=== "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 +1733,11 @@ $$
=== "C"
```c title="time_complexity.c"
/* 对数阶（递归实现） */
int logRecur(float n) {
if (n <= 1) return 0;
return logRecur(n / 2) + 1;
}
```
=== "C#"
@ -1720,7 +1844,16 @@ $$
=== "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 +1978,15 @@ $$
=== "C"
```c title="time_complexity.c"
/* 阶乘阶（递归实现） */
int factorialRecur(int n) {
if (n == 0) return 1;
int count = 0;
for (int i = 0; i < n; i++) {
count += factorialRecur(n - 1);
}
return count;
}
```
=== "C#"
@ -2061,7 +2202,52 @@ $$
=== "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 = ");
printArray(nums, n);
printf("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#"

Write Preview
Loading…
Cancel
Save