fuhouyin/hello-algo
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Update time complexity and space complexity.

Browse Source
This commit is contained in:
Yudong Jin 2022-12-13 23:24:12 +08:00
parent f0c6de961a
commit bec787b751
15 changed files with 168 additions and 382 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

2
codes/cpp/chapter_computational_complexity/space_complexity_types.cpp → codes/cpp/chapter_computational_complexity/space_complexity.cpp
View File

@ -1,5 +1,5 @@
/*
* File: space_complexity_types.cpp
* File: space_complexity.cpp
* Created Time: 2022-11-25
* Author: Krahets (krahets@163.com)
*/

2
codes/cpp/chapter_computational_complexity/time_complexity_types.cpp → codes/cpp/chapter_computational_complexity/time_complexity.cpp
View File

@ -1,5 +1,5 @@
/*
* File: time_complexity_types.cpp
* File: time_complexity.cpp
* Created Time: 2022-11-25
* Author: Krahets (krahets@163.com)
*/

2
codes/go/chapter_computational_complexity/time_complexity/time_complexity.go → codes/go/chapter_computational_complexity/time_complexity.go
View File

@ -2,7 +2,7 @@
// Created Time: 2022-12-13
// Author: msk397 (machangxinq@gmail.com)
package time_complexity
package chapter_computational_complexity
/* 常数阶 */
func constant(n int) int {

45
codes/go/chapter_computational_complexity/time_complexity/worst_best_time_complexity.go
View File

@ -1,45 +0,0 @@
// File: worst_best_time_complexity.go
// Created Time: 2022-12-13
// Author: msk397 (machangxinq@gmail.com)
package time_complexity
import (
"fmt"
"math/rand"
)
/* 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
}
/* 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
}
/* Driver Code */
func main() {
for i := 0; i < 10; i++ {
n := 100
nums := randomNumbers(n)
index := findOne(nums)
fmt.Println("\n数组 [ 1, 2, ..., n ] 被打乱后 =", nums)
fmt.Println("数字 1 的索引为", index)
}
}

2
codes/go/chapter_computational_complexity/time_complexity/time_complexity_test.go → codes/go/chapter_computational_complexity/time_complexity_test.go
View File

@ -2,7 +2,7 @@
// Created Time: 2022-12-13
// Author: msk397 (machangxinq@gmail.com)
package time_complexity
package chapter_computational_complexity
import (
"fmt"

134
codes/go/chapter_computational_complexity/time_complexity_types.go
View File

@ -1,134 +0,0 @@
// 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
}
// factorialRecur 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
}

49
codes/go/chapter_computational_complexity/time_complexity_types_test.go
View File

@ -1,49 +0,0 @@
// 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)
}

22
codes/go/chapter_computational_complexity/worst_best_time_complexity.go
View File

@ -1,12 +1,15 @@
// File: worst_best_time_complexity.go
// Created Time: 2022-12-13
// Author: cathay (cathaycchen@gmail.com)
// Author: msk397 (machangxinq@gmail.com), cathay (cathaycchen@gmail.com)
package chapter_computational_complexity
import "math/rand"
import (
"fmt"
"math/rand"
)
// randomNumbers 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 */
func randomNumbers(n int) []int {
nums := make([]int, n)
// 生成数组 nums = { 1, 2, 3, ..., n }
@ -20,7 +23,7 @@ func randomNumbers(n int) []int {
return nums
}
// findOne 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 */
func findOne(nums []int) int {
for i := 0; i < len(nums); i++ {
if nums[i] == 1 {
@ -29,3 +32,14 @@ func findOne(nums []int) int {
}
return -1
}
/* Driver Code */
func main() {
for i := 0; i < 10; i++ {
n := 100
nums := randomNumbers(n)
index := findOne(nums)
fmt.Println("\n数组 [ 1, 2, ..., n ] 被打乱后 =", nums)
fmt.Println("数字 1 的索引为", index)
}
}

6
codes/go/chapter_computational_complexity/worst_best_time_complexity_test.go
View File

@ -1,6 +1,6 @@
// 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.
// File: worst_best_time_complexity.go
// Created Time: 2022-12-13
// Author: msk397 (machangxinq@gmail.com), cathay (cathaycchen@gmail.com)
package chapter_computational_complexity

4
codes/java/chapter_computational_complexity/space_complexity_types.java → codes/java/chapter_computational_complexity/space_complexity.java
View File

@ -1,5 +1,5 @@
/*
* File: space_complexity_types.java
* File: space_complexity.java
* Created Time: 2022-11-25
* Author: Krahets (krahets@163.com)
*/
@ -9,7 +9,7 @@ package chapter_computational_complexity;
import include.*;
import java.util.*;
public class space_complexity_types {
public class space_complexity {
/* 函数 */
static int function() {
// do something

4
codes/java/chapter_computational_complexity/time_complexity_types.java → codes/java/chapter_computational_complexity/time_complexity.java
View File

@ -1,12 +1,12 @@
/*
* File: time_complexity_types.java
* File: time_complexity.java
* Created Time: 2022-11-25
* Author: Krahets (krahets@163.com)
*/
package chapter_computational_complexity;
public class time_complexity_types {
public class time_complexity {
/* 常数阶 */
static int constant(int n) {
int count = 0;

2
codes/python/chapter_computational_complexity/space_complexity_types.py → codes/python/chapter_computational_complexity/space_complexity.py
View File

@ -1,5 +1,5 @@
'''
File: space_complexity_types.py
File: space_complexity.py
Created Time: 2022-11-25
Author: Krahets (krahets@163.com)
'''

2
codes/python/chapter_computational_complexity/time_complexity_types.py → codes/python/chapter_computational_complexity/time_complexity.py
View File

@ -1,5 +1,5 @@
'''
File: time_complexity_types.py
File: time_complexity.py
Created Time: 2022-11-25
Author: Krahets (krahets@163.com)
'''

96
docs/chapter_computational_complexity/space_complexity.md
View File

@ -317,7 +317,7 @@ $$
=== "Java"
```java title="space_complexity_types.java"
```java title="space_complexity.java"
/* 常数阶 */
void constant(int n) {
// 常量、变量、对象占用 O(1) 空间
@ -338,7 +338,7 @@ $$
=== "C++"
```cpp title="space_complexity_types.cpp"
```cpp title="space_complexity.cpp"
/* 常数阶 */
void constant(int n) {
// 常量、变量、对象占用 O(1) 空间
@ -359,7 +359,7 @@ $$
=== "Python"
```python title="space_complexity_types.py"
```python title="space_complexity.py"
""" 常数阶 """
def constant(n):
# 常量、变量、对象占用 O(1) 空间
@ -376,31 +376,31 @@ $$
=== "Go"
```go title="space_complexity_types.go"
```go title="space_complexity.go"
```
=== "JavaScript"
```js title="space_complexity_types.js"
```js title="space_complexity.js"
```
=== "TypeScript"
```typescript title="space_complexity_types.ts"
```typescript title="space_complexity.ts"
```
=== "C"
```c title="space_complexity_types.c"
```c title="space_complexity.c"
```
=== "C#"
```csharp title="space_complexity_types.cs"
```csharp title="space_complexity.cs"
```
@ -410,7 +410,7 @@ $$
=== "Java"
```java title="space_complexity_types.java"
```java title="space_complexity.java"
/* 线性阶 */
void linear(int n) {
// 长度为 n 的数组占用 O(n) 空间
@ -430,7 +430,7 @@ $$
=== "C++"
```cpp title="space_complexity_types.cpp"
```cpp title="space_complexity.cpp"
/* 线性阶 */
void linear(int n) {
// 长度为 n 的数组占用 O(n) 空间
@ -450,7 +450,7 @@ $$
=== "Python"
```python title="space_complexity_types.py"
```python title="space_complexity.py"
""" 线性阶 """
def linear(n):
# 长度为 n 的列表占用 O(n) 空间
@ -463,31 +463,31 @@ $$
=== "Go"
```go title="space_complexity_types.go"
```go title="space_complexity.go"
```
=== "JavaScript"
```js title="space_complexity_types.js"
```js title="space_complexity.js"
```
=== "TypeScript"
```typescript title="space_complexity_types.ts"
```typescript title="space_complexity.ts"
```
=== "C"
```c title="space_complexity_types.c"
```c title="space_complexity.c"
```
=== "C#"
```csharp title="space_complexity_types.cs"
```csharp title="space_complexity.cs"
```
@ -495,7 +495,7 @@ $$
=== "Java"
```java title="space_complexity_types.java"
```java title="space_complexity.java"
/* 线性阶（递归实现） */
void linearRecur(int n) {
System.out.println("递归 n = " + n);
@ -506,7 +506,7 @@ $$
=== "C++"
```cpp title="space_complexity_types.cpp"
```cpp title="space_complexity.cpp"
/* 线性阶（递归实现） */
void linearRecur(int n) {
cout << "递归 n = " << n << endl;
@ -517,7 +517,7 @@ $$
=== "Python"
```python title="space_complexity_types.py"
```python title="space_complexity.py"
""" 线性阶（递归实现） """
def linearRecur(n):
print("递归 n =", n)
@ -527,31 +527,31 @@ $$
=== "Go"
```go title="space_complexity_types.go"
```go title="space_complexity.go"
```
=== "JavaScript"
```js title="space_complexity_types.js"
```js title="space_complexity.js"
```
=== "TypeScript"
```typescript title="space_complexity_types.ts"
```typescript title="space_complexity.ts"
```
=== "C"
```c title="space_complexity_types.c"
```c title="space_complexity.c"
```
=== "C#"
```csharp title="space_complexity_types.cs"
```csharp title="space_complexity.cs"
```
@ -565,7 +565,7 @@ $$
=== "Java"
```java title="space_complexity_types.java"
```java title="space_complexity.java"
/* 平方阶 */
void quadratic(int n) {
// 矩阵占用 O(n^2) 空间
@ -584,7 +584,7 @@ $$
=== "C++"
```cpp title="space_complexity_types.cpp"
```cpp title="space_complexity.cpp"
/* 平方阶 */
void quadratic(int n) {
// 二维列表占用 O(n^2) 空间
@ -601,7 +601,7 @@ $$
=== "Python"
```python title="space_complexity_types.py"
```python title="space_complexity.py"
""" 平方阶 """
def quadratic(n):
# 二维列表占用 O(n^2) 空间
@ -610,31 +610,31 @@ $$
=== "Go"
```go title="space_complexity_types.go"
```go title="space_complexity.go"
```
=== "JavaScript"
```js title="space_complexity_types.js"
```js title="space_complexity.js"
```
=== "TypeScript"
```typescript title="space_complexity_types.ts"
```typescript title="space_complexity.ts"
```
=== "C"
```c title="space_complexity_types.c"
```c title="space_complexity.c"
```
=== "C#"
```csharp title="space_complexity_types.cs"
```csharp title="space_complexity.cs"
```
@ -642,7 +642,7 @@ $$
=== "Java"
```java title="space_complexity_types.java"
```java title="space_complexity.java"
/* 平方阶（递归实现） */
int quadraticRecur(int n) {
if (n <= 0) return 0;
@ -654,7 +654,7 @@ $$
=== "C++"
```cpp title="space_complexity_types.cpp"
```cpp title="space_complexity.cpp"
/* 平方阶（递归实现） */
int quadraticRecur(int n) {
if (n <= 0) return 0;
@ -666,7 +666,7 @@ $$
=== "Python"
```python title="space_complexity_types.py"
```python title="space_complexity.py"
""" 平方阶（递归实现） """
def quadratic_recur(n):
if n <= 0: return 0
@ -677,31 +677,31 @@ $$
=== "Go"
```go title="space_complexity_types.go"
```go title="space_complexity.go"
```
=== "JavaScript"
```js title="space_complexity_types.js"
```js title="space_complexity.js"
```
=== "TypeScript"
```typescript title="space_complexity_types.ts"
```typescript title="space_complexity.ts"
```
=== "C"
```c title="space_complexity_types.c"
```c title="space_complexity.c"
```
=== "C#"
```csharp title="space_complexity_types.cs"
```csharp title="space_complexity.cs"
```
@ -715,7 +715,7 @@ $$
=== "Java"
```java title="space_complexity_types.java"
```java title="space_complexity.java"
/* 指数阶（建立满二叉树） */
TreeNode buildTree(int n) {
if (n == 0) return null;
@ -728,7 +728,7 @@ $$
=== "C++"
```cpp title="space_complexity_types.cpp"
```cpp title="space_complexity.cpp"
/* 指数阶（建立满二叉树） */
TreeNode* buildTree(int n) {
if (n == 0) return nullptr;
@ -741,7 +741,7 @@ $$
=== "Python"
```python title="space_complexity_types.py"
```python title="space_complexity.py"
""" 指数阶（建立满二叉树） """
def build_tree(n):
if n == 0: return None
@ -753,31 +753,31 @@ $$
=== "Go"
```go title="space_complexity_types.go"
```go title="space_complexity.go"
```
=== "JavaScript"
```js title="space_complexity_types.js"
```js title="space_complexity.js"
```
=== "TypeScript"
```typescript title="space_complexity_types.ts"
```typescript title="space_complexity.ts"
```
=== "C"
```c title="space_complexity_types.c"
```c title="space_complexity.c"
```
=== "C#"
```csharp title="space_complexity_types.cs"
```csharp title="space_complexity.cs"
```

176
docs/chapter_computational_complexity/time_complexity.md
View File

@ -505,7 +505,7 @@ $$
=== "Java"
```java title="time_complexity_types.java"
```java title="time_complexity.java"
/* 常数阶 */
int constant(int n) {
int count = 0;
@ -518,7 +518,7 @@ $$
=== "C++"
```cpp title="time_complexity_types.cpp"
```cpp title="time_complexity.cpp"
/* 常数阶 */
int constant(int n) {
int count = 0;
@ -531,7 +531,7 @@ $$
=== "Python"
```python title="time_complexity_types.py"
```python title="time_complexity.py"
""" 常数阶 """
def constant(n):
count = 0
@ -543,7 +543,7 @@ $$
=== "Go"
```go title="time_complexity_types.go"
```go title="time_complexity.go"
/* 常数阶 */
func constant(n int) int {
count := 0
@ -557,25 +557,25 @@ $$
=== "JavaScript"
```js title="time_complexity_types.js"
```js title="time_complexity.js"
```
=== "TypeScript"
```typescript title="time_complexity_types.ts"
```typescript title="time_complexity.ts"
```
=== "C"
```c title="time_complexity_types.c"
```c title="time_complexity.c"
```
=== "C#"
```csharp title="time_complexity_types.cs"
```csharp title="time_complexity.cs"
```
@ -585,7 +585,7 @@ $$
=== "Java"
```java title="time_complexity_types.java"
```java title="time_complexity.java"
/* 线性阶 */
int linear(int n) {
int count = 0;
@ -597,7 +597,7 @@ $$
=== "C++"
```cpp title="time_complexity_types.cpp"
```cpp title="time_complexity.cpp"
/* 线性阶 */
int linear(int n) {
int count = 0;
@ -609,7 +609,7 @@ $$
=== "Python"
```python title="time_complexity_types.py"
```python title="time_complexity.py"
""" 线性阶 """
def linear(n):
count = 0
@ -620,7 +620,7 @@ $$
=== "Go"
```go title="time_complexity_types.go"
```go title="time_complexity.go"
/* 线性阶 */
func linear(n int) int {
count := 0
@ -633,25 +633,25 @@ $$
=== "JavaScript"
```js title="time_complexity_types.js"
```js title="time_complexity.js"
```
=== "TypeScript"
```typescript title="time_complexity_types.ts"
```typescript title="time_complexity.ts"
```
=== "C"
```c title="time_complexity_types.c"
```c title="time_complexity.c"
```
=== "C#"
```csharp title="time_complexity_types.cs"
```csharp title="time_complexity.cs"
```
@ -663,7 +663,7 @@ $$
=== "Java"
```java title="time_complexity_types.java"
```java title="time_complexity.java"
/* 线性阶（遍历数组） */
int arrayTraversal(int[] nums) {
int count = 0;
@ -677,7 +677,7 @@ $$
=== "C++"
```cpp title="time_complexity_types.cpp"
```cpp title="time_complexity.cpp"
/* 线性阶（遍历数组） */
int arrayTraversal(vector<int>& nums) {
int count = 0;
@ -691,7 +691,7 @@ $$
=== "Python"
```python title="time_complexity_types.py"
```python title="time_complexity.py"
""" 线性阶（遍历数组）"""
def array_traversal(nums):
count = 0
@ -703,7 +703,7 @@ $$
=== "Go"
```go title="time_complexity_types.go"
```go title="time_complexity.go"
/* 线性阶（遍历数组） */
func arrayTraversal(nums []int) int {
count := 0
@ -717,25 +717,25 @@ $$
=== "JavaScript"
```js title="time_complexity_types.js"
```js title="time_complexity.js"
```
=== "TypeScript"
```typescript title="time_complexity_types.ts"
```typescript title="time_complexity.ts"
```
=== "C"
```c title="time_complexity_types.c"
```c title="time_complexity.c"
```
=== "C#"
```csharp title="time_complexity_types.cs"
```csharp title="time_complexity.cs"
```
@ -745,7 +745,7 @@ $$
=== "Java"
```java title="time_complexity_types.java"
```java title="time_complexity.java"
/* 平方阶 */
int quadratic(int n) {
int count = 0;
@ -761,7 +761,7 @@ $$
=== "C++"
```cpp title="time_complexity_types.cpp"
```cpp title="time_complexity.cpp"
/* 平方阶 */
int quadratic(int n) {
int count = 0;
@ -777,7 +777,7 @@ $$
=== "Python"
```python title="time_complexity_types.py"
```python title="time_complexity.py"
""" 平方阶 """
def quadratic(n):
count = 0
@ -790,7 +790,7 @@ $$
=== "Go"
```go title="time_complexity_types.go"
```go title="time_complexity.go"
/* 平方阶 */
func quadratic(n int) int {
count := 0
@ -806,25 +806,25 @@ $$
=== "JavaScript"
```js title="time_complexity_types.js"
```js title="time_complexity.js"
```
=== "TypeScript"
```typescript title="time_complexity_types.ts"
```typescript title="time_complexity.ts"
```
=== "C"
```c title="time_complexity_types.c"
```c title="time_complexity.c"
```
=== "C#"
```csharp title="time_complexity_types.cs"
```csharp title="time_complexity.cs"
```
@ -840,7 +840,7 @@ $$
=== "Java"
```java title="time_complexity_types.java"
```java title="time_complexity.java"
/* 平方阶（冒泡排序） */
int bubbleSort(int[] nums) {
int count = 0; // 计数器
@ -863,7 +863,7 @@ $$
=== "C++"
```cpp title="time_complexity_types.cpp"
```cpp title="time_complexity.cpp"
/* 平方阶（冒泡排序） */
int bubbleSort(vector<int>& nums) {
int count = 0; // 计数器
@ -886,7 +886,7 @@ $$
=== "Python"
```python title="time_complexity_types.py"
```python title="time_complexity.py"
""" 平方阶（冒泡排序）"""
def bubble_sort(nums):
count = 0 # 计数器
@ -905,7 +905,7 @@ $$
=== "Go"
```go title="time_complexity_types.go"
```go title="time_complexity.go"
/* 平方阶（冒泡排序） */
func bubbleSort(nums []int) int {
count := 0 // 计数器
@ -928,25 +928,25 @@ $$
=== "JavaScript"
```js title="time_complexity_types.js"
```js title="time_complexity.js"
```
=== "TypeScript"
```typescript title="time_complexity_types.ts"
```typescript title="time_complexity.ts"
```
=== "C"
```c title="time_complexity_types.c"
```c title="time_complexity.c"
```
=== "C#"
```csharp title="time_complexity_types.cs"
```csharp title="time_complexity.cs"
```
@ -960,7 +960,7 @@ $$
=== "Java"
```java title="time_complexity_types.java"
```java title="time_complexity.java"
/* 指数阶（循环实现） */
int exponential(int n) {
int count = 0, base = 1;
@ -978,7 +978,7 @@ $$
=== "C++"
```cpp title="time_complexity_types.cpp"
```cpp title="time_complexity.cpp"
/* 指数阶（循环实现） */
int exponential(int n) {
int count = 0, base = 1;
@ -996,7 +996,7 @@ $$
=== "Python"
```python title="time_complexity_types.py"
```python title="time_complexity.py"
""" 指数阶（循环实现）"""
def exponential(n):
count, base = 0, 1
@ -1011,7 +1011,7 @@ $$
=== "Go"
```go title="time_complexity_types.go"
```go title="time_complexity.go"
/* 指数阶（循环实现）*/
func exponential(n int) int {
count, base := 0, 1
@ -1029,25 +1029,25 @@ $$
=== "JavaScript"
```js title="time_complexity_types.js"
```js title="time_complexity.js"
```
=== "TypeScript"
```typescript title="time_complexity_types.ts"
```typescript title="time_complexity.ts"
```
=== "C"
```c title="time_complexity_types.c"
```c title="time_complexity.c"
```
=== "C#"
```csharp title="time_complexity_types.cs"
```csharp title="time_complexity.cs"
```
@ -1059,7 +1059,7 @@ $$
=== "Java"
```java title="time_complexity_types.java"
```java title="time_complexity.java"
/* 指数阶（递归实现） */
int expRecur(int n) {
if (n == 1) return 1;
@ -1069,7 +1069,7 @@ $$
=== "C++"
```cpp title="time_complexity_types.cpp"
```cpp title="time_complexity.cpp"
/* 指数阶（递归实现） */
int expRecur(int n) {
if (n == 1) return 1;
@ -1079,7 +1079,7 @@ $$
=== "Python"
```python title="time_complexity_types.py"
```python title="time_complexity.py"
""" 指数阶（递归实现）"""
def exp_recur(n):
if n == 1: return 1
@ -1088,7 +1088,7 @@ $$
=== "Go"
```go title="time_complexity_types.go"
```go title="time_complexity.go"
/* 指数阶（递归实现）*/
func expRecur(n int) int {
if n == 1 {
@ -1100,25 +1100,25 @@ $$
=== "JavaScript"
```js title="time_complexity_types.js"
```js title="time_complexity.js"
```
=== "TypeScript"
```typescript title="time_complexity_types.ts"
```typescript title="time_complexity.ts"
```
=== "C"
```c title="time_complexity_types.c"
```c title="time_complexity.c"
```
=== "C#"
```csharp title="time_complexity_types.cs"
```csharp title="time_complexity.cs"
```
@ -1132,7 +1132,7 @@ $$
=== "Java"
```java title="time_complexity_types.java"
```java title="time_complexity.java"
/* 对数阶（循环实现） */
int logarithmic(float n) {
int count = 0;
@ -1146,7 +1146,7 @@ $$
=== "C++"
```cpp title="time_complexity_types.cpp"
```cpp title="time_complexity.cpp"
/* 对数阶（循环实现） */
int logarithmic(float n) {
int count = 0;
@ -1160,7 +1160,7 @@ $$
=== "Python"
```python title="time_complexity_types.py"
```python title="time_complexity.py"
""" 对数阶（循环实现）"""
def logarithmic(n):
count = 0
@ -1172,7 +1172,7 @@ $$
=== "Go"
```go title="time_complexity_types.go"
```go title="time_complexity.go"
/* 对数阶（循环实现）*/
func logarithmic(n float64) int {
count := 0
@ -1186,25 +1186,25 @@ $$
=== "JavaScript"
```js title="time_complexity_types.js"
```js title="time_complexity.js"
```
=== "TypeScript"
```typescript title="time_complexity_types.ts"
```typescript title="time_complexity.ts"
```
=== "C"
```c title="time_complexity_types.c"
```c title="time_complexity.c"
```
=== "C#"
```csharp title="time_complexity_types.cs"
```csharp title="time_complexity.cs"
```
@ -1216,7 +1216,7 @@ $$
=== "Java"
```java title="time_complexity_types.java"
```java title="time_complexity.java"
/* 对数阶（递归实现） */
int logRecur(float n) {
if (n <= 1) return 0;
@ -1226,7 +1226,7 @@ $$
=== "C++"
```cpp title="time_complexity_types.cpp"
```cpp title="time_complexity.cpp"
/* 对数阶（递归实现） */
int logRecur(float n) {
if (n <= 1) return 0;
@ -1236,7 +1236,7 @@ $$
=== "Python"
```python title="time_complexity_types.py"
```python title="time_complexity.py"
""" 对数阶（递归实现）"""
def log_recur(n):
if n <= 1: return 0
@ -1245,7 +1245,7 @@ $$
=== "Go"
```go title="time_complexity_types.go"
```go title="time_complexity.go"
/* 对数阶（递归实现）*/
func logRecur(n float64) int {
if n <= 1 {
@ -1257,25 +1257,25 @@ $$
=== "JavaScript"
```js title="time_complexity_types.js"
```js title="time_complexity.js"
```
=== "TypeScript"
```typescript title="time_complexity_types.ts"
```typescript title="time_complexity.ts"
```
=== "C"
```c title="time_complexity_types.c"
```c title="time_complexity.c"
```
=== "C#"
```csharp title="time_complexity_types.cs"
```csharp title="time_complexity.cs"
```
@ -1287,7 +1287,7 @@ $$
=== "Java"
```java title="time_complexity_types.java"
```java title="time_complexity.java"
/* 线性对数阶 */
int linearLogRecur(float n) {
if (n <= 1) return 1;
@ -1302,7 +1302,7 @@ $$
=== "C++"
```cpp title="time_complexity_types.cpp"
```cpp title="time_complexity.cpp"
/* 线性对数阶 */
int linearLogRecur(float n) {
if (n <= 1) return 1;
@ -1317,7 +1317,7 @@ $$
=== "Python"
```python title="time_complexity_types.py"
```python title="time_complexity.py"
""" 线性对数阶 """
def linear_log_recur(n):
if n <= 1: return 1
@ -1330,7 +1330,7 @@ $$
=== "Go"
```go title="time_complexity_types.go"
```go title="time_complexity.go"
/* 线性对数阶 */
func linearLogRecur(n float64) int {
if n <= 1 {
@ -1347,25 +1347,25 @@ $$
=== "JavaScript"
```js title="time_complexity_types.js"
```js title="time_complexity.js"
```
=== "TypeScript"
```typescript title="time_complexity_types.ts"
```typescript title="time_complexity.ts"
```
=== "C"
```c title="time_complexity_types.c"
```c title="time_complexity.c"
```
=== "C#"
```csharp title="time_complexity_types.cs"
```csharp title="time_complexity.cs"
```
@ -1385,7 +1385,7 @@ $$
=== "Java"
```java title="time_complexity_types.java"
```java title="time_complexity.java"
/* 阶乘阶（递归实现） */
int factorialRecur(int n) {
if (n == 0) return 1;
@ -1400,7 +1400,7 @@ $$
=== "C++"
```cpp title="time_complexity_types.cpp"
```cpp title="time_complexity.cpp"
/* 阶乘阶（递归实现） */
int factorialRecur(int n) {
if (n == 0) return 1;
@ -1415,7 +1415,7 @@ $$
=== "Python"
```python title="time_complexity_types.py"
```python title="time_complexity.py"
""" 阶乘阶（递归实现）"""
def factorial_recur(n):
if n == 0: return 1
@ -1428,7 +1428,7 @@ $$
=== "Go"
```go title="time_complexity_types.go"
```go title="time_complexity.go"
/* 阶乘阶（递归实现） */
func factorialRecur(n int) int {
if n == 0 {
@ -1445,25 +1445,25 @@ $$
=== "JavaScript"
```js title="time_complexity_types.js"
```js title="time_complexity.js"
```
=== "TypeScript"
```typescript title="time_complexity_types.ts"
```typescript title="time_complexity.ts"
```
=== "C"
```c title="time_complexity_types.c"
```c title="time_complexity.c"
```
=== "C#"
```csharp title="time_complexity_types.cs"
```csharp title="time_complexity.cs"
```