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Update time complexity and space complexity.

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Yudong Jin
2022-12-13 23:24:12 +08:00
parent f0c6de961a
commit bec787b751
15 changed files with 168 additions and 382 deletions
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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"
```