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krahets
2023-04-09 05:12:22 +08:00
parent 01d05cc1f0
commit 37f11aff68
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chapter_computational_complexity/time_complexity.md
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@@ -820,7 +820,7 @@ $$
```python title="time_complexity.py"
def constant(n: int) -> int:
""" 常数阶 """
"""常数阶"""
count: int = 0
size: int = 100000
for _ in range(size):
@@ -948,7 +948,7 @@ $$
```python title="time_complexity.py"
def linear(n: int) -> int:
""" 线性阶 """
"""线性阶"""
count: int = 0
for _ in range(n):
count += 1
@@ -1074,7 +1074,7 @@ $$
```python title="time_complexity.py"
def array_traversal(nums: list[int]) -> int:
""" 线性阶（遍历数组）"""
"""线性阶（遍历数组）"""
count: int = 0
# 循环次数与数组长度成正比
for num in nums:
@@ -1214,7 +1214,7 @@ $$
```python title="time_complexity.py"
def quadratic(n: int) -> int:
""" 平方阶 """
"""平方阶"""
count: int = 0
# 循环次数与数组长度成平方关系
for i in range(n):
@@ -1390,7 +1390,7 @@ $$
```python title="time_complexity.py"
def bubble_sort(nums: list[int]) -> int:
""" 平方阶（冒泡排序）"""
"""平方阶（冒泡排序）"""
count: int = 0 # 计数器
# 外循环：待排序元素数量为 n-1, n-2, ..., 1
for i in range(len(nums) - 1, 0, -1):
@@ -1603,7 +1603,7 @@ $$
```python title="time_complexity.py"
def exponential(n: int) -> int:
""" 指数阶（循环实现）"""
"""指数阶（循环实现）"""
count: int = 0
base: int = 1
# cell 每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)
@@ -1768,8 +1768,9 @@ $$
```python title="time_complexity.py"
def exp_recur(n: int) -> int:
""" 指数阶（递归实现）"""
if n == 1: return 1
"""指数阶（递归实现）"""
if n == 1:
return 1
return exp_recur(n - 1) + exp_recur(n - 1) + 1
```
@@ -1884,7 +1885,7 @@ $$
```python title="time_complexity.py"
def logarithmic(n: float) -> int:
""" 对数阶（循环实现）"""
"""对数阶（循环实现）"""
count: int = 0
while n > 1:
n = n / 2
@@ -2017,8 +2018,9 @@ $$
```python title="time_complexity.py"
def log_recur(n: float) -> int:
""" 对数阶（递归实现）"""
if n <= 1: return 0
"""对数阶（递归实现）"""
if n <= 1:
return 0
return log_recur(n / 2) + 1
```
@@ -2133,10 +2135,10 @@ $$
```python title="time_complexity.py"
def linear_log_recur(n: float) -> int:
""" 线性对数阶 """
if n <= 1: return 1
count: int = linear_log_recur(n // 2) + \
linear_log_recur(n // 2)
"""线性对数阶"""
if n <= 1:
return 1
count: int = linear_log_recur(n // 2) + linear_log_recur(n // 2)
for _ in range(n):
count += 1
return count
@@ -2290,8 +2292,9 @@ $$
```python title="time_complexity.py"
def factorial_recur(n: int) -> int:
""" 阶乘阶（递归实现）"""
if n == 0: return 1
"""阶乘阶（递归实现）"""
if n == 0:
return 1
count: int = 0
# 从 1 个分裂出 n 个
for _ in range(n):
@@ -2480,7 +2483,7 @@ $$
```python title="worst_best_time_complexity.py"
def random_numbers(n: int) -> list[int]:
""" 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"""
# 生成数组 nums =: 1, 2, 3, ..., n
nums: list[int] = [i for i in range(1, n + 1)]
# 随机打乱数组元素
@@ -2488,7 +2491,7 @@ $$
return nums
def find_one(nums: list[int]) -> int:
""" 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"""
for i in range(len(nums)):
# 当元素 1 在数组头部时，达到最佳时间复杂度 O(1)
# 当元素 1 在数组尾部时，达到最差时间复杂度 O(n)