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krahets
2023-03-03 02:46:12 +08:00
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commit cf9d102ed5
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chapter_computational_complexity/time_complexity.md
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@@ -821,8 +821,8 @@ $$
=== "Python"
```python title="time_complexity.py"
""" 常数阶 """
def constant(n):
""" 常数阶 """
count = 0
size = 100000
for _ in range(size):
@@ -949,8 +949,8 @@ $$
=== "Python"
```python title="time_complexity.py"
""" 线性阶 """
def linear(n):
""" 线性阶 """
count = 0
for _ in range(n):
count += 1
@@ -1075,8 +1075,8 @@ $$
=== "Python"
```python title="time_complexity.py"
""" 线性阶（遍历数组）"""
def array_traversal(nums):
""" 线性阶（遍历数组）"""
count = 0
# 循环次数与数组长度成正比
for num in nums:
@@ -1215,8 +1215,8 @@ $$
=== "Python"
```python title="time_complexity.py"
""" 平方阶 """
def quadratic(n):
""" 平方阶 """
count = 0
# 循环次数与数组长度成平方关系
for i in range(n):
@@ -1391,8 +1391,8 @@ $$
=== "Python"
```python title="time_complexity.py"
""" 平方阶（冒泡排序）"""
def bubble_sort(nums):
""" 平方阶（冒泡排序）"""
count = 0 # 计数器
# 外循环：待排序元素数量为 n-1, n-2, ..., 1
for i in range(len(nums) - 1, 0, -1):
@@ -1604,8 +1604,8 @@ $$
=== "Python"
```python title="time_complexity.py"
""" 指数阶（循环实现）"""
def exponential(n):
""" 指数阶（循环实现）"""
count, base = 0, 1
# cell 每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)
for _ in range(n):
@@ -1768,8 +1768,8 @@ $$
=== "Python"
```python title="time_complexity.py"
""" 指数阶（递归实现）"""
def exp_recur(n):
""" 指数阶（递归实现）"""
if n == 1: return 1
return exp_recur(n - 1) + exp_recur(n - 1) + 1
```
@@ -1884,8 +1884,8 @@ $$
=== "Python"
```python title="time_complexity.py"
""" 对数阶（循环实现）"""
def logarithmic(n):
""" 对数阶（循环实现）"""
count = 0
while n > 1:
n = n / 2
@@ -2017,8 +2017,8 @@ $$
=== "Python"
```python title="time_complexity.py"
""" 对数阶（递归实现）"""
def log_recur(n):
""" 对数阶（递归实现）"""
if n <= 1: return 0
return log_recur(n / 2) + 1
```
@@ -2133,8 +2133,8 @@ $$
=== "Python"
```python title="time_complexity.py"
""" 线性对数阶 """
def linear_log_recur(n):
""" 线性对数阶 """
if n <= 1: return 1
count = linear_log_recur(n // 2) + \
linear_log_recur(n // 2)
@@ -2290,8 +2290,8 @@ $$
=== "Python"
```python title="time_complexity.py"
""" 阶乘阶（递归实现）"""
def factorial_recur(n):
""" 阶乘阶（递归实现）"""
if n == 0: return 1
count = 0
# 从 1 个分裂出 n 个
@@ -2480,16 +2480,16 @@ $$
=== "Python"
```python title="worst_best_time_complexity.py"
""" 生成一个数组，元素为: 1, 2, ..., n ，顺序被打乱 """
def random_numbers(n):
""" 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 = [i for i in range(1, n + 1)]
# 随机打乱数组元素
random.shuffle(nums)
return nums
""" 查找数组 nums 中数字 1 所在索引 """
def find_one(nums):
""" 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)