mirror of
https://github.com/krahets/hello-algo.git
synced 2024-12-27 00:36:28 +08:00
140 lines
3.6 KiB
Python
140 lines
3.6 KiB
Python
"""
|
|
File: time_complexity.py
|
|
Created Time: 2022-11-25
|
|
Author: Krahets (krahets@163.com)
|
|
"""
|
|
|
|
import sys, os.path as osp
|
|
sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
|
|
from include import *
|
|
|
|
""" 常数阶 """
|
|
def constant(n):
|
|
count = 0
|
|
size = 100000
|
|
for _ in range(size):
|
|
count += 1
|
|
return count
|
|
|
|
""" 线性阶 """
|
|
def linear(n):
|
|
count = 0
|
|
for _ in range(n):
|
|
count += 1
|
|
return count
|
|
|
|
""" 线性阶（遍历数组）"""
|
|
def array_traversal(nums):
|
|
count = 0
|
|
# 循环次数与数组长度成正比
|
|
for num in nums:
|
|
count += 1
|
|
return count
|
|
|
|
""" 平方阶 """
|
|
def quadratic(n):
|
|
count = 0
|
|
# 循环次数与数组长度成平方关系
|
|
for i in range(n):
|
|
for j in range(n):
|
|
count += 1
|
|
return count
|
|
|
|
""" 平方阶（冒泡排序）"""
|
|
def bubble_sort(nums):
|
|
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):
|
|
# 内循环：冒泡操作
|
|
for j in range(i):
|
|
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
|
|
|
|
""" 指数阶（循环实现）"""
|
|
def exponential(n):
|
|
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):
|
|
for _ in range(base):
|
|
count += 1
|
|
base *= 2
|
|
# count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1
|
|
return count
|
|
|
|
""" 指数阶（递归实现）"""
|
|
def exp_recur(n):
|
|
if n == 1: return 1
|
|
return exp_recur(n - 1) + exp_recur(n - 1) + 1
|
|
|
|
""" 对数阶（循环实现）"""
|
|
def logarithmic(n):
|
|
count = 0
|
|
while n > 1:
|
|
n = n / 2
|
|
count += 1
|
|
return count
|
|
|
|
""" 对数阶（递归实现）"""
|
|
def log_recur(n):
|
|
if n <= 1: return 0
|
|
return log_recur(n / 2) + 1
|
|
|
|
""" 线性对数阶 """
|
|
def linear_log_recur(n):
|
|
if n <= 1: return 1
|
|
count = linear_log_recur(n // 2) + \
|
|
linear_log_recur(n // 2)
|
|
for _ in range(n):
|
|
count += 1
|
|
return count
|
|
|
|
""" 阶乘阶（递归实现）"""
|
|
def factorial_recur(n):
|
|
if n == 0: return 1
|
|
count = 0
|
|
# 从 1 个分裂出 n 个
|
|
for _ in range(n):
|
|
count += factorial_recur(n - 1)
|
|
return count
|
|
|
|
|
|
""" Driver Code """
|
|
if __name__ == "__main__":
|
|
# 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
|
|
n = 8
|
|
print("输入数据大小 n =", n)
|
|
|
|
count = constant(n)
|
|
print("常数阶的计算操作数量 =", count)
|
|
|
|
count = linear(n)
|
|
print("线性阶的计算操作数量 =", count)
|
|
count = array_traversal([0] * n)
|
|
print("线性阶（遍历数组）的计算操作数量 =", count)
|
|
|
|
count = quadratic(n)
|
|
print("平方阶的计算操作数量 =", count)
|
|
nums = [i for i in range(n, 0, -1)] # [n,n-1,...,2,1]
|
|
count = bubble_sort(nums)
|
|
print("平方阶（冒泡排序）的计算操作数量 =", count)
|
|
|
|
count = exponential(n)
|
|
print("指数阶（循环实现）的计算操作数量 =", count)
|
|
count = exp_recur(n)
|
|
print("指数阶（递归实现）的计算操作数量 =", count)
|
|
|
|
count = logarithmic(n)
|
|
print("对数阶（循环实现）的计算操作数量 =", count)
|
|
count = log_recur(n)
|
|
print("对数阶（递归实现）的计算操作数量 =", count)
|
|
|
|
count = linear_log_recur(n)
|
|
print("线性对数阶（递归实现）的计算操作数量 =", count)
|
|
|
|
count = factorial_recur(n)
|
|
print("阶乘阶（递归实现）的计算操作数量 =", count)
|