Homework3

1.编写 Python程序,判断输入a是否为质数

In [2]:

def is_primer(num):
    if num == 2:
        print("a primer")
        return
    for i in range(2,int(num**0.5)+2):
        if num % i == 0:
            print("not a primer")
            return
print("a primer")
num = int(input("输入整数:"))
is_primer(num)

def is_primer(num): if num == 2: print("a primer") return for i in range(2,int(num**0.5)+2): if num % i == 0: print("not a primer") return print("a primer") num = int(input("输入整数:")) is_primer(num)

a primer
输入整数:33
not a primer

2.用Python实现插入排序该算法，不允许直接调用插入排序函数，需要手动实现其逻辑过程。

In [3]:

def insertion_sort(arr):
    # 从第二个元素开始，因为第一个元素默认已排序
    for i in range(1, len(arr)):
        key = arr[i]
        j = i - 1
        
        while j >= 0 and arr[j] > key:
            arr[j + 1] = arr[j]
            j -= 1
        arr[j + 1] = key

    return arr

# 测试
arr = [12, 11, 13, 5, 6]
sorted_arr = insertion_sort(arr)
print("Sorted array:", sorted_arr)

def insertion_sort(arr): # 从第二个元素开始，因为第一个元素默认已排序 for i in range(1, len(arr)): key = arr[i] j = i - 1 while j >= 0 and arr[j] > key: arr[j + 1] = arr[j] j -= 1 arr[j + 1] = key return arr # 测试 arr = [12, 11, 13, 5, 6] sorted_arr = insertion_sort(arr) print("Sorted array:", sorted_arr)

Sorted array: [5, 6, 11, 12, 13]

3.用Python实现选择排序该算法，不允许直接调用选择排序函数，需要手动实现其逻辑过程。

In [4]:

def selection_sort(arr):
    for i in range(len(arr)):
        min_index = i
        
        # 查找数组中剩余元素的最小值
        for j in range(i + 1, len(arr)):
            if arr[j] < arr[min_index]:
                min_index = j
        
        # 将找到的最小值和当前元素交换
        arr[i], arr[min_index] = arr[min_index], arr[i]
    
    return arr

arr = [64, 25, 12, 22, 11]
sorted_arr = selection_sort(arr)
print("Sorted array:", sorted_arr)

def selection_sort(arr): for i in range(len(arr)): min_index = i # 查找数组中剩余元素的最小值 for j in range(i + 1, len(arr)): if arr[j] < arr[min_index]: min_index = j # 将找到的最小值和当前元素交换 arr[i], arr[min_index] = arr[min_index], arr[i] return arr arr = [64, 25, 12, 22, 11] sorted_arr = selection_sort(arr) print("Sorted array:", sorted_arr)

Sorted array: [11, 12, 22, 25, 64]

4.用Python实现快速排序该算法，不允许直接调用快速排序函数，需要手动实现其逻辑过程。

In [5]:

def quick_sort(arr):
    if len(arr) <= 1:
        return arr
    
    pivot = arr[0]
    
    # 划分数组，分成小于基准值和大于等于基准值的两部分
    left = [x for x in arr[1:] if x < pivot]
    right = [x for x in arr[1:] if x >= pivot]
    
    # 递归排序左半部分和右半部分，并合并
    return quick_sort(left) + [pivot] + quick_sort(right)

arr = [1, 10, 7, 8, 9, 1, 5]
sorted_arr = quick_sort(arr)
print("Sorted array:", sorted_arr)

def quick_sort(arr): if len(arr) <= 1: return arr pivot = arr[0] # 划分数组，分成小于基准值和大于等于基准值的两部分 left = [x for x in arr[1:] if x < pivot] right = [x for x in arr[1:] if x >= pivot] # 递归排序左半部分和右半部分，并合并 return quick_sort(left) + [pivot] + quick_sort(right) arr = [1, 10, 7, 8, 9, 1, 5] sorted_arr = quick_sort(arr) print("Sorted array:", sorted_arr)

Sorted array: [1, 1, 5, 7, 8, 9, 10]

5.使用 Python 随机生成三组长度递增的随机数列，长度分别为100、1000、10000，对生成的随机数组使用不同的排序算法，例如选择排序和归并排序，至少三种排序方法。对这些数列的数据排序，并分析不同排序算法在不同长度数列下的运行效果，例如运行时间等指标。（可以使用排序函数）

In [6]:

import numpy as np
import time

array_100 = np.random.randint(0, 10000, size=100)
array_1000 = np.random.randint(0, 10000, size=1000)
array_10000 = np.random.randint(0, 10000, size=10000)

# 定义一个计时器装饰器，用于计算函数执行时间
def timer(func):
    def wrapper(arr):
        start_time = time.time()
        result = func(arr)
        end_time = time.time()
        return result, end_time - start_time
    return wrapper

@timer
def selection_sort(arr):
    arr = arr.copy()  # 复制数组以防止修改原数组
    for i in range(len(arr)):
        min_index = i
        for j in range(i + 1, len(arr)):
            if arr[j] < arr[min_index]:
                min_index = j
        arr[i], arr[min_index] = arr[min_index], arr[i]
    return arr

@timer
def merge_sort(arr):
    if len(arr) <= 1:
        return arr.copy()
    
    def merge(left, right):
        result = []
        i = j = 0
        while i < len(left) and j < len(right):
            if left[i] <= right[j]:
                result.append(left[i])
                i += 1
            else:
                result.append(right[j])
                j += 1
        result.extend(left[i:])
        result.extend(right[j:])
        return result
    
    mid = len(arr) // 2
    left = merge_sort(arr[:mid])[0]
    right = merge_sort(arr[mid:])[0]
    return merge(left, right)

@timer
def quick_sort(arr):
    if len(arr) <= 1:
        return arr.copy()
    pivot = arr[0]
    left = [x for x in arr[1:] if x < pivot]
    right = [x for x in arr[1:] if x >= pivot]
    return quick_sort(left)[0] + [pivot] + quick_sort(right)[0]

results = []

for arr, length in [(array_100, 100), (array_1000, 1000), (array_10000, 10000)]:
    _, time_selection = selection_sort(arr)
    _, time_merge = merge_sort(arr)
    _, time_quick = quick_sort(arr)
    results.append({
        "Array Length": length,
        "Selection Sort Time (s)": time_selection,
        "Merge Sort Time (s)": time_merge,
        "Quick Sort Time (s)": time_quick
    })

for result in results:
    print(f"Array Length: {result['Array Length']}")
    print(f"Selection Sort Time: {result['Selection Sort Time (s)']:.6f} seconds")
    print(f"Merge Sort Time: {result['Merge Sort Time (s)']:.6f} seconds")
    print(f"Quick Sort Time: {result['Quick Sort Time (s)']:.6f} seconds")
    print("-" * 50)

import numpy as np import time array_100 = np.random.randint(0, 10000, size=100) array_1000 = np.random.randint(0, 10000, size=1000) array_10000 = np.random.randint(0, 10000, size=10000) # 定义一个计时器装饰器，用于计算函数执行时间 def timer(func): def wrapper(arr): start_time = time.time() result = func(arr) end_time = time.time() return result, end_time - start_time return wrapper @timer def selection_sort(arr): arr = arr.copy() # 复制数组以防止修改原数组 for i in range(len(arr)): min_index = i for j in range(i + 1, len(arr)): if arr[j] < arr[min_index]: min_index = j arr[i], arr[min_index] = arr[min_index], arr[i] return arr @timer def merge_sort(arr): if len(arr) <= 1: return arr.copy() def merge(left, right): result = [] i = j = 0 while i < len(left) and j < len(right): if left[i] <= right[j]: result.append(left[i]) i += 1 else: result.append(right[j]) j += 1 result.extend(left[i:]) result.extend(right[j:]) return result mid = len(arr) // 2 left = merge_sort(arr[:mid])[0] right = merge_sort(arr[mid:])[0] return merge(left, right) @timer def quick_sort(arr): if len(arr) <= 1: return arr.copy() pivot = arr[0] left = [x for x in arr[1:] if x < pivot] right = [x for x in arr[1:] if x >= pivot] return quick_sort(left)[0] + [pivot] + quick_sort(right)[0] results = [] for arr, length in [(array_100, 100), (array_1000, 1000), (array_10000, 10000)]: _, time_selection = selection_sort(arr) _, time_merge = merge_sort(arr) _, time_quick = quick_sort(arr) results.append({ "Array Length": length, "Selection Sort Time (s)": time_selection, "Merge Sort Time (s)": time_merge, "Quick Sort Time (s)": time_quick }) for result in results: print(f"Array Length: {result['Array Length']}") print(f"Selection Sort Time: {result['Selection Sort Time (s)']:.6f} seconds") print(f"Merge Sort Time: {result['Merge Sort Time (s)']:.6f} seconds") print(f"Quick Sort Time: {result['Quick Sort Time (s)']:.6f} seconds") print("-" * 50)

Array Length: 100
Selection Sort Time: 0.000973 seconds
Merge Sort Time: 0.000000 seconds
Quick Sort Time: 0.000000 seconds
--------------------------------------------------
Array Length: 1000
Selection Sort Time: 0.054685 seconds
Merge Sort Time: 0.004884 seconds
Quick Sort Time: 0.000975 seconds
--------------------------------------------------
Array Length: 10000
Selection Sort Time: 4.982640 seconds
Merge Sort Time: 0.049804 seconds
Quick Sort Time: 0.021482 seconds
--------------------------------------------------

6.使用python代码获取当前系统时间

In [7]:

import datetime
print(datetime.datetime.now())

import datetime print(datetime.datetime.now())

2024-10-16 16:04:01.711569

7.Homework/data文件夹下的stuGrade.csv文件中包含5位同学的学号、语文成绩、数学成绩和英语成绩，请先用记事本打开该文件，查看文件内容，然后编写Python程序，读取该文件，并计算出各科的平均成绩（保留2位小数）。

In [8]:

import pandas as pd

df = pd.read_csv('data/stuGrade.csv')

average_chinese = round(df['chinese'].mean(), 2)
average_math = round(df['math'].mean(), 2)
average_english = round(df['english'].mean(), 2)

print(f"语文平均成绩: {average_chinese}")
print(f"数学平均成绩: {average_math}")
print(f"英语平均成绩: {average_english}")

import pandas as pd df = pd.read_csv('data/stuGrade.csv') average_chinese = round(df['chinese'].mean(), 2) average_math = round(df['math'].mean(), 2) average_english = round(df['english'].mean(), 2) print(f"语文平均成绩: {average_chinese}") print(f"数学平均成绩: {average_math}") print(f"英语平均成绩: {average_english}")

语文平均成绩: 82.6
数学平均成绩: 81.0
英语平均成绩: 81.8

8.请在第7题的代码继续编写Python程序，将以下内容写入my.txt文件中，一并上传到github中。

第1行：你的学号和姓名

第2行：3门课程的平均成绩（任意课程），保留2位小数，以英文逗号间隔

第3行：系统当前时间，格式例如2020-01-01 12:00:00

第4行：两秒后的系统当前时间（利用sleep()方法）

In [13]:

import time
from datetime import datetime

student_id = "10211900416"
student_name = "郭夏辉"

# 获取当前时间
current_time = datetime.now().strftime('%Y-%m-%d %H:%M:%S')
time.sleep(2)

time1 = datetime.now().strftime('%Y-%m-%d %H:%M:%S')

content = [
    f"{student_id} {student_name}",
    f"{average_chinese},{average_math},{average_english}",
    current_time,
    time1
]

with open('data/my.txt', 'w',encoding='utf-8') as file:
    file.write("\n".join(content))

with open('data/my.txt', 'r', encoding='utf-8') as file:
    print(file.read())

import time from datetime import datetime student_id = "10211900416" student_name = "郭夏辉" # 获取当前时间 current_time = datetime.now().strftime('%Y-%m-%d %H:%M:%S') time.sleep(2) time1 = datetime.now().strftime('%Y-%m-%d %H:%M:%S') content = [ f"{student_id} {student_name}", f"{average_chinese},{average_math},{average_english}", current_time, time1 ] with open('data/my.txt', 'w',encoding='utf-8') as file: file.write("\n".join(content)) with open('data/my.txt', 'r', encoding='utf-8') as file: print(file.read())

10211900416 郭夏辉
82.6,81.0,81.8
2024-10-16 16:20:08
2024-10-16 16:20:10