Python实现活动选择问题的贪心算法和动态规划算法

import random
import time
import matplotlib.pyplot as plt


def generate_activities(n):
    '''
    生成n个活动的开始时间和结束时间

    Args:
        n: 活动数量

    Returns:
        一个列表，包含n个活动的开始时间和结束时间
    '''
    activities = []
    for i in range(n):
        start_time = random.randint(0, 100)
        end_time = start_time + random.randint(1, 10)
        activities.append((start_time, end_time))
    return activities


def greedy_activity_selection(activities):
    '''
    使用贪心算法解决活动选择问题

    Args:
        activities: 一个列表，包含活动的开始时间和结束时间

    Returns:
        一个列表，包含选择的活动
    '''
    activities.sort(key=lambda x: x[1])  # 按结束时间排序
    selected_activities = []
    current_end_time = 0
    for activity in activities:
        if activity[0] >= current_end_time:
            selected_activities.append(activity)
            current_end_time = activity[1]
    return selected_activities


def dynamic_programming_activity_selection(activities):
    '''
    使用动态规划算法解决活动选择问题

    Args:
        activities: 一个列表，包含活动的开始时间和结束时间

    Returns:
        一个列表，包含选择的活动
    '''
    n = len(activities)
    activities.sort(key=lambda x: x[1])  # 按结束时间排序
    dp = [1] * n
    for i in range(1, n):
        for j in range(i):
            if activities[i][0] >= activities[j][1]:
                dp[i] = max(dp[i], dp[j] + 1)
    max_activities = max(dp)
    selected_activities = []
    current_end_time = float('-inf')
    for i in range(n - 1, -1, -1):
        if dp[i] == max_activities and activities[i][1] >= current_end_time:
            selected_activities.append(activities[i])
            current_end_time = activities[i][0]
            max_activities -= 1
    return selected_activities[::-1]


def compare_execution_time():
    '''
    比较贪心算法和动态规划算法的执行时间
    '''
    n_values = [8, 16, 32, 64, 128, 256]  # 增加活动数量范围
    greedy_times = []
    dp_times = []
    for n in n_values:
        total_greedy_time = 0
        total_dp_time = 0
        for _ in range(10):  # 每个数量运行10次取平均值
            activities = generate_activities(n)

            start_time = time.time()
            greedy_activity_selection(activities)
            end_time = time.time()
            total_greedy_time += (end_time - start_time)

            start_time = time.time()
            dynamic_programming_activity_selection(activities)
            end_time = time.time()
            total_dp_time += (end_time - start_time)

        greedy_times.append(total_greedy_time / 10)
        dp_times.append(total_dp_time / 10)

    plt.plot(n_values, greedy_times, label='Greedy')
    plt.plot(n_values, dp_times, label='Dynamic Programming')
    plt.xlabel('Number of activities')
    plt.ylabel('Execution time (seconds)')
    plt.legend()
    plt.title('Execution Time Comparison: Greedy vs. Dynamic Programming')
    plt.show()


compare_execution_time()

为了使曲线更加平滑，代码中将生成活动数量的范围从8增加到256，并且对每个数量运行10次取平均值。这样可以获得更准确的执行时间，并且可以更好地观察到两种算法的性能差异。