Python实现活动选择问题的贪心算法和动态规划算法及时间复杂度比较

import random
import time
import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import interp1d


def generate_activities(n):
    '''生成n个活动的起止时间
    '''
    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):
    '''贪心算法求解活动选择问题
    '''
    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):
    '''动态规划算法求解活动选择问题
    '''
    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时间复杂度
    '''
    n_values = [8, 16, 32, 64, 128, 256]
    greedy_times = []
    dp_times = []
    for n in n_values:
        activities = generate_activities(n)

        start_time = time.time()
        greedy_activity_selection(activities)
        end_time = time.time()
        greedy_times.append(end_time - start_time)

        start_time = time.time()
        dynamic_programming_activity_selection(activities)
        end_time = time.time()
        dp_times.append(end_time - start_time)

    # 使用插值函数将离散数据点画成一条曲线
    x = np.linspace(min(n_values), max(n_values), 100)
    f_greedy = interp1d(n_values, greedy_times, kind='cubic')
    f_dp = interp1d(n_values, dp_times, kind='cubic')

    plt.plot(x, f_greedy(x), label='Greedy')
    plt.plot(x, f_dp(x), label='Dynamic Programming')
    plt.xlabel('Number of activities')
    plt.ylabel('Execution time')
    plt.legend()
    plt.show()


compare_execution_time()