Activity Selection: Comparing Greedy and Dynamic Programming Algorithms

The reason why the graph appears as a line instead of a curve is because the x-axis values (number of activities) are discrete values, not continuous. In other words, the x-axis represents the number of activities as discrete data points, and there is no continuous relationship between these data points. Therefore, the graph shows a line connecting these discrete data points.

import random
import time
import numpy as np
import matplotlib.pyplot as plt


def generate_activities(n):
    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):
    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):
    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():
    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)

    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')
    plt.legend()
    plt.show()


compare_execution_time()