大 O 表示法 - Python

import timeitimport matplotlib.pyplot as pltimport cProfile# O(1)def constant_time_operation():    return 42# O(log n)def logarithmic_time_operation(n):    count = 0    while n > 1:        n //= 2        count += 1    return count# O(n)def linear_time_operation(n):    total = 0    for i in range(n):        total += i    return total# O(n log n)def linear_logarithmic_time_operation(n):    if n <= 1:        return n    else:        return linear_logarithmic_time_operation(n - 1) + n# O(n^2)def quadratic_time_operation(n):    total = 0    for i in range(n):        for j in range(n):            total += i + j    return total# O(2^n)def exponential_time_operation(n):    if n <= 1:        return 1    else:        return exponential_time_operation(n - 1) + exponential_time_operation(n - 1)# O(n!)def factorial_time_operation(n):    if n == 0:        return 1    else:        return n * factorial_time_operation(n - 1)# Function to measure execution time using timeitdef measure_time(func, *args):    execution_time = timeit.timeit(lambda: func(*args), number=1000)    return execution_timedef plot_results(results):    functions, times = zip(*results)    colors = ['skyblue', 'orange', 'green', 'red', 'purple', 'brown', 'pink']    plt.figure(figsize=(14, 8))    plt.bar(functions, times, color=colors)    for i, v in enumerate(times):        plt.text(i, v + 0.5, f"{v:.6f}", ha='center',                 va='bottom', rotation=0, color='black')    plt.xlabel('Function Complexity')    plt.ylabel('Average Time (s)')    plt.title('Execution Time of Different Algorithm Complexities')    plt.grid(axis='y', linestyle='--', linewidth=0.5, color='gray', alpha=0.5)    plt.tight_layout()    plt.show()def main():    results = []    results.append(("O(1)", measure_time(constant_time_operation)))    results.append(("O(log n)", measure_time(logarithmic_time_operation, 10)))    results.append(("O(n)", measure_time(linear_time_operation, 10)))    results.append(("O(n log n)", measure_time(        linear_logarithmic_time_operation, 10)))    results.append(("O(n^2)", measure_time(quadratic_time_operation, 7)))    results.append(("O(2^n)", measure_time(exponential_time_operation, 7)))    results.append(("O(n!)", measure_time(factorial_time_operation, 112)))    plot_results(results)if __name__ == '__main__':    cProfile.run("main()", sort="totime", filename="output_profile.prof")