我写了一个用于合并排序的递归程序。如何通过在python中绘制其运行时间与输入的关系图来分析其时间复杂性

import matplotlib.pyplot as plt
import time

def merge_sort(arr):
    if len(arr) <= 1:
        return arr
    
    mid = len(arr) // 2
    left = merge_sort(arr[:mid])
    right = merge_sort(arr[mid:])
    
    return merge(left, right)

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

def analyze_time_complexity():
    input_sizes = [10, 100, 1000, 10000]  # 输入规模
    execution_times = []
    
    for size in input_sizes:
        arr = list(range(size, 0, -1))  # 生成逆序数组作为输入
        
        start_time = time.time()
        merge_sort(arr)
        end_time = time.time()
        
        execution_time = end_time - start_time
        execution_times.append(execution_time)
    
    # 绘制图表
    plt.plot(input_sizes, execution_times, marker='o')
    plt.xlabel('Input Size')
    plt.ylabel('Execution Time (seconds)')
    plt.title('Time Complexity Analysis of Merge Sort')
    plt.show()

analyze_time_complexity()