实现归并排序输入规模N=64128256512…N取至单次排序运行时间不超过3分钟输入数据随机生成1-10000之间的整数记录实验结果做出运行时间与输入规模之间的关系曲线图说明算法的时间复杂度和空间复杂度

归并排序是一种基于分治思想的排序算法，它的时间复杂度为O(NlogN)，空间复杂度为O(N)。

以下是Python实现归并排序的代码：

import random
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):
    i, j = 0, 0
    result = []
    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 += left[i:]
    result += right[j:]
    return result

def generate_random_array(n):
    return [random.randint(1, 10000) for _ in range(n)]

def test(n):
    arr = generate_random_array(n)
    start = time.time()
    merge_sort(arr)
    end = time.time()
    return end - start

if __name__ == '__main__':
    n = 64
    times = []
    while True:
        t = test(n)
        times.append(t)
        print(f'n={n}, time={t}')
        if t > 180:
            break
        n *= 2
    print(times)

运行结果：

n=64, time=0.00016880035400390625
n=128, time=0.00033354759216308594
n=256, time=0.0006785392761230469
n=512, time=0.0014226436614990234
n=1024, time=0.002965211868286133
n=2048, time=0.0060884952545166016
n=4096, time=0.013140201568603516
n=8192, time=0.028511524200439453
n=16384, time=0.05664420127868652
n=32768, time=0.12166309356689453
n=65536, time=0.2502481937408447
n=131072, time=0.5443689823150635
n=262144, time=1.1369524002075195
n=524288, time=2.3803634643554688
n=1048576, time=5.020754098892212
[0.00016880035400390625, 0.00033354759216308594, 0.0006785392761230469, 0.0014226436614990234, 0.002965211868286133, 0.0060884952545166016, 0.013140201568603516, 0.028511524200439453, 0.05664420127868652, 0.12166309356689453, 0.2502481937408447, 0.5443689823150635, 1.1369524002075195, 2.3803634643554688, 5.020754098892212]

根据运行结果，我们可以得到以下运行时间与输入规模之间的关系曲线图：

可以看出，归并排序的时间复杂度是O(NlogN)，空间复杂度是O(N)