合并排序与线性排序:用Python证明时间复杂性

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

# 示例用法
arr = [5, 2, 9, 1, 7, 6]
sorted_arr = merge_sort(arr)
print(sorted_arr)

def counting_sort(arr):
    max_val = max(arr)
    count = [0] * (max_val + 1)
    sorted_arr = [0] * len(arr)
    
    for num in arr:
        count[num] += 1
    
    for i in range(1, max_val + 1):
        count[i] += count[i - 1]
    
    for num in arr:
        sorted_arr[count[num] - 1] = num
        count[num] -= 1
    
    return sorted_arr

# 示例用法
arr = [5, 2, 9, 1, 7, 6]
sorted_arr = counting_sort(arr)
print(sorted_arr)