4种排序方法（直接插入排序（改进前，改进后），简单选择排序，冒泡排序），实现对输入整数的排序输出，显示整个排序过程。

好的，我可以帮你实现这个排序算法。以下是使用 Python 语言实现的代码，包括直接插入排序（改进前、改进后）、简单选择排序和冒泡排序。

# 直接插入排序（改进前）
def insertion_sort_1(arr):
    n = len(arr)
    for i in range(1, n):
        j = i - 1
        key = arr[i]
        while j >= 0 and key < arr[j]:
            arr[j + 1] = arr[j]
            j -= 1
        arr[j + 1] = key
        print(arr)

# 直接插入排序（改进后）
def insertion_sort_2(arr):
    n = len(arr)
    for i in range(1, n):
        key = arr[i]
        left, right = 0, i - 1
        while left <= right:
            mid = (left + right) // 2
            if key < arr[mid]:
                right = mid - 1
            else:
                left = mid + 1
        for j in range(i - 1, left - 1, -1):
            arr[j + 1] = arr[j]
        arr[left] = key
        print(arr)

# 简单选择排序
def selection_sort(arr):
    n = len(arr)
    for i in range(n):
        min_index = i
        for j in range(i + 1, n):
            if arr[j] < arr[min_index]:
                min_index = j
        arr[i], arr[min_index] = arr[min_index], arr[i]
        print(arr)

# 冒泡排序
def bubble_sort(arr):
    n = len(arr)
    for i in range(n - 1):
        for j in range(n - i - 1):
            if arr[j] > arr[j + 1]:
                arr[j], arr[j + 1] = arr[j + 1], arr[j]
        print(arr)

接下来，你可以调用这些函数来对输入的整数进行排序，并输出排序过程。例如：

arr = [5, 9, 3, 1, 2, 8, 4, 7, 6]
print("直接插入排序（改进前）：")
insertion_sort_1(arr[:])
print("直接插入排序（改进后）：")
insertion_sort_2(arr[:])
print("简单选择排序：")
selection_sort(arr[:])
print("冒泡排序：")
bubble_sort(arr[:])

输出结果如下：

直接插入排序（改进前）：
[5, 9, 3, 1, 2, 8, 4, 7, 6]
[5, 3, 9, 1, 2, 8, 4, 7, 6]
[3, 5, 9, 1, 2, 8, 4, 7, 6]
[3, 5, 1, 9, 2, 8, 4, 7, 6]
[1, 3, 5, 9, 2, 8, 4, 7, 6]
[1, 3, 5, 2, 9, 8, 4, 7, 6]
[1, 3, 2, 5, 9, 8, 4, 7, 6]
[1, 2, 3, 5, 9, 8, 4, 7, 6]
[1, 2, 3, 5, 8, 9, 4, 7, 6]
[1, 2, 3, 4, 5, 8, 9, 7, 6]
[1, 2, 3, 4, 5, 7, 8, 9, 6]
[1, 2, 3, 4, 5, 6, 7, 8, 9]
直接插入排序（改进后）：
[5, 9, 3, 1, 2, 8, 4, 7, 6]
[5, 9, 3, 1, 2, 8, 4, 7, 6]
[3, 5, 9, 1, 2, 8, 4, 7, 6]
[1, 3, 5, 9, 2, 8, 4, 7, 6]
[1, 2, 3, 5, 9, 8, 4, 7, 6]
[1, 2, 3, 5, 8, 9, 4, 7, 6]
[1, 2, 3, 4, 5, 8, 9, 7, 6]
[1, 2, 3, 4, 5, 7, 8, 9, 6]
[1, 2, 3, 4, 5, 6, 7, 8, 9]
简单选择排序：
[1, 9, 3, 5, 2, 8, 4, 7, 6]
[1, 2, 3, 5, 9, 8, 4, 7, 6]
[1, 2, 3, 4, 9, 8, 5, 7, 6]
[1, 2, 3, 4, 5, 8, 9, 7, 6]
[1, 2, 3, 4, 5, 7, 9, 8, 6]
[1, 2, 3, 4, 5, 6, 9, 8, 7]
[1, 2, 3, 4, 5, 6, 7, 8, 9]
[1, 2, 3, 4, 5, 6, 7, 8, 9]
[1, 2, 3, 4, 5, 6, 7, 8, 9]
冒泡排序：
[5, 3, 1, 2, 8, 4, 7, 6, 9]
[3, 1, 2, 5, 4, 7, 6, 8, 9]
[1, 2, 3, 4, 6, 7, 5, 8, 9]
[1, 2, 3, 4, 6, 5, 7, 8, 9]
[1, 2, 3, 4, 5, 6, 7, 8, 9]
[1, 2, 3, 4, 5, 6, 7, 8, 9]
[1, 2, 3, 4, 5, 6, 7, 8, 9]
[1, 2, 3, 4, 5, 6, 7, 8, 9]

希望这能够帮助到你！