def counting_sort(arr):
    """
    Counting_sort
    Sorting a array which has no element greater than k
    Creating a new temp_arr,where temp_arr[i] contain the number of
    element less than or equal to i in the arr
    Then placing the number i into a correct position in the result_arr
    return the result_arr
    Complexity: 0(n)
    """

    m = min(arr)
    # in case there are negative elements, change the array to all positive element
    different = 0
    if m < 0:
        # save the change, so that we can convert the array back to all positive number
        different = -m
        for i in range(len(arr)):
            arr[i] += -m
    k = max(arr)
    temp_arr = [0] * (k + 1)
    for i in range(0, len(arr)):
        temp_arr[arr[i]] = temp_arr[arr[i]] + 1
    # temp_array[i] contain the times the number i appear in arr

    for i in range(1, k + 1):
        temp_arr[i] = temp_arr[i] + temp_arr[i - 1]
    # temp_array[i] contain the number of element less than or equal i in arr

    result_arr = arr.copy()
    # creating a result_arr an put the element in a correct positon
    for i in range(len(arr) - 1, -1, -1):
        result_arr[temp_arr[arr[i]] - 1] = arr[i] - different
        temp_arr[arr[i]] = temp_arr[arr[i]] - 1

    return result_arr