def counting_sort(a, k):
    """ k為a數(shù)組中的最大值 """

    # 構(gòu)造臨時緩存數(shù)組c
    c = [0 for _ in range(k + 1)]

    # 初始化結(jié)果數(shù)組b
    b = [0 for _ in range(len(a))]

    # c[a[j]] 表示的是，a[j]元素的數(shù)值在c中有對應(yīng)的下標(biāo)數(shù)值，則加1
    # c數(shù)組中的元素代表對應(yīng)下標(biāo)數(shù)字在a數(shù)組中存在的個數(shù)
    # c = [0, 0, 0]   a = [2, 1, 1]
    # >>> c = [0, 2, 1]
    for n in range(0, len(a)):
        c[a[n]] = c[a[n]] + 1

    # 計(jì)算有多少個元素小于等于c的下標(biāo)元素?cái)?shù)值
    for _ in range(1, k + 1):
        c[_] = c[_] + c[_ - 1]

    # a = [2, 5, 3, 0, 2, 3, 0, 3]
    # c = [2, 2, 4, 7, 7, 8]
    # b[c[a[8]] - 1] = b[c[3] - 1] = b[7 - 1] = a[8] = 3
    # b = [0, 0, 0, 0, 0, 0, 3, 0]
    # b[c[a[7]] - 1] = b[c[0] - 1] = b[2 - 1] = a[7] = 0
    # b = [0, 0, 0, 0, 0, 0, 3, 0]
    # b[c[a[6]] - 1] = b[c[3] - 1] = b[6 - 1] = a[6] = 3
    # b = [0, 0, 0, 0, 0, 3, 3, 0]
    # ...
    for m in range(len(a) - 1, -1, -1):
        b[c[a[m]] - 1] = a[m]
        c[a[m]] = c[a[m]] - 1
    return b

if __name__ == '__main__':
    a = [2, 5, 3, 0, 2, 3, 0, 3]
    print(counting_sort(a, 5))
    # [0, 0, 2, 2, 3, 3, 3, 5]