def _counting_sort(A, B, k):
    """計數排序，偽碼如下：
    COUNTING-SORT(A, B, k)
    1  for i ← 0 to k // 初始化存儲區的值
    2    do C[i] ← 0
    3  for j ← 1 to length[A] // 為各值計數
    4    do C[A[j]] ← C[A[j]] + 1
    5  ▷ C[i]包含等于i的元素個數
    6  for i ← 1 to k // 求計數和，確定<=各值的元素數
    7    do C[i] ← C[i] + C[i-1]
    8  ▷ C[i]包含小于或等于i的元素個數
    9  for j ← length[A] downto 1
    10   do B[C[A[j]]] ← A[j] // 將A[j]值放到對應位置
    11      C[A[j]] ← C[A[j]] - 1 // 避免元素相同時覆蓋同一位置

    T(n) = θ(n)

    Args:
        A (Sequence): 原數組
        B (Sequence): 結果數組
        k (int): 值上限，假定了所有元素介于[0,k]
    """
    len_c = k + 1
    C = [0] * len_c
    for a in A:
        C[a] = C[a] + 1
    for i in range(1, len_c):
        C[i] = C[i] + C[i-1]
    for a in A[::-1]:
        B[C[a]-1] = a
        C[a] = C[a] - 1

def counting_sort(A):
    """假定A數組所有元素都介于[0,len(A)-1]"""
    B = [0] * len(A)
    _counting_sort(A, B, len(A) - 1)
    return B

if __name__ == '__main__':
    import random, timeit

    items = range(10000)
    random.shuffle(items)

    def test_sorted():
        print(items)
        sorted_items = sorted(items)
        print(sorted_items)

    def test_counting_sort():
        print(items)
        sorted_items = counting_sort(items)
        print(sorted_items)

    test_methods = [test_sorted, test_counting_sort]
    for test in test_methods:
        name = test.__name__ # test.func_name
        t = timeit.Timer(name + '()', 'from __main__ import ' + name)
        print(name + ' takes time : %f' % t.timeit(1))