快速排序的两种实现 -- 种轴partition ： 比值partition(更精巧)

实现1：种轴partition，not in place--取定枢轴，将小于等于枢轴的放到枢轴左边，大于枢轴的放到右边

# python algorithm en_2nd edition p125
def partition_mlh(arr):
#     3-partition, use extra place
    pt, seq = arr[0], arr[1:]
    lt = [x for x in seq if x <= pt ]
    rt = [x for x in seq if x > pt]
    return lt, pt, rt

def qsort_mlh(arr):
    if len(arr) <= 1: return arr
    lt, pt, rt = partition_mlh(arr)
    return qsort_mlh(lt) + [pt] + qsort_mlh(rt)

实现2：种轴partition，in place--取出枢轴，将小于等于枢轴的放到枢轴左边，大于枢轴的放到右边

def partition_dfq(arr, stt, end):
    lt, rt = stt, end - 1　　# for [stt, end)
    pvt = arr[lt]   
    
    while lt < rt:
        while lt < rt and arr[rt] >= pvt: rt -= 1
        arr[lt] = arr[rt]
        while lt < rt and arr[lt] < pvt: lt += 1
        arr[rt] = arr[lt]
    arr[lt] = pvt   # 种轴partition
    return lt

def qsort_dfq(arr, stt, end):　　# for [stt, end)
#     if len(arr) <= 1: return arr
    if end - stt < 2: return arr
    pvt = partition_dfq(arr, stt, end)
    qsort_dfq(arr, stt, pvt)
    qsort_dfq(arr, pvt + 1, end)
    return arr

实现3：比值partition，in place--以某个值为参考，大于该值的向右移，小于该值的向左移，等于该值的可能左移or右移

def qsort_zxh(arr, beg, end):　　#[beg, end]
#     assert(len(arr) > 0 and beg >= 0 and end > beg and end < len(arr))
    lt, rt = beg, end
    pvt = arr[lt + (rt - lt)//2]
#    pvt = arr[lt + random.randint(0, rt - lt)]

while lt < rt:
        while arr[lt] < pvt and lt < end: lt += 1   # lt < end 可以写在后面
        while arr[rt] > pvt and rt > beg: rt -= 1
        if lt <= rt:
            arr[lt], arr[rt] = arr[rt], arr[lt]
            lt, rt = lt + 1, rt - 1

if lt < end: qsort_zxh(arr, lt, end)
    if rt > beg: qsort_zxh(arr, beg, rt)
    return arr