计数排序、基数排序及桶排序

计数排序思想：

　　对每一个元素，确定小于其的元素个数，利用这一信息即可将其放入正确的位置。

计数排序时间复杂度：Θ(n)

计数排序示例：

from random import randint

def counting_sort(a,b,max_number):
    #用于记录各元素出现次数
    c = []
    for i in range(max_number+1):
        c.append(0)
    for number in a:
        c[number] += 1
    for i in range(1,max_number+1):
        c[i] += c[i-1]
    for number in a[::-1]:
        b[c[number]-1] = number
        c[number] -= 1
    return b

def main(args):
    a = []
    b = []
    for i in range(100):
        a.append(randint(0,100))
        b.append(0)
    print(a)
    print(counting_sort(a,b,max(a)))
    return 0

if __name__ == '__main__':
    import sys
    sys.exit(main(sys.argv))

基数排序思想：

　　对欲排序数组按最低有效位（即数字的最后一位）进行排序，之后，用同样的方法对次低有效位进行排序，重复该过程直至所有位数都已排好序。

基数排序时间复杂度：Θ(n)

示例代码：

from random import randint
import copy

def counting_sort(a,max_number):
    c = []
    b = []
    for i in range(len(a)):
        b.append(a[i])
    for i in range(max_number+1):
        c.append(0)
    for numbers in a:
        c[numbers.b] += 1
    for i in range(1,max_number+1):
        c[i] += c[i-1]
    #利用某一位数进行排序
    for numbers in a[::-1]:
        b[c[numbers.b]-1] = numbers
        c[numbers.b] -= 1
    return b
        
    
def radix_sort(a,d):
    c = []
    for i in range(len(a)):
        c.append(Numbers(a[i],0))
    for index in range(1,d+1):
        b = [] 
        for i in range(len(a)): 
            #得到某一位数的值
            b.append((c[i].a % (10 ** index))//(10 ** (index - 1)))
            c[i].b = b[i]
        c = counting_sort(c,9)
    for i in range(len(a)):
        a[i] = c[i].a

#用于储存每个数的值与其某一位数的值            
class Numbers():
    def __init__(self,a,b):
        self.a = a
        self.b = b
    
def main(args):
    a = []
    for i in range(10):
        a.append(randint(0,10000))
    print(a)
    radix_sort(a,4)
    print(a)
    return 0

if __name__ == '__main__':
    import sys
    sys.exit(main(sys.argv))

桶排序思想：

　　将[0,1)区间划分为n个大小相同的子区间，然后将欲排序数组分别放到各个桶中。之后对每个桶进行排序。

桶排序的期望时间复杂度：Θ(n)

示例代码：

from random import random
from random import randint

def quick_sort(a,i,j):
    if i < j:
        q = randomized_partition(a,i,j)
        quick_sort(a,i,q-1)
        quick_sort(a,q+1,j)
    
def randomized_partition(a,i,j):
    ret = i - 1
    int_random = randint(i,j)
    tmp = a[j]
    a[j] = a[int_random]
    a[int_random] = a[j]
    for k in range(j-i):
        if a[i+k] < a[j]:
            ret += 1
            tmp = a[i+k]
            a[i+k] = a[ret]
            a[ret] = tmp
    ret += 1
    tmp = a[j]
    a[j] = a[ret]
    a[ret] = tmp
    return ret

def bucket_sort(a):
    #b为列表，储存各个区间的值
    b = []
    for i in range(len(a)):
        tmp = []
        b.append(tmp)
    for number in a:
        b[int((len(a)-1) * number)].append(number)
    #划分完毕后利用快排对每个桶进行排序
    for list_b in b:
        quick_sort(list_b,0,len(list_b)-1)
    i = 0
    for list_b in b:
        for number in list_b:
            a[i] = number
            i += 1


def main(args):
    a = []
    for i in range(100):
        a.append(round(random(),2))
    print(a)
    bucket_sort(a)
    print(a)
    return 0

if __name__ == '__main__':
    import sys
    sys.exit(main(sys.argv))