python-快速排序

核心思想：取一个初始值，将数组中比该值小的放在其左边，比其大的放在右边， 再对左、右子数组进行相同操作，直到数组排好序。

def quicksort(nums):
    l = 0
    r = len(nums) - 1
    _quicksort(nums,l,r)
def _quicksort(nums,l,r):
    if l < r:
        p = partition(nums,l,r)
        _quicksort(nums,l,p-1)
        _quicksort(nums,p+1,r)
def partition(nums,l,r):
    base = nums[l]
    j = l+1
    for i in range(l+1,r+1):
        if nums[i]<base:
            nums[i],nums[j]=nums[j],nums[i]
            j+=1
    nums[l],nums[j-1]=nums[j-1],nums[l]
    return j-1

nums = [6,2,5,3,4,8,1,7]
quicksort(nums)
print(nums)

改进：随机选择初始值，避免数组有序使算法退化。从两边开始遍历，减少遍历时间。

import random
def quicksort(nums):
    l = 0
    r = len(nums) - 1
    _quicksort(nums,l,r)
def _quicksort(nums,l,r):
    if l < r:
        p = partition(nums,l,r)
        _quicksort(nums,l,p-1)
        _quicksort(nums,p+1,r)
def partition(nums, l, r):
    ind = random.randint(l, r)
    nums[l], nums[ind] = nums[ind], nums[l]
    base = nums[l]
    i, j = l+1, r
    while True:
        while i <= r and nums[i] < base:  # 不能改为nums[i] <= base          
            i += 1
        while j >= l + 1 and nums[j] > base:  # 不能改为nums[j] >= base.
            j -= 1
        if i > j:
            break
        else:
            nums[i], nums[j] = nums[j], nums[i]
            i += 1
            j -= 1
    nums[j], nums[l] = nums[l], nums[j]
    return j

nums = [6,2,5,3,4,8,1,7]
quicksort(nums)
print(nums)

改进：三路快排，用于解决数组中有较多重复的值。

import random
def quicksort(nums):
    l = 0
    r = len(nums) - 1
    _quicksort(nums,l,r)
def _quicksort(nums,l,r):
    if l < r:
        lt,gt = partition(nums,l,r)
        _quicksort(nums,l,lt-1)
        _quicksort(nums,gt,r)
def partition(nums, l, r):
    ind = random.randint(l, r)
    nums[l], nums[ind] = nums[ind], nums[l]
    base = nums[l]
    lt = l  # nums[l+1...lt] < base
    gt = r + 1  # nums[gt...r] > base
    i = l + 1  # nums[lt+1...i] == base
    while (i < gt):
        # i==gt时表示已经比较结束
        if (nums[i] < base):
            nums[i], nums[lt+1] = nums[lt+1], nums[i]
            lt += 1
            i += 1
        elif (nums[i] > base):
            nums[i], nums[gt-1] = nums[gt-1], nums[i]
            gt -= 1
        else:  # nums[i] == base
            i += 1
    nums[l], nums[lt] = nums[lt], nums[l]
    return lt, gt

nums = [6,2,5,3,4,8,1,7]
quicksort(nums)
print(nums)