数据结构之排序算法

快速排序

应该是数据结构中排序中最重要的一个，包括其中的patition思想，以及后面的整体的分治思想，都对于解决实际问题有很大的借鉴。快速排序是一种交换排序的方法，不稳定，也就是说如果两个相同的数，快排之后二者可能交换位置。

1.首先来看partition函数，函数名partition(data, l, r)，在data[l,r]中找到第l个数的位置i，使得i左侧的数都小于该数，i右侧的数都大于该数，并返回位置i

def partition(data, l, r):
	i = l
	j = r
	x = data[i]
	while i<j:
		while i<j&data[j]>x:
			j -= 1
		if i<j:
			data[i] = data[j]
			i += 1
		while i<j&data[i]<x:
			i += 1
		if i<j:
			data[j] = data[i]
			j -= 1
	data[i] = x
	return i

2.然后对整个数组分治递归操作即可

def qsort(data, l, r):
	if l<r:
		i = partition(data, l, r)
		qsort(data, l, i-1)
		qsort(data, i+1, r)
	
	
def quicksort(data):
	qsort(data, 0, len(data)-1)

 

归并排序：

def mergearray(nums, first, mid, last):
    tmp = []
    mid2 = mid + 1
    k = 0
    while first<=mid and mid2<=last:
        if nums[first]<nums[mid2]:
            tmp[k] = nums[first]
            first += 1
        else:
            tmp[k] = nums[mid2]
            mid2 += 1
        k += 1
    while  first<=mid:
        tmp[k] = nums[first]
        first += 1
        k += 1
    while mid2<=last:
        tmp[k] = nums[mid2]
        mid2 += 1
        k += 1
    for i in range(k):
        nums[first+i] = tmp[i]


def mergesort(nums, first, last):
    if first<last:
        mid = first + (last-first)/2
        mergesort(nums,first, mid)
        mergesort(nums, mid+1, last)
        mergearray(nums, first, mid, last)

def msort(nums):
    mergesort(nums, 0, len(nums)-1)

　　

堆排序

def heapAdjust(nums, i):
    lchild = 2*i+1
    rchild = 2*i+2
    max = i
    if i <= len(nums)/2:
        if lchild<=len(nums) and nums[lchild]>nums[max]:
            max = lchild
        if rchild<=len(nums) and nums[rchild]>nums[max]:
            max = rchild
    if max != i:
        nums[max], nums[i] = nums[i], nums[max]

def buildHeap(nums):
    i = len(nums)/2
    while i >=0:
        heapAdjust(nums,i)

def headSort(nums):
    buildHeap(nums)
    i = len(nums) - 1
    while i>=0:
        nums[i], nums[0] = nums[0], nums[i]
        heapAdjust(nums[:-1],0)