insertion mergesort bubble sort 复习 python

最近重新开始复习算法那本书，整理了一下关于insertion mergesort以及 divide and conquer的思路

insertion sort is O(n^2)  best case when it is already sorted it will be O(n) worse case is the array is reversed sorted.

the main idea is we put an iterator in the array and make sure everything infront of the iterator is sorted.

for index in range(1,len(array)): 

key=arrray[index]

j=index

while j>0 and array[j-1]>key://如果比当前的大就往后移动，得到的是递增的序列

array[j]=array[j-1]

j-=1

array[index]=key

def insertion(num):    for index in range(1,len(num)):        key=num[index]        j=index        while j>0 and num[j-1]>key:            num[j]=num[j-1]            j-=1        num[j]=key

关于mergesort的思路是将整个array每次除以2往下分，直到长度为1，然后依次排列 

所以整个array可以分成

n

n/2 n/2

n/4 n/4 n/4 n/4

.....一共log(n)层

每层排列需要n次运算因此为nlogn

def mergesort(num):    if len(num)==1:        return num    def merge(left,right):        merged=[]        while left and right:            merged.append(left.pop(0) if left[0]<=right[0] else right.pop(0))        while left:            merged.append(left.pop(0))        while right:            merged.append(right.pop(0))        return merged    mid=len(num)/2    left=mergesort(num[:mid])    right=mergesort(num[mid:])    return merge(left,right)

除此以外bubble sort是最最基本的算法。

就不具体阐述了。

def bubble(num):    for i in range(len(num)-1):        for j in range(len(num)-i-1):            if num[j+1]>num[j]:                num[j+1],num[j]=num[j],num[j+1]    return num

radix sort.

def radixsort(num):    radix=10    tmp,placement=-1,1    maxlen=False    while not maxlen:        maxlen=True        buckets=[list() for _ in range(radix)]        for i in num:            tmp=i/placement            buckets[tmp%radix].append(i)            if maxlen and tmp>0:                maxlen=False        a=0        for b in range(radix):            buck=buckets[b]            for i in buck:                num[a]=i                a+=1        placement*=radix    print numdef main():    num=[18,5,100,3,1,19,6,0,7,4,2]    radixsort(num)    print numif __name__=="__main__":    main()

heap sort

def siftdown(a,start,end):    root=start    while 2*root+1<end:        child = 2*root+1        if child+1<=end and a[child]<a[child+1]:            child+=1        if a[root]<a[child]:            a[root],a[child]=a[child],a[root]            root=child        else:            returndef heapify(a):    start=(len(a)-2)/2    while start>=0:        siftdown(a,start,len(a)-1)        start-=1    end=len(a)-1    while end>0:        a[end],a[0]=a[0],a[end]        end-=1        siftdown(a,0,end)    return adef main():    num=[8,1,2,9,11,10,4,5,100]        print heapify(num)if __name__=="__main__":    main()