#堆排序#基本思想：1.将初始待排序数字列表(R1,R2,...,Rn)构建成大顶堆，此堆为初始的无序列表# 2.将堆顶元素R1与最后一个元素Rn交换，此时得到新的无序列表(R1,R2,...,Rn-1)和新的有序列表(Rn)# 3.由于交换后新的堆顶R1可能违反堆的性质，因此需要对当前无序列表(R1,R2,...,Rn-1)调整为新堆，# 然后再次将R1与无序列表最后一个元素交换，得到新的无序列表(R1,R2,...,Rn-2)和新的有序列表(Rn-1,Rn).# 不断重复此过程直到有序列表的元素个数为n-1，则整个排序过程完成。#sift_down通过从下而上比较每个节点与其子节点的大小（Ri<R2i,Ri<R2i+1）,将最大的数放置到堆顶def sift_down(numList, start, end): root = start while True: child = 2 * root + 1 if child >end: break if child + 1 <=end and numList[child] < numList[child+1]: child += 1 if numList[root] < numList[child]: numList[root], numList[child] = numList[child], numList[root] root = child else: breakdef heap_sort(numList): #将初始列表组成大顶堆 first = len(numList) // 2 - 1 for start in reversed(range(0, first+1)): sift_down(numList, start, len(numList)-1) print(numList) #将最大的数放置到最后，对前n-1个元素进行堆调整 for end in range(len(numList)-1, 0, -1): numList[0], numList[end] = numList[end], numList[0] sift_down(numList, 0, end-1) print(numList) return numListprint(heap_sort([16, 7, 3,20,17,8,99,76]))# [99, 76, 16, 20, 17, 8, 3, 7]# [76, 20, 16, 7, 17, 8, 3, 99]# [20, 17, 16, 7, 3, 8, 76, 99]# [17, 8, 16, 7, 3, 20, 76, 99]# [16, 8, 3, 7, 17, 20, 76, 99]# [8, 7, 3, 16, 17, 20, 76, 99]# [7, 3, 8, 16, 17, 20, 76, 99]# [3, 7, 8, 16, 17, 20, 76, 99]# 归并排序：# 基本思想：首先归并排序使用了二分法，归根到底的思想还是分而治之。拿到一个长数组，将其不停的分为左边和右边两份，# 然后以此递归分下去。然后再将她们按照两个有序数组的样子合并起来。# 举例[4,7,8,3,5,9]# 第一步：分：[4,8,7] [3,9,5] ->[4,8] [7] [3,9] [5] -> [4] [8] [7] [3] [9] [5]# 第二步：并：[4,8] [7] [3,9] [5] ->[4,7,8] [3,5,9] -> [3,4,5,7,8,9]def merge(a,b):#此时a和b都为已经排序好的列表 c = [] h = j = 0 while j<len(a) and h<len(b):#依次比较直到a或b的元素被全部排完 if a[j]<b[h]: c.append(a[j]) j+=1 else: c.append(b[h]) h+=1 if j==len(a): #当a里的元素全部排完了，将b里剩下的元素依次排入c for i in b[h:]: c.append(i) else: #当b里的元素全部排完了，将a里剩下的元素依次排入c for i in a[j:]: c.append(i) return c#递归法def mergesort(numList): print(numList) if len(numList) <= 1: return numList middle = len(numList) / 2 left = mergesort(numList[:middle]) right = mergesort(numList[middle:]) return merge(left, right)print(mergesort([1,2,-1,8,6,7,-2]))# [1, 2, -1, 8, 6, 7, -2]# [1, 2, -1]# [1]# [2, -1]# [2]# [-1]# [8, 6, 7, -2]# [8, 6]# [8]# [6]# [7, -2]# [7]# [-2]#遍历法def mergesort1(numList): lenList = len(numList) while lenList>1: newList = [] if lenList % 2 == 0: for i in range(lenList/2): a = [numList[2*i]] if type(numList[2*i]) == int else numList[2*i] b = [numList[2*i+1]] if type(numList[2*i+1]) == int else numList[2*i+1] newList.append(merge(a, b)) numList = newList lenList = len(numList) else: for i in range(lenList/2): a = [numList[2 * i]] if type(numList[2*i]) == int else numList[2 * i] b = [numList[2 * i + 1]] if type(numList[2*i+1]) == int else numList[2 * i + 1] newList.append(merge(a, b)) last = [numList[-1]] if type(numList[-1]) == int else numList[-1] newList.append(last) numList = newList lenList = len(numList) print(newList) print(lenList) return numList[0]#print(mergesort1([1,2,-1,8,7,6,-2]))print(mergesort1([1,2,-1,8,6,7,-2,-13,58,30,-15,18]))# [[1, 2], [-1, 8], [6, 7], [-2]]# 4# [[-1, 1, 2, 8], [-2, 6, 7]]# 2# [[-2, -1, 1, 2, 6, 7, 8]]# 1# [-2, -1, 1, 2, 6, 7, 8]#希尔排序（在直接插入排序的基础上加上间隔）#基本思想：1.定义步长序列t为[k,...,1]# 2.按照步长序列个数k，对排序队列进行k趟排序# 3.每趟排序，根据对应的步长ti，将待排序列分割成ti个子序列，分别对# 各个子序列进行直接插入排序。def insertsort(numList): leng = len(numList) gap = leng while(gap>1): gap = gap // 2 print(gap) for i in range(gap,leng): if numList[i] < numList[i-gap]: midnum = numList[i] j=i-gap while numList[j] >midnum and j >= 0: numList[j+gap] = numList[j] j -=gap numList[j + gap] = midnum print(numList) return numListprint(insertsort([1,2,-1,8,6,7,-2,-13]))
[1,2,-1,8,6,7,-2,-13]
# 间隔为4# [1, 2, -1, 8, 6, 7, -2, -13]# [1, 2, -1, 8, 6, 7, -2, -13]# [1, 2, -2, 8, 6, 7, -1, -13]# [1, 2, -2, -13, 6, 7, -1, 8]# 间隔为2# [-2, 2, 1, -13, 6, 7, -1, 8]# [-2, -13, 1, 2, 6, 7, -1, 8]# [-2, -13, 1, 2, 6, 7, -1, 8]# [-2, -13, 1, 2, 6, 7, -1, 8]# [-2, -13, -1, 2, 1, 7, 6, 8]# [-2, -13, -1, 2, 1, 7, 6, 8]# 间隔为1# [-13, -2, -1, 2, 1, 7, 6, 8]# [-13, -2, -1, 2, 1, 7, 6, 8]# [-13, -2, -1, 2, 1, 7, 6, 8]# [-13, -2, -1, 1, 2, 7, 6, 8]# [-13, -2, -1, 1, 2, 7, 6, 8]# [-13, -2, -1, 1, 2, 6, 7, 8]# [-13, -2, -1, 1, 2, 6, 7, 8]
来源：https://www.cnblogs.com/xhw19950606/p/12301081.html