ef fib(n):
""" 递归：时间复杂度O(2**n),空间复杂度O(N),树的高度"""
if n < 3:
return 1
else:
return fib(n - 1) + fib(n - 2)
# fib(6)=fib(5)+fib(4)
# 1,1,2,3,5,8
def fib2(n):
""" 循环：时间复杂度O(N),空间复杂度O(1)"""
a,b =0,1
for x in range(n):
a,b = b,a+b
return b
def fib_while(n):
""" 循环：T=O(N),S=O(1)"""
a,b=0,1
i=1
while i<=n :
print(b,end=" ")
i =i+1
a,b =b,a+b
# 二分法：
s = list(range(1,10))
def bin_search(arr,x):
l,r = 0,len(arr)-1
# 左边小于右边
while l <=r :
mid = (l + r )// 2
if x < arr[mid]:
r = mid -1
elif x > arr[mid]:
l = mid +1
else :
return mid
return False
# 左大于右边
def bin_search_recur(arr,x):
k = len(arr)
if k<1:
return False
mid = k//2
if x< arr[mid]:
return bin_search_recur(arr[:mid-1],x)
elif x> arr[mid]:
return bin_search_recur(arr[mid+1:],x)
else :
return True
def insert_sort(arr):
for j in range(1,len(arr)):
# j-1,j =3,1
while arr[j] < arr[j-1]:
temp = arr[j - 1]
arr[j-1] = arr[j]
arr[j] =temp
j =j-1
return arr
def bin_x(arr,x):
mid =len(arr)// 2
if x< arr[mid]:
bin_x(arr[:mid-1],x)
elif x > arr[mid]:
bin_x(arr[mid+1:],x)
else:
return mid
def bin_whiles(arr,x):
"""
:param arr:
:param x:
:return: mid index 索引
"""
l,r = 0 ,len(arr)-1
while l<=r:
mid = (l+r)// 2
if x< arr[mid] :
r = mid-1
elif x> arr[mid] :
l =mid +1
else :
return mid
def quick_sort(arr):
"""快速排序"""
if len(arr) < 2:
return arr
# 选取基准，随便选哪个都可以，选中间的便于理解
mid = arr[len(arr) // 2]
# 定义基准值左右两个数列
left, right = [], []
# 从原始数组中移除基准值
arr.remove(mid)
for item in arr:
# 大于基准值放右边
if item >= mid:
right.append(item)
else:
# 小于基准值放左边
left.append(item)
# 使用迭代进行比较
return quick_sort(left) + [mid] + quick_sort(right)
def sr(arr):
""" T= nlog(N),S= nlog(N)"""
if len(arr)<2:
return arr
mid =arr[len(arr) // 2]
arr.remove(mid)
l,r = [],[]
for k in arr:
if k >= mid:
r.append(k)
else:
l.append(k)
return sr(l)+[mid]+sr(r)
def hashT(arr,const=10):
hashMap={}
for x in range(len(arr)):
y = const-arr[x]
# 在hash表值，y 对应的索引不等于
if y in arr and hashMap.get(y) != arr[x]:
print(arr[x],x,y,arr.index(y))
hashMap[arr[x]]=y
print(hashMap)
# for x in range(len(arr)):
# y = const-arr[x]
# # 在hash表值，且在arr,不等于自己
# if y in hashMap.values() and y !=x and y in arr:
# print(arr[x],y)
if __name__ == '__main__':
s= [5,1,6,3,7,1,4,5]
print(insert_sort(s))
