python算法之递归

#递归思想
#基本原理：函数内部调用函数本身，注意：至少有一个终止条件
#例1.斐波那契数列
def fib(x):
    if x==1 or x==2:
        return 1
    else:
        return fib(x-1) + fib(x-2)
def fibList(x):
    fibList = []
    for i in range(x):
        fibList.append(fib(i+1))
    return fibList
print(fibList(9))

#例2.n的阶乘（n*(n-1)*(n-2)*...2*1）
def jiecheng(n):
    if n==1:
        return 1
    else:
        return n*jiecheng(n-1)
print(jiecheng(4))

#例3.用递归实现二分查找
def binarysearch(numList, x, low, high):
    if low > high:
        return None
    mid = (low + high) // 2
    if x == numList[mid]:
        return mid
    elif x > numList[mid]:
        return binarysearch(numList, x, mid+1, high)
    else:
        return binarysearch(numList, x ,low, mid-1)
numList = [1,2,4,5,6,8,12,24,32,44]
print(binarysearch(numList, 8, 0, len(numList)-1))