81 Search in Rotated Sorted Array II

def search(self,num,target):
        if len(num) == 0:
            return False
        lef,rig,start_index,end_index = 0,len(num)-1,0,0
        if target == num[0] or target == num[len(num)-1]:
            return True
        elif target < num[0] and target > num[len(num)-1]:
            return False
        #find the turning point !
        while lef+1 < len(num) and num[lef] <= num[lef+1]:
            lef += 1
        #there might not have the turning point !
        if lef+1 == len(num):
            start_index,end_index = 0,lef
        #we found the turning point !
        elif num[lef] > num[lef+1]:
            if target > num[0]:
                start_index,end_index = 0,lef
            elif target < num[len(num)-1]:
                start_index,end_index = lef+1,len(num)-1
        #let start_index and end_index be sorted array leftmost and rightmost position, we use binary search to solve !
        while start_index <= end_index:
            middle_index = int((start_index+end_index)/2)
            if target == num[middle_index]:
                return True
            elif target > num[middle_index]:
                start_index = middle_index + 1
            else:
                end_index = middle_index - 1
        return False