Problem
Suppose an array sorted in ascending order is rotated at some pivot unknown to you beforehand.
(i.e., [0,0,1,2,2,5,6] might become [2,5,6,0,0,1,2]).
You are given a target value to search. If found in the array return true, otherwise return false.
Example 1:
Input: nums = [2,5,6,0,0,1,2], target = 0
Output: true
Example 2:
Input: nums = [2,5,6,0,0,1,2], target = 3
Output: false
Follow up:
This is a follow up problem to Search in Rotated Sorted Array, where nums may contain duplicates.
Would this affect the run-time complexity? How and why?
Solution
Note:
Consider the problem in two part:
- when the left part is in order
- when the right part is in order
Important: How to guarentee the left part is in order when there is duplicates in the array:
We can use a while to eliminate the duplicates if nums[left] == nums[mid]
class Solution:
def search(self, nums: List[int], target: int) -> bool:
if not nums:
return False
left = 0
right = len(nums) - 1
while left < right:
mid = (left + right) // 2
if nums[mid] == target:
return True
while left < mid and nums[left] == nums[mid]:
left += 1
if nums[mid] >= nums[left]:
if nums[mid] > target >= nums[left]:
right = mid - 1
else:
left = mid + 1
else:
if nums[mid] < target <= nums[right]:
left = mid + 1
else:
right = mid - 1
print(left, right)
return target == nums[left]