81. search rotation sort array II

after A spin Find the given value in an ordered array of , And there may be repeat Elements . The difficulty here is that there may be repeating elements , It makes it difficult to judge the position of the rotation point . If there are no repeating elements , Then just compare left, mid, right Three position values , You can determine which half the rotation point is on .

Ideas

1. Try to find the point of rotation

First , To try to find the rotation point in this array , Divide the entire array into left and right sides , And then determine :

1. Can you confirm that the rotation point is on the left half ？
2. Can you confirm that the rotation point is on the right half ？
3. If you can't be sure on the left half / Right half , that l++.

How to determine the rotation point ？ Remember a trick : When reverse order occurs at both ends of the interval , Represents that the rotation point is inside the interval .
When nums[left] > nums[mid] when , The point of rotation must be on the left half , Why? ？ Because the reverse order appears on the left half , Then there is at least one rotation point on the left side . There is at most one rotation point in the array , So the right side must be sequential .

Empathy , When nums[mid] > nums[right] when , The point of rotation must be on the right half .

Why is it only when there is a reverse order between the endpoint and the midpoint , To determine that the rotation point is sitting in the half zone ？ because Only in reverse order , To determine that there is a rotation point in this interval , If