Problem description:

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.

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Example 1:

Input: nums = [2,5,6,0,0,1,2], target = 0
Output: true

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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:

1) everytime check if target == nums[mid], if so, we find it.
2) otherwise, we check if the first half is in order (i.e. nums[left]<=nums[mid])
and if so, go to step 3), otherwise, the second half is in order, go to step 4)
3) check if target in the range of [left, mid-1] (i.e. nums[left]<=target < nums[mid]), if so, do search in the first half, i.e. right = mid-1; otherwise, search in the second half left = mid+1;
4) check if target in the range of [mid+1, right] (i.e. nums[mid]<target <= nums[right]), if so, do search in the second half, i.e. left = mid+1; otherwise search in the first half right = mid-1;

The only difference is that due to the existence of duplicates, we can have nums[left] == nums[mid] and in that case, the first half could be out of order (i.e. NOT in the ascending order, e.g. [3 1 2 3 3 3 3]) and we have to deal this case separately. In that case, it is guaranteed that nums[right] also equals to nums[mid], so what we can do is to check if nums[mid]== nums[left] == nums[right] before the original logic, and if so, we can move left and right both towards the middle by 1. and repeat.

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class Solution:
    def search(self, nums: List[int], target: int) -> bool:
        l, r = 0, len(nums)-1
        while l<= r:
            mid = (r+l)//2
            if nums[mid] == target:
                return True
            
            if nums[l] == nums[mid] and nums[r] == nums[mid]:
                l += 1
                r -= 1
            elif nums[l] <= nums[mid]:
                if nums[l] <= target and nums[mid] > target:
                    r = mid-1
                else:
                    l = mid+1
            else:
                if nums[r] >= target and nums[mid] < target:
                    l = mid+1
                else:
                    r = mid-1
        return False
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class Solution {
public:
    bool search(vector<int>& nums, int target) {
        int left = 0, right =  nums.size()-1, mid;
        
        while(left<=right)
        {
            mid = (left + right) >> 1;
            if(nums[mid] == target) return true;

            // the only difference from the first one, trickly case, just updat left and right
            if( (nums[left] == nums[mid]) && (nums[right] == nums[mid]) ) {++left; --right;}

            else if(nums[left] <= nums[mid])
            {
                if( (nums[left]<=target) && (nums[mid] > target) ) right = mid-1;
                else left = mid + 1; 
            }
            else
            {
                if((nums[mid] < target) &&  (nums[right] >= target) ) left = mid+1;
                else right = mid-1;
            }
        }
        return false;
    }
};