2568. Minimum Impossible OR

Problem

You are given a 0-indexed integer array nums.

We say that an integer x is expressible from nums if there exist some integers 0 <= index1 < index2 < ... < indexk < nums.length for which nums[index1] | nums[index2] | ... | nums[indexk] = x. In other words, an integer is expressible if it can be written as the bitwise OR of some subsequence of nums.

Return **the minimum *positive non-zero integer* that is not ****expressible from **nums.

  Example 1:

Input: nums = [2,1]
Output: 4
Explanation: 1 and 2 are already present in the array. We know that 3 is expressible, since nums[0] | nums[1] = 2 | 1 = 3. Since 4 is not expressible, we return 4.

Example 2:

Input: nums = [5,3,2]
Output: 1
Explanation: We can show that 1 is the smallest number that is not expressible.

  Constraints:

• 1 <= nums.length <= 105

• 1 <= nums[i] <= 109

Solution (Java)

class Solution {
    public int minImpossibleOR(int[] A) {
        Set<Integer> s = new HashSet<>();
        for (int a : A)
            s.add(a);
        int a = 1;
        while (s.contains(a))
            a <<= 1;
        return a;
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).