minimum-impossible-or

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Algorithms

You are given a 0-indexed&nbsp;integer array <code>nums</code>.

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

Return the minimum positive non-zero integer&nbsp;that is not expressible from <code>nums</code>.

&nbsp;
Example 1:

<pre>
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.
</pre>

Example 2:

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

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= nums.length &lt;= 105</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 109</code></li>
</ul>

minImpossibleOR

Minimum Impossible OR

Bit Manipulation

Brainteaser

Array

给你一个下标从 0&nbsp;开始的整数数组&nbsp;<code>nums</code>&nbsp;。

如果存在一些整数满足&nbsp;<code>0 &lt;= index1 &lt; index2 &lt; ... &lt; indexk &lt; nums.length</code>&nbsp;，得到&nbsp;<code>nums[index1] | nums[index2] | ... | nums[indexk] = x</code>&nbsp;，那么我们说&nbsp;<code>x</code>&nbsp;是&nbsp;可表达的&nbsp;。换言之，如果一个整数能由&nbsp;<code>nums</code>&nbsp;的某个子序列的或运算得到，那么它就是可表达的。

请你返回 <code>nums</code>&nbsp;不可表达的 最小非零整数&nbsp;。

&nbsp;

示例 1：

<pre>输入：nums = [2,1]
输出：4
解释：1 和 2 已经在数组中，因为 nums[0] | nums[1] = 2 | 1 = 3 ，所以 3 是可表达的。由于 4 是不可表达的，所以我们返回 4 。
</pre>

示例 2：

<pre>输入：nums = [5,3,2]
输出：1
解释：1 是最小不可表达的数字。
</pre>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= nums.length &lt;= 105</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 109</code></li>
</ul>