largest-combination-with-bitwise-and-greater-than-zero

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Algorithms

The bitwise AND of an array <code>nums</code> is the bitwise AND of all integers in <code>nums</code>.

<ul>
	<li>For example, for <code>nums = [1, 5, 3]</code>, the bitwise AND is equal to <code>1 &amp; 5 &amp; 3 = 1</code>.</li>
	<li>Also, for <code>nums = [7]</code>, the bitwise AND is <code>7</code>.</li>
</ul>

You are given an array of positive integers <code>candidates</code>. Compute the bitwise AND for all possible combinations of elements in the <code>candidates</code> array.

Return the size of the largest combination of <code>candidates</code> with a bitwise AND greater than <code>0</code>.

&nbsp;
Example 1:

<pre>
Input: candidates = [16,17,71,62,12,24,14]
Output: 4
Explanation: The combination [16,17,62,24] has a bitwise AND of 16 &amp; 17 &amp; 62 &amp; 24 = 16 &gt; 0.
The size of the combination is 4.
It can be shown that no combination with a size greater than 4 has a bitwise AND greater than 0.
Note that more than one combination may have the largest size.
For example, the combination [62,12,24,14] has a bitwise AND of 62 &amp; 12 &amp; 24 &amp; 14 = 8 &gt; 0.
</pre>

Example 2:

<pre>
Input: candidates = [8,8]
Output: 2
Explanation: The largest combination [8,8] has a bitwise AND of 8 &amp; 8 = 8 &gt; 0.
The size of the combination is 2, so we return 2.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= candidates.length &lt;= 105</code></li>
	<li><code>1 &lt;= candidates[i] &lt;= 107</code></li>
</ul>

largestCombination

Largest Combination With Bitwise AND Greater Than Zero

Count Number of Maximum Bitwise-OR Subsets

count-number-of-maximum-bitwise-or-subsets

统计按位或能得到最大值的子集数目

Bit Manipulation

Array

Hash Table

Counting

对数组&nbsp;<code>nums</code> 执行 按位与 相当于对数组&nbsp;<code>nums</code> 中的所有整数执行 按位与 。

<ul>
	<li>例如，对 <code>nums = [1, 5, 3]</code> 来说，按位与等于 <code>1 &amp; 5 &amp; 3 = 1</code> 。</li>
	<li>同样，对 <code>nums = [7]</code> 而言，按位与等于 <code>7</code> 。</li>
</ul>

给你一个正整数数组 <code>candidates</code> 。计算 <code>candidates</code> 中的数字每种组合下 按位与 的结果。

返回按位与结果大于 <code>0</code> 的 最长 组合的长度。

&nbsp;

示例 1：

<pre>
输入：candidates = [16,17,71,62,12,24,14]
输出：4
解释：组合 [16,17,62,24] 的按位与结果是 16 &amp; 17 &amp; 62 &amp; 24 = 16 &gt; 0 。
组合长度是 4 。
可以证明不存在按位与结果大于 0 且长度大于 4 的组合。
注意，符合长度最大的组合可能不止一种。
例如，组合 [62,12,24,14] 的按位与结果是 62 &amp; 12 &amp; 24 &amp; 14 = 8 &gt; 0 。
</pre>

示例 2：

<pre>
输入：candidates = [8,8]
输出：2
解释：最长组合是 [8,8] ，按位与结果 8 &amp; 8 = 8 &gt; 0 。
组合长度是 2 ，所以返回 2 。
</pre>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= candidates.length &lt;= 105</code></li>
	<li><code>1 &lt;= candidates[i] &lt;= 107</code></li>
</ul>