898. Bitwise ORs of Subarrays

Description

Given an integer array arr, return the number of distinct bitwise ORs of all the non-empty subarrays of arr.

The bitwise OR of a subarray is the bitwise OR of each integer in the subarray. The bitwise OR of a subarray of one integer is that integer.

A subarray is a contiguous non-empty sequence of elements within an array.

 

Example 1:

Input: arr = [0]
Output: 1
Explanation: There is only one possible result: 0.

Example 2:

Input: arr = [1,1,2]
Output: 3
Explanation: The possible subarrays are [1], [1], [2], [1, 1], [1, 2], [1, 1, 2].
These yield the results 1, 1, 2, 1, 3, 3.
There are 3 unique values, so the answer is 3.

Example 3:

Input: arr = [1,2,4]
Output: 6
Explanation: The possible results are 1, 2, 3, 4, 6, and 7.

 

Constraints:

• 1 <= arr.length <= 5 * 104
• 0 <= arr[i] <= 109

 

Solutions

Solution: Dynamic Programming

• Time complexity: O(nlogMax(arr))
• Space complexity: O(n)

 

JavaScript

/**
 * @param {number[]} arr
 * @return {number}
 */
const subarrayBitwiseORs = function (arr) {
  const result = new Set();
  let orsSet = new Set();

  for (const num of arr) {
    const newOrsSet = new Set();

    newOrsSet.add(num);

    for (const or of orsSet) {
      newOrsSet.add(or | num);
    }

    for (const or of newOrsSet) {
      result.add(or);
    }

    orsSet = newOrsSet;
  }

  return result.size;
};