LeetCode-in-Java

2588. Count the Number of Beautiful Subarrays

Medium

You are given a 0-indexed integer array nums. In one operation, you can:

• Choose two different indices i and j such that 0 <= i, j < nums.length.
• Choose a non-negative integer k such that the kth bit (0-indexed) in the binary representation of nums[i] and nums[j] is 1.
• Subtract 2k from nums[i] and nums[j].

A subarray is beautiful if it is possible to make all of its elements equal to 0 after applying the above operation any number of times.

Return the number of beautiful subarrays in the array nums.

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

Example 1:

Input: nums = [4,3,1,2,4]

Output: 2

Explanation: There are 2 beautiful subarrays in nums: [4,3,1,2,4] and [4,3,1,2,4].

• We can make all elements in the subarray [3,1,2] equal to 0 in the following way:
  • Choose [3, 1, 2] and k = 1. Subtract 2¹ from both numbers. The subarray becomes [1, 1, 0].
  • Choose [1, 1, 0] and k = 0. Subtract 2⁰ from both numbers. The subarray becomes [0, 0, 0].
• We can make all elements in the subarray [4,3,1,2,4] equal to 0 in the following way:
  • Choose [4, 3, 1, 2, 4] and k = 2. Subtract 2² from both numbers. The subarray becomes [0, 3, 1, 2, 0].
  • Choose [0, 3, 1, 2, 0] and k = 0. Subtract 2⁰ from both numbers. The subarray becomes [0, 2, 0, 2, 0].
  • Choose [0, 2, 0, 2, 0] and k = 1. Subtract 2¹ from both numbers. The subarray becomes [0, 0, 0, 0, 0].

Example 2:

Input: nums = [1,10,4]

Output: 0

Explanation: There are no beautiful subarrays in nums.

Constraints:

• 1 <= nums.length <= 105
• 0 <= nums[i] <= 106

Solution

import java.util.HashMap;
import java.util.Map;

public class Solution {
    public long beautifulSubarrays(int[] nums) {
        long count = 0;
        int xor = 0;
        Map<Integer, Integer> map = new HashMap<>();
        map.put(0, 1);
        for (int num : nums) {
            xor ^= num;
            count += map.merge(xor, 1, Integer::sum) - 1;
        }
        return count;
    }
}

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