How do you solve Count the Number of Beautiful Subarrays on LeetCode?

Count the Number of Beautiful Subarrays (LeetCode #2588) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: A subarray is beautiful if its XOR is zero.

What is the time complexity of Count the Number of Beautiful Subarrays?

The optimal solution for Count the Number of Beautiful Subarrays runs in O(n) time and uses O(n) space. The time complexity is O(n) because we traverse the array once. The space complexity is O(n) due to the hashmap storing the prefix XOR frequencies.

What is the brute force solution for Count the Number of Beautiful Subarrays?

The brute force approach for Count the Number of Beautiful Subarrays is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach checks every possible subarray to see if its elements can be made zero. This is done by calculating the XOR for each subarray and checking if it equals zero. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Count the Number of Beautiful Subarrays?

Count the Number of Beautiful Subarrays uses the following concepts: Array, Hash Table, Bit Manipulation, Prefix Sum. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Count the Number of Beautiful Subarrays?

Think about how to reduce the problem size using mathematical properties like XOR. Practice recognizing patterns in problems that can be solved with prefix sums or XOR. Be prepared to explain your thought process clearly, especially when transitioning from brute force to optimal solutions.

What are common mistakes when solving Count the Number of Beautiful Subarrays?

Not recognizing that XOR can be used to determine subarray properties. Failing to handle the case where the prefix XOR itself is zero.

#2588

Count the Number of Beautiful Subarrays

Medium

ArrayHash TableBit ManipulationPrefix SumHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

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Intuition

Time O(n)Space O(n)

The optimal solution uses the prefix XOR technique to efficiently count beautiful subarrays. By maintaining a count of prefix XOR values, we can determine how many times a specific XOR value has occurred, allowing us to find subarrays with an XOR of zero quickly.

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Algorithm

5 steps

1Step 1: Initialize a hashmap to store the frequency of prefix XOR values and a variable for the current prefix XOR.
2Step 2: Iterate through the array, updating the prefix XOR with each element.
3Step 3: For each prefix XOR, check if it has been seen before. If yes, add its frequency to the count of beautiful subarrays.
4Step 4: If the prefix XOR is zero, increment the count as it indicates a beautiful subarray from the start.
5Step 5: Update the hashmap with the current prefix XOR frequency.

solution.py9 lines

1def countBeautifulSubarrays(nums):
2    prefix_xor = 0
3    count = 0
4    xor_count = {0: 1}
5    for num in nums:
6        prefix_xor ^= num
7        count += xor_count.get(prefix_xor, 0)
8        xor_count[prefix_xor] = xor_count.get(prefix_xor, 0) + 1
9    return count

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Complexity note: The time complexity is O(n) because we traverse the array once. The space complexity is O(n) due to the hashmap storing the prefix XOR frequencies.

1A subarray is beautiful if its XOR is zero.
2Using prefix XOR allows for efficient counting of beautiful subarrays.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.