Is Maximum XOR Score Subarray Queries easy or hard?

Maximum XOR Score Subarray Queries is categorized as a Hard problem because it combines multiple concepts: prefix XOR properties, dynamic programming over ranges, and trie-based bit manipulation for optimization.

Maximum XOR Score Subarray Queries Python/Java solution

Python implementations typically use the prefix XOR and dynamic programming approach due to its simplicity. Java solutions often implement the optimized version with a binary trie for better performance on large inputs. Both approaches rely on fast XOR operations and prefix preprocessing.

How to solve Maximum XOR Score Subarray Queries in O(n log A)?

Build a prefix XOR array and insert prefix values into a binary trie. For each prefix, query the trie to find another prefix that maximizes the XOR value by greedily selecting opposite bits. Because the trie depth equals the number of bits in the integers, each insert and query takes O(log A) time.

What is the best approach for Maximum XOR Score Subarray Queries?

The most practical approach combines prefix XOR with advanced structures such as a binary trie. Prefix XOR allows constant-time calculation of any subarray XOR, while the trie efficiently finds the maximum XOR pairing among prefixes. This reduces query processing to roughly O(log A) time where A is the maximum integer value.

Is Maximum XOR Score Subarray Queries asked at Google/Amazon/Meta?

XOR maximization problems and trie-based bit manipulation questions frequently appear in interviews at companies like Google, Amazon, and Meta. Variants such as maximum XOR pair, maximum XOR subarray, and range XOR queries test understanding of prefix XOR and bitwise tries.

What data structure is used in Maximum XOR Score Subarray Queries?

The main structures are a prefix XOR array and a binary trie. The prefix array enables constant-time subarray XOR computation, while the trie helps efficiently search for values that maximize the XOR result during query processing.

What is the time complexity of Maximum XOR Score Subarray Queries?

The prefix XOR with dynamic programming approach requires O(n^2) preprocessing and answers each query in O(1). A trie-based optimization improves scalability with about O((n + q) log A) time, where A represents the bit-length of numbers stored in the trie.

Description Hints 3 Solution Video 38:03

3277. Maximum XOR Score Subarray Queries

Hard43.4% acceptance1 company

You are given an array nums of n integers, and a 2D integer array queries of size q, where queries[i] = [l_i, r_i].

For each query, you must find the maximum XOR score of any subarray of nums[l_i..r_i].

The XOR score of an array a is found by repeatedly applying the following operations on a so that only one element remains, that is the score:

Simultaneously replace a[i] with a[i] XOR a[i + 1] for all indices i except the last one.
Remove the last element of a.

Return an array answer of size q where answer[i] is the answer to query i.

Example 1:

Input: nums = [2,8,4,32,16,1], queries = [[0,2],[1,4],[0,5]]

Output: [12,60,60]

Explanation:

In the first query, nums[0..2] has 6 subarrays [2], [8], [4], [2, 8], [8, 4], and [2, 8, 4] each with a respective XOR score of 2, 8, 4, 10, 12, and 6. The answer for the query is 12, the largest of all XOR scores.

In the second query, the subarray of nums[1..4] with the largest XOR score is nums[1..4] with a score of 60.

In the third query, the subarray of nums[0..5] with the largest XOR score is nums[1..4] with a score of 60.

Example 2:

Input: nums = [0,7,3,2,8,5,1], queries = [[0,3],[1,5],[2,4],[2,6],[5,6]]

Output: [7,14,11,14,5]

Explanation:

Index	nums[l_i..r_i]	Maximum XOR Score Subarray	Maximum Subarray XOR Score
0	[0, 7, 3, 2]	[7]	7
1	[7, 3, 2, 8, 5]	[7, 3, 2, 8]	14
2	[3, 2, 8]	[3, 2, 8]	11
3	[3, 2, 8, 5, 1]	[2, 8, 5, 1]	14
4	[5, 1]	[5]	5

Constraints:

1 <= n == nums.length <= 2000
0 <= nums[i] <= 2³¹ - 1
1 <= q == queries.length <= 10⁵
queries[i].length == 2
queries[i] = [l_i, r_i]
0 <= l_i <= r_i <= n - 1

Asked at 1 company

Google

Topics

Array Dynamic Programming

Hints open one at a time

Hint 1

Precompute the XOR score of every subarray.

Hint 2

Try to find a relationship between XOR score of nums[i..j], nums[i..j + 1], nums[i..j + 2], …. Do you notice any pattern?

Hint 3

If dp[i][j] is the XOR score of subarray nums[i..j], dp[i][j] = dp[i - 1][j] XOR dp[i - 1][j + 1].

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