Is Partition Array to Minimize XOR easy or hard?

The problem is generally classified as Medium difficulty. The challenge comes from recognizing the partition DP pattern and using prefix XOR to avoid recomputing XOR values for every subarray.

Partition Array to Minimize XOR Python/Java solution

The typical implementation uses a DP array and prefix XOR array. For each index i, iterate through previous indices j and update dp[i] using dp[j] plus the XOR of the segment (j+1..i). This approach translates directly to Python, Java, C++, Go, or TypeScript.

How to solve Partition Array to Minimize XOR in O(n)?

A strict O(n) solution generally isn't achievable because each index may depend on many previous partition points. The typical optimal approach uses dynamic programming with prefix XOR and runs in O(n^2) time while computing each subarray XOR in O(1).

What is the best approach for Partition Array to Minimize XOR?

Dynamic programming with prefix XOR is the most effective approach. Define dp[i] as the minimum XOR cost for the prefix ending at index i and try all previous partition points. Prefix XOR allows constant-time subarray XOR calculation, resulting in O(n^2) time and O(n) space complexity.

Is Partition Array to Minimize XOR asked at Google/Amazon/Meta?

Partitioning and XOR optimization problems frequently appear in interviews at companies like Google, Amazon, and Meta. Variants testing prefix XOR, dynamic programming, and bit manipulation are especially common in mid‑level algorithm interviews.

What data structure is used in Partition Array to Minimize XOR?

The main structures are arrays for dynamic programming and prefix XOR storage. The algorithm relies on bit manipulation to compute XOR quickly and uses prefix accumulation to answer subarray XOR queries in constant time.

What is the time complexity of Partition Array to Minimize XOR?

The optimized dynamic programming solution runs in O(n^2) time because each position checks all earlier partition points. Space complexity is O(n) for storing the DP array and prefix XOR values.

Description Hints 4 Solution Video 15:35

3599. Partition Array to Minimize XOR

Medium41.2% acceptance1 company

You are given an integer array nums and an integer k.

Your task is to partition nums into k non-empty subarrays. For each subarray, compute the bitwise XOR of all its elements.

Return the minimum possible value of the maximum XOR among these k subarrays.

Example 1:

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

Output: 1

Explanation:

The optimal partition is [1] and [2, 3].

XOR of the first subarray is 1.
XOR of the second subarray is 2 XOR 3 = 1.

The maximum XOR among the subarrays is 1, which is the minimum possible.

Example 2:

Input: nums = [2,3,3,2], k = 3

Output: 2

Explanation:

The optimal partition is [2], [3, 3], and [2].

XOR of the first subarray is 2.
XOR of the second subarray is 3 XOR 3 = 0.
XOR of the third subarray is 2.

The maximum XOR among the subarrays is 2, which is the minimum possible.

Example 3:

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

Output: 0

Explanation:

The optimal partition is [1, 1] and [2, 3, 1].

XOR of the first subarray is 1 XOR 1 = 0.
XOR of the second subarray is 2 XOR 3 XOR 1 = 0.

The maximum XOR among the subarrays is 0, which is the minimum possible.

Constraints:

1 <= nums.length <= 250
1 <= nums[i] <= 10⁹
1 <= k <= n

Asked at 1 company

Google

Topics

Hints open one at a time

Hint 1

Use dynamic programming.

Hint 2

Precompute pre[i] = nums[0] ^ … ^ nums[i-1] so any subarray XOR is pre[r] ^ pre[l].

Hint 3

Define dp[i][j] = minimum possible “max‑XOR” when splitting the first i elements into j parts.

Hint 4

For each dp[i][j], try all splits t < i and take the minimum over max(dp[t][j-1], pre[i] ^ pre[t]).

15:35

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1class Solution:
2    def minXor(self, nums: List[int], k: int) -> int:
3        

Starter codePython 3Spaces: 4

Examples

Case 1Case 2Case 3

Input

[1,2,3]
2

Input

[2,3,3,2]
3

Input

[1,1,2,3,1]
2

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