How do you solve Split Array Into Maximum Number of Subarrays on LeetCode?

Split Array Into Maximum Number of Subarrays (LeetCode #2871) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: The overall AND of the array determines the possibility of splitting.

What is the brute force solution for Split Array Into Maximum Number of Subarrays?

The brute force approach for Split Array Into Maximum Number of Subarrays is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves checking every possible way to split the array into subarrays and calculating the score for each split. This ensures that we explore all combinations, but it's inefficient for larger arrays. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Split Array Into Maximum Number of Subarrays?

Split Array Into Maximum Number of Subarrays uses the following concepts: Array, Greedy, Bit Manipulation. The recommended patterns to study are: Bit Manipulation, Greedy.

What are the interview tips for Split Array Into Maximum Number of Subarrays?

Always check for edge cases, such as arrays with all zeros or all ones. Explain your thought process clearly, especially when transitioning from brute force to optimal solutions. Practice recognizing patterns in problems to improve your problem-solving speed.

What are common mistakes when solving Split Array Into Maximum Number of Subarrays?

Not considering the overall AND before attempting splits. Failing to account for zeros in the array.

#2871

Split Array Into Maximum Number of Subarrays

Medium

ArrayGreedyBit ManipulationBit ManipulationGreedy

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n)Space O(1)

The optimal solution focuses on the properties of the bitwise AND operation. If the overall AND of the array is 0, we can split it into multiple subarrays. If not, we can only have one subarray. This drastically reduces the complexity.

⚙️

Algorithm

4 steps

1Step 1: Calculate the overall AND of the entire array.
2Step 2: If the overall AND is 0, iterate through the array to count how many times we encounter a 0, which indicates a potential split point.
3Step 3: Return the count of splits plus one (for the last subarray).
4Step 4: If the overall AND is not 0, return 1 as we can only have one subarray.

solution.py7 lines

1def maxSubarrays(nums):
2    overall_and = nums[0]
3    for num in nums:
4        overall_and &= num
5    if overall_and == 0:
6        return nums.count(0) + 1
7    return 1

ℹ

Complexity note: The time complexity is O(n) because we only need to traverse the array a couple of times. The space complexity is O(1) since we are using a constant amount of extra space.

1The overall AND of the array determines the possibility of splitting.
2A score of 0 allows for maximum splits.

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