Is Split Array With Minimum Difference easy or hard?

Split Array With Minimum Difference is typically considered a Medium difficulty problem. The brute force idea is simple, but identifying the prefix sum optimization and maintaining monotonic helpers to achieve O(n) time requires stronger array problem-solving skills.

Split Array With Minimum Difference Python/Java solution

Implement the optimal solution by computing a prefix sum array and iterating through possible split indices. At each step, derive left and right partition sums from the prefix values and update the minimum difference. The same logic works in Python, Java, C++, Go, and TypeScript with O(n) time complexity.

How to solve Split Array With Minimum Difference in O(n)?

First compute the prefix sum array so you know the cumulative sum at each index. The total array sum lets you derive the right partition sum as total minus the prefix. Maintain monotonic helper arrays to track the best prefix values while scanning once through the array, allowing the minimum difference to be updated in constant time per split.

What is the best approach for Split Array With Minimum Difference?

The most efficient approach uses a prefix sum array combined with monotonic helper arrays to track optimal prefix values. This allows you to evaluate each split point in constant time after preprocessing. The overall complexity becomes O(n) time with O(n) extra space.

Is Split Array With Minimum Difference asked at Google/Amazon/Meta?

Array partitioning and prefix sum optimization problems frequently appear in interviews at companies like Google, Amazon, and Meta. Variations of minimizing sum differences or balancing partitions are common because they test array traversal, prefix sums, and optimization techniques.

What data structure is used in Split Array With Minimum Difference?

The solution primarily uses arrays and a prefix sum structure. Additional helper arrays store monotonic prefix values to efficiently track the best candidates while scanning possible split positions.

What is the time complexity of Split Array With Minimum Difference?

The optimal solution runs in O(n) time using prefix sums and a single pass through the array. Building the prefix array takes O(n), and evaluating each split also takes O(1) per position. A naive brute force approach would take O(n^2) time because it recomputes sums repeatedly.

Description Hints 4 Solution Video 10:11

3698. Split Array With Minimum Difference

Medium33.6% acceptance1 company

You are given an integer array nums.

Split the array into exactly two subarrays, left and right, such that left is strictly increasing and right is strictly decreasing.

Return the minimum possible absolute difference between the sums of left and right. If no valid split exists, return -1.

Example 1:

Input: nums = [1,3,2]

Output: 2

Explanation:

`i`	`left`	`right`	Validity	`left` sum	`right` sum	Absolute difference
0	[1]	[3, 2]	Yes	1	5	`\|1 - 5\| = 4`
1	[1, 3]	[2]	Yes	4	2	`\|4 - 2\| = 2`

Thus, the minimum absolute difference is 2.

Example 2:

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

Output: 4

Explanation:

`i`	`left`	`right`	Validity	`left` sum	`right` sum	Absolute difference
0	[1]	[2, 4, 3]	No	1	9	-
1	[1, 2]	[4, 3]	Yes	3	7	`\|3 - 7\| = 4`
2	[1, 2, 4]	[3]	Yes	7	3	`\|7 - 3\| = 4`

Thus, the minimum absolute difference is 4.

Example 3:

Input: nums = [3,1,2]

Output: -1

Explanation:

No valid split exists, so the answer is -1.

Constraints:

2 <= nums.length <= 10⁵
1 <= nums[i] <= 10⁵

Asked at 1 company

Google

Topics

Array Prefix Sum

Hints open one at a time

Hint 1

Build a prefix boolean inc[i] that is true iff the subarray nums[0..i] is strictly increasing.

Hint 2

Build a suffix boolean dec[i] that is true iff the subarray nums[i..n - 1] is strictly decreasing.

Hint 3

A split after index i (where 0 <= i < n - 1) is valid iff inc[i] && dec[i + 1].

Hint 4

Build a prefix-sum array pref, and use it to check if a valid split exists. If no valid split exists return -1.

10:11

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

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Examples

Case 1Case 2Case 3

Input

[1,3,2]

Input

[1,2,4,3]

Input

[3,1,2]

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