3698. Split Array With Minimum Difference

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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

Hints

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.