Find the Value of the Partition

arraysorting

Problem Statement

You are given a positive integer array nums .

Partition nums into two arrays, nums1 and nums2 , such that:

Each element of the array nums belongs to either the array nums1 or the array nums2 .

Both arrays are non-empty .

The value of the partition is minimized .

The value of the partition is |max(nums1) - min(nums2)| .

Here, max(nums1) denotes the maximum element of the array nums1 , and min(nums2) denotes the minimum element of the array nums2 .

Return the integer denoting the value of such partition .

Examples

Example 1

Input: nums = [1,3,2,4]
Output: 1
We can partition the array nums into nums1 = [1,2] and nums2 = [3,4].
- The maximum element of the array nums1 is equal to 2.
- The minimum element of the array nums2 is equal to 3.
The value of the partition is |2 - 3| = 1. 
It can be proven that 1 is the minimum value out of all partitions.

Example 2

Input: nums = [100,1,10]
Output: 9
We can partition the array nums into nums1 = [10] and nums2 = [100,1].
- The maximum element of the array nums1 is equal to 10.
- The minimum element of the array nums2 is equal to 1.
The value of the partition is |10 - 1| = 9.
It can be proven that 9 is the minimum value out of all partitions.

Constraints

2 <= nums.length <= 10 ^5

1 <= nums[i] <= 10 ^9

🤔

Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicSorting