LeetCode #2740 — MEDIUM

Find the Value of the Partition

Move from brute-force thinking to an efficient approach using array strategy.

Solve on LeetCode

The Problem

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.

Example 1:

Input: nums = [1,3,2,4]
Output: 1
Explanation: 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
Explanation: 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 <= 10⁵
1 <= nums[i] <= 10⁹

Step 01

Brute Force Baseline

Problem summary: 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.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array

Example 1

[1,3,2,4]

Example 2

[100,1,10]

Step 02

Core Insight

What unlocks the optimal approach

Sort the array.
The answer is min(nums[i+1] - nums[i]) for all i in the range [0, n-2].

Interview move: turn each hint into an invariant you can check after every iteration/recursion step.

Step 03

Algorithm Walkthrough

Iteration Checklist

Define state (indices, window, stack, map, DP cell, or recursion frame).
Apply one transition step and update the invariant.
Record answer candidate when condition is met.
Continue until all input is consumed.

Use the first example testcase as your mental trace to verify each transition.

Step 04

Edge Cases

Minimum Input

Single element / shortest valid input

Validate boundary behavior before entering the main loop or recursion.

Duplicates & Repeats

Repeated values / repeated states

Decide whether duplicates should be merged, skipped, or counted explicitly.

Extreme Constraints

Upper-end input sizes

Re-check complexity target against constraints to avoid time-limit issues.

Invalid / Corner Shape

Empty collections, zeros, or disconnected structures

Handle special-case structure before the core algorithm path.

Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #2740: Find the Value of the Partition
class Solution {
    public int findValueOfPartition(int[] nums) {
        Arrays.sort(nums);
        int ans = 1 << 30;
        for (int i = 1; i < nums.length; ++i) {
            ans = Math.min(ans, nums[i] - nums[i - 1]);
        }
        return ans;
    }
}

// Accepted solution for LeetCode #2740: Find the Value of the Partition
func findValueOfPartition(nums []int) int {
	sort.Ints(nums)
	ans := 1 << 30
	for i, x := range nums[1:] {
		ans = min(ans, x-nums[i])
	}
	return ans
}

# Accepted solution for LeetCode #2740: Find the Value of the Partition
class Solution:
    def findValueOfPartition(self, nums: List[int]) -> int:
        nums.sort()
        return min(b - a for a, b in pairwise(nums))

// Accepted solution for LeetCode #2740: Find the Value of the Partition
impl Solution {
    pub fn find_value_of_partition(mut nums: Vec<i32>) -> i32 {
        nums.sort();
        let mut ans = i32::MAX;
        for i in 1..nums.len() {
            ans = ans.min(nums[i] - nums[i - 1]);
        }
        ans
    }
}

// Accepted solution for LeetCode #2740: Find the Value of the Partition
function findValueOfPartition(nums: number[]): number {
    nums.sort((a, b) => a - b);
    let ans = Infinity;
    for (let i = 1; i < nums.length; ++i) {
        ans = Math.min(ans, Math.abs(nums[i] - nums[i - 1]));
    }
    return ans;
}

Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Custom checkpoints (one per line)

Press Step or Run All to begin.

Step 07

Complexity Analysis

Time

O(n × log n)

Space

O(log n)

Approach Breakdown

BRUTE FORCE

O(n²) time

O(1) space

Two nested loops check every pair or subarray. The outer loop fixes a starting point, the inner loop extends or searches. For n elements this gives up to n²/2 operations. No extra space, but the quadratic time is prohibitive for large inputs.

OPTIMIZED

O(n) time

O(1) space

Most array problems have an O(n²) brute force (nested loops) and an O(n) optimal (single pass with clever state tracking). The key is identifying what information to maintain as you scan: a running max, a prefix sum, a hash map of seen values, or two pointers.

Shortcut: If you are using nested loops on an array, there is almost always an O(n) solution. Look for the right auxiliary state.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.