Divide Array Into Arrays With Max Difference

Divide Array Into Arrays With Max Difference

What is this problem about?

In the Divide Array Into Arrays With Max Difference coding problem, you are given an array of integers and an integer $k$. You need to divide the array into several groups, each of size exactly 3. Each group must satisfy one condition: the difference between the maximum and minimum elements in the group must be at most $k$. If it's impossible to divide the entire array, return an empty list.

Why is this asked in interviews?

This "Medium" problem is popular at Salesforce and Amazon because it tests whether you can identify that Sorting is the prerequisite for a Greedy approach. It evaluations your understanding that to minimize the range of a group, the elements should be as close to each other as possible, which naturally happens in a sorted sequence.

Algorithmic pattern used

This problem uses Greedy logic with Sorting.

1. Sort the input array.
2. Once sorted, the best candidates to form a group of 3 are three adjacent elements: arr[i], arr[i+1], arr[i+2].
3. Check the condition: arr[i+2] - arr[i] <= k.
4. If the condition holds for every group of three, return the list of groups.
5. If any group fails the condition, it means no valid partition exists, so return an empty result.

Example explanation

nums = [1, 3, 4, 8, 7, 9], $k = 2$.

1. Sorted: [1, 3, 4, 7, 8, 9].
2. Group 1: [1, 3, 4]. Max - Min = $4 - 1 = 3$. $3 > 2$. Result: Empty list. If $k = 3$:
3. Group 1: [1, 3, 4]. $4 - 1 = 3 \le 3$. (Valid).
4. Group 2: [7, 8, 9]. $9 - 7 = 2 \le 3$. (Valid). Result: [[1, 3, 4], [7, 8, 9]].

Common mistakes candidates make

• Not Sorting: Trying to use backtracking or complex matching to find groups, which is $O(N!)$.
• Wrong Grouping: Attempting to put non-adjacent elements together, which can only make the range larger, never smaller.
• Return format: Forgetting to return an empty array if even one group fails.

Interview preparation tip

The "Max Difference" constraint in an array almost always implies sorting. Once the data is ordered, the "closest" elements are neighbors, which simplifies the decision-making process to a simple linear scan.