Convert an Array Into a 2D Array With Conditions

Problem Statement

Given an integer array nums, the task is to construct a two-dimensional (2D) array that adheres to certain rules. Firstly, the 2D array must only include elements from nums. Each row in this 2D array must consist of distinct integers, meaning no row should have repeated numbers. Additionally, the challenge is to organize these rows such that the total count of rows is minimized. The 2D array can vary in the number of elements per row. The goal is to find a possible configuration for this array and return it. It is important to note that if multiple valid configurations exist, returning any one of them is acceptable.

Examples

Example 1

Input:

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

Output:

[[1,3,4,2],[1,3],[1]]

Explanation:

We can create a 2D array that contains the following rows:
- 1,3,4,2
- 1,3
- 1
All elements of nums were used, and each row of the 2D array contains distinct integers, so it is a valid answer.
It can be shown that we cannot have less than 3 rows in a valid array.

Example 2

Input:

nums = [1,2,3,4]

Output:

[[4,3,2,1]]

Explanation:

All elements of the array are distinct, so we can keep all of them in the first row of the 2D array.

Constraints

• 1 <= nums.length <= 200
• 1 <= nums[i] <= nums.length

Approach and Intuition

To tackle this problem, we can use a frequency-based approach combined with a strategy to reduce the number of rows. Below are steps to illustrate a possible solution:

1. Calculate Frequency: First, determine the frequency of each integer in nums. This helps in understanding the maximum number of rows needed because the number with the highest frequency determines the minimal number of rows required.

2. Prepare the Rows: Initialize an empty list of lists (2D array). The length of this initialization often equals the highest frequency found in the previous step, as this dictates the minimal number of rows needed.

3. Fill Each Row: Iterate through each element in nums:

   • For each number, place it in the next available row where it hasn't been placed yet to ensure all rows contain distinct numbers.
   • Rotate through the rows to distribute numbers evenly and meet the distinct requirement.

4. Result Compilation: After processing all numbers in nums, the list of lists prepared should meet all requirements. The structure ensures each element is placed appropriately, rows contain distinct integers, and the configuration uses the minimal number of rows possible based on the constraints.

For example, in Example 1 from the problem's statement:

• We have numbers like 1 appearing three times, which directly leads us to need at least three rows.
• By placing each instance of the numbers in successive rows and rotating back to the first row after reaching the last initialized row, we ensure all requirements are met efficiently.

Using this basic but effective scheme helps in achieving the desired configuration with respect to the constraints and requirements specified.

Solutions

class Solution {
public:
    vector<vector<int>> gatherMatrix(vector<int>& elements) {
        vector<int> count(elements.size() + 1);
    
        vector<vector<int>> result;
        for (int element : elements) {
            if (count[element] >= result.size()) {
                result.push_back({});
            }
    
            // Add the element to the subgroup indexed by current count
            result[count[element]].push_back(element);
            count[element]++;
        }
    
        return result;
    }
};