LeetCode #3447 — MEDIUM

Assign Elements to Groups with Constraints

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

Solve on LeetCode
The Problem

Problem Statement

You are given an integer array groups, where groups[i] represents the size of the ith group. You are also given an integer array elements.

Your task is to assign one element to each group based on the following rules:

  • An element at index j can be assigned to a group i if groups[i] is divisible by elements[j].
  • If there are multiple elements that can be assigned, assign the element with the smallest index j.
  • If no element satisfies the condition for a group, assign -1 to that group.

Return an integer array assigned, where assigned[i] is the index of the element chosen for group i, or -1 if no suitable element exists.

Note: An element may be assigned to more than one group.

Example 1:

Input: groups = [8,4,3,2,4], elements = [4,2]

Output: [0,0,-1,1,0]

Explanation:

  • elements[0] = 4 is assigned to groups 0, 1, and 4.
  • elements[1] = 2 is assigned to group 3.
  • Group 2 cannot be assigned any element.

Example 2:

Input: groups = [2,3,5,7], elements = [5,3,3]

Output: [-1,1,0,-1]

Explanation:

  • elements[1] = 3 is assigned to group 1.
  • elements[0] = 5 is assigned to group 2.
  • Groups 0 and 3 cannot be assigned any element.

Example 3:

Input: groups = [10,21,30,41], elements = [2,1]

Output: [0,1,0,1]

Explanation:

elements[0] = 2 is assigned to the groups with even values, and elements[1] = 1 is assigned to the groups with odd values.

Constraints:

  • 1 <= groups.length <= 105
  • 1 <= elements.length <= 105
  • 1 <= groups[i] <= 105
  • 1 <= elements[i] <= 105

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: You are given an integer array groups, where groups[i] represents the size of the ith group. You are also given an integer array elements. Your task is to assign one element to each group based on the following rules: An element at index j can be assigned to a group i if groups[i] is divisible by elements[j]. If there are multiple elements that can be assigned, assign the element with the smallest index j. If no element satisfies the condition for a group, assign -1 to that group. Return an integer array assigned, where assigned[i] is the index of the element chosen for group i, or -1 if no suitable element exists. Note: An element may be assigned to more than one group.

Baseline thinking

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

Pattern signal: Array · Hash Map

Example 1

[8,4,3,2,4]
[4,2]

Example 2

[2,3,5,7]
[5,3,3]

Example 3

[10,21,30,41]
[2,1]
Step 02

Core Insight

What unlocks the optimal approach

  • Can a sieve-like approach be applied here?
  • Starting from the smallest index, iterate through the multiples of the element and assign it to groups divisible by that value.
  • Process each element once.
  • Find all divisors of each group, then match them with elements.
Interview move: turn each hint into an invariant you can check after every iteration/recursion step.
Step 03

Algorithm Walkthrough

Iteration Checklist

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. 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 #3447: Assign Elements to Groups with Constraints
class Solution {
    public int[] assignElements(int[] groups, int[] elements) {
        int mx = Arrays.stream(groups).max().getAsInt();
        int[] d = new int[mx + 1];
        Arrays.fill(d, -1);
        for (int j = 0; j < elements.length; ++j) {
            int x = elements[j];
            if (x > mx || d[x] != -1) {
                continue;
            }
            for (int y = x; y <= mx; y += x) {
                if (d[y] == -1) {
                    d[y] = j;
                }
            }
        }
        int n = groups.length;
        int[] ans = new int[n];
        for (int i = 0; i < n; ++i) {
            ans[i] = d[groups[i]];
        }
        return ans;
    }
}
Step 06

Interactive Study Demo

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

Press Step or Run All to begin.
Step 07

Complexity Analysis

Time
O(M × log m + n)
Space
O(M)

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.

Mutating counts without cleanup

Wrong move: Zero-count keys stay in map and break distinct/count constraints.

Usually fails on: Window/map size checks are consistently off by one.

Fix: Delete keys when count reaches zero.