LeetCode #2766 — MEDIUM

Relocate Marbles

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

Solve on LeetCode
The Problem

Problem Statement

You are given a 0-indexed integer array nums representing the initial positions of some marbles. You are also given two 0-indexed integer arrays moveFrom and moveTo of equal length.

Throughout moveFrom.length steps, you will change the positions of the marbles. On the ith step, you will move all marbles at position moveFrom[i] to position moveTo[i].

After completing all the steps, return the sorted list of occupied positions.

Notes:

  • We call a position occupied if there is at least one marble in that position.
  • There may be multiple marbles in a single position.

Example 1:

Input: nums = [1,6,7,8], moveFrom = [1,7,2], moveTo = [2,9,5]
Output: [5,6,8,9]
Explanation: Initially, the marbles are at positions 1,6,7,8.
At the i = 0th step, we move the marbles at position 1 to position 2. Then, positions 2,6,7,8 are occupied.
At the i = 1st step, we move the marbles at position 7 to position 9. Then, positions 2,6,8,9 are occupied.
At the i = 2nd step, we move the marbles at position 2 to position 5. Then, positions 5,6,8,9 are occupied.
At the end, the final positions containing at least one marbles are [5,6,8,9].

Example 2:

Input: nums = [1,1,3,3], moveFrom = [1,3], moveTo = [2,2]
Output: [2]
Explanation: Initially, the marbles are at positions [1,1,3,3].
At the i = 0th step, we move all the marbles at position 1 to position 2. Then, the marbles are at positions [2,2,3,3].
At the i = 1st step, we move all the marbles at position 3 to position 2. Then, the marbles are at positions [2,2,2,2].
Since 2 is the only occupied position, we return [2].

Constraints:

  • 1 <= nums.length <= 105
  • 1 <= moveFrom.length <= 105
  • moveFrom.length == moveTo.length
  • 1 <= nums[i], moveFrom[i], moveTo[i] <= 109
  • The test cases are generated such that there is at least a marble in moveFrom[i] at the moment we want to apply the ith move.

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 a 0-indexed integer array nums representing the initial positions of some marbles. You are also given two 0-indexed integer arrays moveFrom and moveTo of equal length. Throughout moveFrom.length steps, you will change the positions of the marbles. On the ith step, you will move all marbles at position moveFrom[i] to position moveTo[i]. After completing all the steps, return the sorted list of occupied positions. Notes: We call a position occupied if there is at least one marble in that position. There may be multiple marbles in a single position.

Baseline thinking

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

Pattern signal: Array · Hash Map

Example 1

[1,6,7,8]
[1,7,2]
[2,9,5]

Example 2

[1,1,3,3]
[1,3]
[2,2]
Step 02

Core Insight

What unlocks the optimal approach

  • Can we solve this problem using a set or map?
  • Sequentially process pairs from moveFrom[i] and moveTo[i]. In each step, remove the occurrence of moveFrom[i] and add moveTo[i] into the set.
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 #2766: Relocate Marbles
class Solution {
    public List<Integer> relocateMarbles(int[] nums, int[] moveFrom, int[] moveTo) {
        Set<Integer> pos = new HashSet<>();
        for (int x : nums) {
            pos.add(x);
        }
        for (int i = 0; i < moveFrom.length; ++i) {
            pos.remove(moveFrom[i]);
            pos.add(moveTo[i]);
        }
        List<Integer> ans = new ArrayList<>(pos);
        ans.sort((a, b) -> a - b);
        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(n × log n)
Space
O(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.

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.