LeetCode #3828 — MEDIUM

Final Element After Subarray Deletions

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 nums.

Two players, Alice and Bob, play a game in turns, with Alice playing first.

  • In each turn, the current player chooses any subarray nums[l..r] such that r - l + 1 < m, where m is the current length of the array.
  • The selected subarray is removed, and the remaining elements are concatenated to form the new array.
  • The game continues until only one element remains.

Alice aims to maximize the final element, while Bob aims to minimize it. Assuming both play optimally, return the value of the final remaining element.

Example 1:

Input: nums = [1,5,2]

Output: 2

Explanation:

One valid optimal strategy:

  • Alice removes [1], array becomes [5, 2].
  • Bob removes [5], array becomes [2]​​​​​​​. Thus, the answer is 2.

Example 2:

Input: nums = [3,7]

Output: 7

Explanation:

Alice removes [3], leaving the array [7]. Since Bob cannot play a turn now, the answer is 7.

Constraints:

  • 1 <= nums.length <= 105
  • 1 <= nums[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 nums. Two players, Alice and Bob, play a game in turns, with Alice playing first. In each turn, the current player chooses any subarray nums[l..r] such that r - l + 1 < m, where m is the current length of the array. The selected subarray is removed, and the remaining elements are concatenated to form the new array. The game continues until only one element remains. Alice aims to maximize the final element, while Bob aims to minimize it. Assuming both play optimally, return the value of the final remaining element.

Baseline thinking

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

Pattern signal: Array · Math

Example 1

[1,5,2]

Example 2

[3,7]
Step 02

Core Insight

What unlocks the optimal approach

  • Observe which positions Alice can force to survive her first move so that Bob cannot remove them afterward.
  • Any middle element can always be removed by Bob, so only the endpoints can be protected.
  • Alice chooses the better endpoint: the answer is <code>max(nums[0], nums[len(nums) - 1])</code>.
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 #3828: Final Element After Subarray Deletions
class Solution {
    public int finalElement(int[] nums) {
        return Math.max(nums[0], nums[nums.length - 1]);
    }
}
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(1)
Space
O(1)

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.

Overflow in intermediate arithmetic

Wrong move: Temporary multiplications exceed integer bounds.

Usually fails on: Large inputs wrap around unexpectedly.

Fix: Use wider types, modular arithmetic, or rearranged operations.