LeetCode #2831 — MEDIUM

Find the Longest Equal Subarray

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 and an integer k.

A subarray is called equal if all of its elements are equal. Note that the empty subarray is an equal subarray.

Return the length of the longest possible equal subarray after deleting at most k elements from nums.

A subarray is a contiguous, possibly empty sequence of elements within an array.

Example 1:

Input: nums = [1,3,2,3,1,3], k = 3
Output: 3
Explanation: It's optimal to delete the elements at index 2 and index 4.
After deleting them, nums becomes equal to [1, 3, 3, 3].
The longest equal subarray starts at i = 1 and ends at j = 3 with length equal to 3.
It can be proven that no longer equal subarrays can be created.

Example 2:

Input: nums = [1,1,2,2,1,1], k = 2
Output: 4
Explanation: It's optimal to delete the elements at index 2 and index 3.
After deleting them, nums becomes equal to [1, 1, 1, 1].
The array itself is an equal subarray, so the answer is 4.
It can be proven that no longer equal subarrays can be created.

Constraints:

  • 1 <= nums.length <= 105
  • 1 <= nums[i] <= nums.length
  • 0 <= k <= nums.length
Patterns Used

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 and an integer k. A subarray is called equal if all of its elements are equal. Note that the empty subarray is an equal subarray. Return the length of the longest possible equal subarray after deleting at most k elements from nums. A subarray is a contiguous, possibly empty sequence of elements within an array.

Baseline thinking

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

Pattern signal: Array · Hash Map · Binary Search · Sliding Window

Example 1

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

Example 2

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

Core Insight

What unlocks the optimal approach

  • <div class="_1l1MA">For each number <code>x</code> in <code>nums</code>, create a sorted list <code>indices<sub>x</sub></code> of all indices <code>i</code> such that <code>nums[i] == x</code>.</div>
  • <div class="_1l1MA">On every <code>indices<sub>x</sub></code>, execute a sliding window technique.</div>
  • <div class="_1l1MA">For each <code>indices<sub>x</sub></code>, find <code>i, j</code> such that <code>(indices<sub>x</sub>[j] - indices<sub>x</sub>[i]) - (j - i) <= k</code> and <code>j - i + 1</code> is maximized.</div>
  • <div class="_1l1MA">The answer would be the maximum of <code>j - i + 1</code> for all <code>indices<sub>x</sub></code>.</div>
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 #2831: Find the Longest Equal Subarray
class Solution {
    public int longestEqualSubarray(List<Integer> nums, int k) {
        Map<Integer, Integer> cnt = new HashMap<>();
        int mx = 0, l = 0;
        for (int r = 0; r < nums.size(); ++r) {
            cnt.merge(nums.get(r), 1, Integer::sum);
            mx = Math.max(mx, cnt.get(nums.get(r)));
            if (r - l + 1 - mx > k) {
                cnt.merge(nums.get(l++), -1, Integer::sum);
            }
        }
        return mx;
    }
}
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)
Space
O(n)

Approach Breakdown

LINEAR SCAN
O(n) time
O(1) space

Check every element from left to right until we find the target or exhaust the array. Each comparison is O(1), and we may visit all n elements, giving O(n). No extra space needed.

BINARY SEARCH
O(log n) time
O(1) space

Each comparison eliminates half the remaining search space. After k comparisons, the space is n/2ᵏ. We stop when the space is 1, so k = log₂ n. No extra memory needed — just two pointers (lo, hi).

Shortcut: Halving the input each step → O(log n). Works on any monotonic condition, not just sorted arrays.
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.

Boundary update without `+1` / `-1`

Wrong move: Setting `lo = mid` or `hi = mid` can stall and create an infinite loop.

Usually fails on: Two-element ranges never converge.

Fix: Use `lo = mid + 1` or `hi = mid - 1` where appropriate.

Shrinking the window only once

Wrong move: Using `if` instead of `while` leaves the window invalid for multiple iterations.

Usually fails on: Over-limit windows stay invalid and produce wrong lengths/counts.

Fix: Shrink in a `while` loop until the invariant is valid again.