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347. Top K Frequent Elements

mediumAsked at Duolingo

Return the k most frequent elements from an array — the heap or bucket-sort technique Duolingo's recommendation engine uses to surface the k words a learner encounters most so they can be promoted to the next spaced-repetition review slot.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Problem

Given an integer array nums and an integer k, return the k most frequent elements. You may return the answer in any order. It is guaranteed that the answer is unique.

Constraints

  • 1 <= nums.length <= 10^5
  • k is in the range [1, the number of unique elements in the array]
  • It is guaranteed that the answer is unique

Examples

Example 1

Input
nums = [1,1,1,2,2,3], k = 2
Output
[1,2]

Example 2

Input
nums = [1], k = 1
Output
[1]

Approaches

1. Sort by frequency

Count frequencies with a Map, then sort entries by frequency descending and take the first k.

Time
O(n log n)
Space
O(n)
function topKFrequent(nums, k) {
  const freq = new Map();
  for (const n of nums) freq.set(n, (freq.get(n) ?? 0) + 1);
  return [...freq.entries()]
    .sort((a, b) => b[1] - a[1])
    .slice(0, k)
    .map(e => e[0]);
}

Tradeoff:

2. Optimal — bucket sort O(n)

Place each number into a frequency bucket (index = frequency), then read buckets from highest to lowest until k elements are collected.

Time
O(n)
Space
O(n)
function topKFrequent(nums, k) {
  const freq = new Map();
  for (const n of nums) freq.set(n, (freq.get(n) ?? 0) + 1);

  const buckets = new Array(nums.length + 1).fill(null).map(() => []);
  for (const [num, cnt] of freq) buckets[cnt].push(num);

  const result = [];
  for (let i = buckets.length - 1; i >= 1 && result.length < k; i--) {
    for (const num of buckets[i]) {
      result.push(num);
      if (result.length === k) return result;
    }
  }
  return result;
}

Tradeoff:

Duolingo-specific tips

Duolingo interviewers ask this to test whether you know heap vs. bucket sort — both are acceptable but the O(n) bucket approach shows deeper understanding. The key insight: maximum frequency is bounded by n, so bucket indices never overflow. Tie this to Duolingo's use case: surfacing the k words a user has seen most often to schedule them for active recall. Interviewers often follow up with 'What if the stream is infinite?' — that is where a min-heap of size k becomes the right answer.

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Output

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