Let's start with the description for Top K Frequent Elements:

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

For example:

topKFrequent([1, 1, 1, 2, 2, 3], 2);
// -> Output: [1, 2]

topKFrequent([1], 1);
// -> Output: [1]

One of the constraints indicates that it is guaranteed that the answer is unique.

The first obvious idea is to keep a frequency map. We can do it easily like:

let count = new Map();

nums.forEach(n => {
  count.set(n, (count.get(n) ?? 0) + 1);
});

Since we need to return the k most frequent elements, we need to do a bit more work. My idea is to sort the count map by values (the frequencies) in reverse order to keep the most frequent elements in front, then get only the keys (the numbers), and slice it until k:

return [...count.entries()]
  .sort(([, a], [, b]) => b - a)
  .map((i) => i[0])
  .slice(0, k);

All in all, it looks like this:

function topKFrequent(nums: number[], k: number): number[] {
  let count = new Map();

  nums.forEach(n => {
    count.set(n, (count.get(n) ?? 0) + 1);
  });

  return [...count.entries()]
    .sort(([, a], [, b]) => b - a)
    .map(i => i[0])
    .slice(0, k);
};

Time and space complexity

Since we have a sorting operation, the time complexity cannot be better than $O(n \ log \ n)$ . The space complexity is $O(n)$ as it will grow linearly as the nums array grows.

Using Python

After one deep breath, we can try converting the above code into Python:

class Solution:
    def topKFrequent(self, nums: List[int], k: int) -> List[int]:
        count = {}

        for n in nums:
            count[n] = count.get(n, 0) + 1

        sorted_items = sorted(count.items(), key=lambda i: i[1], reverse=True)

        return list(map(lambda x: x[0], sorted_items))[:k]

What we do is pretty much the same as the TypeScript version above.

The problem description also adds a "follow up," that the algorithm's time complexity must be better than $O(n \ log \ n)$ , where $n$ is the array's size. Because we're doing the sorting, it doesn't satisfy this criterion. So, after one more deep breath, let's see NeetCode's solution.

It turns out, there is a better solution with $O(n)$ time complexity using the bucket sort algorithm.

We can create an array of size $n$ where each index corresponds to the count of elements. So, the values that occur twice will be stored in the second index, if all the elements are unique, all of them will be in the index 1, etc.

In that case, if all elements are the same, they will be at the very last index because the count of that element will be $n$ , the length of the nums array.

class Solution:
    def topKFrequent(self, nums: List[int], k: int) -> List[int]:
        count = {}
        freq = [[] for i in range(len(nums) + 1)]

        for n in nums:
            count[n] = 1 + count.get(n, 0)
        for n, c in count.items():
            freq[c].append(n)

        res = []
        for i in range(len(freq) - 1, 0, -1):
            for n in freq[i]:
                res.append(n)
                if len(res) == k:
                    return res

Note that in the last loop, we go in reverse, because higher the index, higher the frequency of values.

In TypeScript, it might look like this:

function topKFrequent(nums: number[], k: number): number[] {
  let count = new Map();
  let freq = Array.from({ length: nums.length + 1 }, () => []);

  for (const n of nums) {
    count.set(n, (count.get(n) ?? 0) + 1);
  }

  for (const [n, c] of count.entries()) {
    freq[c].push(n);
  }

  let res = [];
  for (let i = freq.length - 1; i > 0; i--) {
    for (const n of freq[i]) {
      res.push(n);
      if (res.length === k) { 
        return res;
      }
    }
  }
};

Time and space complexity

The time complexity is $O(n)$ this time, because in the worst case where each element is unique, each loop will iterate over $n$ elements at most. And, the space complexity is $O(n)$ as well, because the storage we use will grow linearly as the nums itself grows.

Next up is the problem Product of Array Except Self. Until then, don't forget to take deep breaths, and happy coding.