Top K Frequent Elements
Given an integer array and integer k, return the k most frequent elements in any order.
Output space-separated, sorted.
Example:
1,1,1,2,2,3 2
1 2
- First, we count the frequency of each element in the array: 1 appears 3 times, 2 appears 2 times, and 3 appears 1 time.
- Then, we sort the elements by their frequency in descending order: 1 (3 times), 2 (2 times), 3 (1 time).
- Next, we select the top k=2 most frequent elements, which are 1 and 2.
- The final output is the selected elements in sorted order: 1 2
Constraints:
- 1 <= len(nums) <= 10^5
- -10^4 <= nums[i] <= 10^4
- k is always valid (1 <= k <= number of unique elements)
Background Knowledge
The "Top K Frequent Elements" problem involves finding the most frequent elements in an array. To solve this, it's essential to understand hash maps, which are data structures that store key-value pairs. In this context, we can use a hash map to count the frequency of each element in the array. The key concept here is that hash maps allow for efficient lookups, insertions, and deletions, with an average time complexity of O(1).
Another crucial concept is counting, which is a fundamental technique in algorithm design. Counting involves keeping track of the number of occurrences of each element in the array. This can be done using a hash map, where the keys are the elements and the values are their corresponding counts. Understanding how to iterate through the array, update the counts, and retrieve the top k elements is vital to solving this problem.
The problem also requires an understanding of sorting and priority queues, as we need to return the top k frequent elements in sorted order. However, since the problem statement allows for any order, we can focus on finding the top k elements first and then sorting them if necessary. The key idea is to use a data structure that allows us to efficiently extract the top k elements, such as a heap or a sorted array.
Algorithm/Approach
The general approach to solving this problem involves using a hash map to count the frequency of each element, followed by a priority queue or sorting step to extract the top k elements. The algorithm pattern is as follows:
- Count the frequency of each element using a hash map
- Use a priority queue or sorting to extract the top k elements
- Return the top k elements in the required order
Step-by-Step Strategy
To implement the solution, follow these steps:
- Create a hash map to store the frequency of each element
- Iterate through the array, updating the frequency count for each element in the hash map
- Use a priority queue or sorting to extract the top k elements from the hash map
- Return the top k elements in the required order
Common Pitfalls
When implementing the solution, watch out for the following:
- Forgetting to handle edge cases, such as an empty array or k = 0
- Using an inefficient data structure, such as a linear search, to extract the top k elements
- Not considering the time and space complexity of the solution
Time & Space Complexity
The expected time complexity is O(nlogk), where n is the length of the array and k is the number of top elements to return. The space complexity is O(n), as we need to store the frequency count for each element in the hash map. Note that the actual time and space complexity may vary depending on the specific implementation and data structure used.