Here is the Leetcode problem link —347. Top K frequent elements

Problem Statement

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

Example 1:

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

Example 2:

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

Constraints:

• 1 <= nums.length <= 10^5

• -10^4 <= nums[i] <= 10^4

• k is in the range [1, the number of unique elements in the array].

• It is guaranteed that the answer is unique.

High Level Approach

The goal is to determine the frequency of each element in the input array and return the top k elements with the highest frequencies.

First, we store the frequency of each element in a map. Next, we use a min-heap to store the {frequency, element} pairs from the map. We then iterate over each entry in the map:

• If the heap size is less than k, we create a {frequency, element} pair and push it to the heap.

• If the heap size is ≥ k, and the frequency of the element at the top of the heap is less than the current element’s frequency, we remove the lower frequency element and insert the higher frequency element into the heap.

The top of the min-heap will always contain the element with the lowest frequency among those in the heap, making it safe to remove when a higher frequency element is encountered. This ensures that, in the end, the heap contains the top k elements with the highest frequencies, which can then be returned as the answer.

Code Implementation in C++

class Solution {
public:
    vector<int> topKFrequent(vector<int>& nums, int k) {
        unordered_map<int, int> count;
        for(int& x: nums) {
            count[x]++;
        }

        priority_queue<pair<int, int>, vector<pair<int, int>>, 
greater<pair<int, int>> > pq;

        for(auto& it: count) {
            if(pq.size() < k) {
                pq.push({it.second, it.first});
            }
            else {
                if(pq.top().first < it.second) {
                    pq.pop();
                    pq.push({it.second, it.first});
                }
            }
        }

        vector<int> ans;

        while(!pq.empty()) {
            ans.push_back(pq.top().second);
            pq.pop();
        }

        return ans;
    }
};

Detailed Code Breakdown:

Frequency Counting:

• We create an unordered_map named count. This map will store each element in the array nums as the key and its frequency (the number of times it appears) as the value.

• We iterate through the nums array using a range-based for loop, incrementing the corresponding element's count in the count map.

Priority Queue with Custom Comparison:

• We declare a priority_queue named pq. This queue will hold pairs of (frequency, element) values.

• The greater<pair<int, int>> comparison function ensures the priority queue prioritizes elements with lower frequencies which is being stored as the first element of the pair (lower frequency value will be at the top of the queue).

Populating the Priority Queue:

• We iterate through the count map using a range-based for loop.

• If the pq size is less than k (we haven't reached the desired number of elements yet), we directly add the (frequency, element) pair to the queue.

• If the pq is already full and the current element's frequency is higher than the lowest frequency element in the queue:

\=> We remove the element with the lowest frequency using pq.pop().

\=> We add the current element with its higher frequency to the queue using pq.push().

Extracting Frequent Elements:

• We create a vector named ans to store the final result (the k most frequent elements).

• We iterate through the pq while it's not empty. For each iteration:

\=> We extract the element (the second value in the pair) from the priority queue using pq.top().second and add it to the ans vector.

\=> We remove the top from the queue using pq.pop().

Returning the Result:

The function returns the ans vector, which contains the k most frequent elements in the array.

Code Dry Run with Test Case:

Let’s consider the test case nums = [1,1,1,2,2,3], k = 2:

Frequency Counting:

The counter map is built as: count = {1: 3, 2: 2, 3: 1}

Priority Queue Population:

Iteration 1: Adding (3, 1)

• Element: 1 (frequency: 3)

• Since the heap is initially empty (pq.size() = 0 < k is true where k = 2), we directly add the (frequency, element) pair, which is (3, 1), to the priority queue.

Iteration 2: Adding (2, 2)

• Element: 2 (frequency: 2)

• The queue now has one element, and we need to consider two elements (pq.size() < k is still true).

• The new element (2) has a frequency of 2, which is higher than the current lowest frequency (3) in the queue. This means element 2 appears less frequently than element 1.

• Since the priority queue prioritizes lower frequencies, the new element (2, 2) is added directly to the heap.

• Heap State: The heap now becomes [(2, 2), (3, 1)]. The element (2, 2) remains at the root because it has the lowest frequency(2)

Iteration 3: Adding (1, 3)

• Element: 3 (frequency: 1)

• The queue now has two elements, and k is still 2.

• The new element (3) has a frequency of 1, which is not greater than the frequency(2) of the heap’s top element(2).

• So we don't modify the queue and continue, ending the iteration over the counter map.

• Heap State: The heap remains unchanged: [(2, 2), (3, 1)]. The element (3, 1) stays at the root as it maintains the lowest frequency.

Extracting Frequent Elements:

1. Heap state: [(2, 2), (3, 1)] — so we first push 2 to the ans vector

2. pop (2, 2) from the heap

3. get the heap’s top element which is 1 and push it to the ans vector.

4. pop the top element from the heap

5. since the heap is empty now:

the while loop is terminated and ans = {2, 1} is returned as the final output.

Note: the order of elements in the output doesn’t matter as mentioned in the problem.

Time and Space Complexity Analysis

The time and space complexity of the provided solution for finding the k most frequent elements can be analyzed as follows:

Time Complexity:

O(n log k): This is the dominant factor in the overall time complexity.

Iterating through the array: We iterate through the input array nums using a for loop. In the worst case, this loop iterates n times (where n is the number of elements in the array).

Priority Queue Operations:

• Adding elements to the priority queue (pq.push()): The time complexity of adding an element to a min-heap is typically logarithmic, around O(log k) in most implementations. In our case, we potentially add elements up to k times (depending on the number of unique elements and their frequencies).

• Removing elements from the priority queue (pq.pop()): Similar to adding, removing an element from a min-heap is also O(log k). We might perform this operation up to k times during the population stage.

• Since the priority queue operations (push and pop) involve logarithmic time complexity and are potentially repeated up to k times, the overall time complexity is dominated by O(n log k).

Space Complexity:

O(n): This is primarily due to the usage of the hash map count.

• The hash map count stores each element in the array as the key and its frequency as the value. In the worst case, the hash map can potentially store all unique elements from the input array, leading to a space complexity of O(n).

• The priority queue pq itself stores a maximum of k elements (the k most frequent elements). While this contributes to space usage, it's typically considered negligible compared to the potentially larger count hash map, especially when k is a relatively small value compared to n.

Real-World Applications

• Customer Analysis and Recommendation Systems: Online retail stores analyze customer purchase history to identify frequently bought items together. This information helps recommend complementary products, personalize promotions, and optimize product placement for better sales (e.g., suggesting frequently purchased groceries alongside main dishes).

• Social Media and Trending Topics: Social media platforms like Twitter utilize algorithms to identify trending topics and hashtags in real-time. By analyzing the frequency of mentions and retweets, they can surface trending conversations and keep users engaged with the latest discussions.

• Network Security and Intrusion Detection Systems (IDS): Network security systems monitor network traffic for suspicious activity. Identifying frequently occurring IP addresses attempting to access unauthorized resources or ports can be a red flag for potential attacks. By finding these frequent occurrences, security systems can trigger alerts and take preventive measures.

Conclusion

By employing a hash map for frequency counting and a priority queue with a custom comparison function, we efficiently identified the k most frequent elements in an array. This approach highlights the power of data structures for solving common data analysis problems in C++.

References

• Blog cover photo by Waldemar on Unsplash

• https://www.ibm.com/docs/SSNN4U_1.0.0/c_fan_rpt_customer_behavior_db.html

• https://www.technologyreview.com/author/mit-technology-review-insights/

• https://www.fortinet.com/resources/cyberglossary/intrusion-detection-system

• Diagrams are made using Canva

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