Top K Frequent Elements Using Heap in DSA Go - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main idea behind using a heap to find the top K frequent elements?

Use a heap to keep track of the K elements with the highest frequency by pushing elements and popping the least frequent when size exceeds K.

beginner

In Go, which heap type is commonly used to find top K frequent elements efficiently?

A min-heap is used to keep the smallest frequency at the top, so when the heap size exceeds K, the least frequent element can be removed.

intermediate

Why do we use a min-heap instead of a max-heap for the top K frequent elements problem?

A min-heap keeps the smallest frequency at the top, allowing easy removal of the least frequent element when the heap size exceeds K, maintaining only the top K frequent elements.

beginner

What data structure is used to count the frequency of elements before using the heap?

A map (dictionary) is used to count how many times each element appears in the input list.

intermediate

Explain the time complexity of finding top K frequent elements using a heap.

Counting frequencies takes O(N). Building and maintaining a heap of size K takes O(N log K). Overall complexity is O(N log K), efficient for large N and small K.

What is the first step in finding the top K frequent elements using a heap?

A Remove duplicates

B Build a max-heap of all elements

C Sort the array

D Count the frequency of each element using a map

We first count how many times each element appears using a map before using a heap.

Which heap type is best to maintain the top K frequent elements efficiently?

A Max-heap

B Min-heap

C Binary search tree

D Stack

A min-heap keeps the smallest frequency on top, so we can remove the least frequent element when size exceeds K.

If the heap size exceeds K, what should you do?

A Remove the element with the lowest frequency

B Remove the element with the highest frequency

C Add more elements

D Clear the heap

Remove the element with the lowest frequency to keep only the top K frequent elements.

What is the overall time complexity of the top K frequent elements algorithm using a heap?

A O(N^2)

B O(N log N)

C O(N log K)

D O(K log N)

Counting frequencies is O(N), and maintaining a heap of size K is O(N log K), so overall O(N log K).

What data structure is used to store the frequency counts before pushing to the heap?

A Map (dictionary)

B Array

C Queue

D Linked list

A map stores each element's frequency count efficiently.

Describe the step-by-step process to find the top K frequent elements using a heap.

Think about counting first, then using a heap to keep only the most frequent.

Explain why a min-heap is preferred over a max-heap in the top K frequent elements problem.

Focus on how to keep the heap size limited to K.

Practice

1. What is the main purpose of using a heap in the Top K Frequent Elements Using Heap algorithm?

easy

A. To efficiently find and keep track of the top K frequent elements

B. To sort all elements in ascending order

C. To store elements without any order

D. To remove duplicates from the list

Solution

1. Step 1: Understand the role of heap in frequency tracking

   A heap helps keep track of elements based on their frequency efficiently, especially when we want only the top K frequent elements.

2. Step 2: Compare with other options

   Sorting all elements or removing duplicates is not the main goal here; the heap is used for efficient frequency comparison and retrieval.

3. Final Answer:

   To efficiently find and keep track of the top K frequent elements -> Option A

4. Quick Check:

   Heap usage = Efficient top K tracking [OK]

Hint: Heap keeps top K frequent elements efficiently [OK]

Common Mistakes:

• Thinking heap sorts all elements fully
• Confusing heap with simple list storage
• Assuming heap removes duplicates

2. Which of the following Go code snippets correctly initializes a min-heap to store pairs of (frequency, element) for the top K frequent elements problem?

easy

A. heap := new([]int); heap.Init(heap)

B. heap := make([]int, 0); heap.Push(heap, pair)

C. heap := &IntHeap{}; heap.Init(heap)

D. var h IntHeap; heap.Init(&h)

Solution

1. Step 1: Understand Go heap initialization

   In Go, a heap is usually implemented by defining a type that implements heap.Interface, then initializing it with heap.Init(&heap).

2. Step 2: Analyze options

   var h IntHeap; heap.Init(&h) correctly declares a variable of type IntHeap and initializes it by passing its address to heap.Init. Other options misuse pointers or heap methods.

3. Final Answer:

   var h IntHeap; heap.Init(&h) -> Option D

4. Quick Check:

   Correct heap init = var h IntHeap; heap.Init(&h) [OK]

Hint: Use heap.Init with pointer to heap variable [OK]

Common Mistakes:

• Calling heap.Init on non-pointer
• Using make for heap without type
• Incorrect pointer usage with new([]int)

3. What will be the output of the following Go code snippet that finds top 2 frequent elements?

nums := []int{1,1,1,2,2,3}
result := topKFrequent(nums, 2)
fmt.Println(result)

Assuming topKFrequent is correctly implemented using a min-heap.

medium

A. [1, 3]

B. [2, 3]

C. [1, 2]

D. [3, 2]

Solution

1. Step 1: Count frequencies of elements

   1 appears 3 times, 2 appears 2 times, 3 appears 1 time.

2. Step 2: Extract top 2 frequent elements

   The top 2 frequent elements are 1 (3 times) and 2 (2 times). So the result is [1, 2].

3. Final Answer:

   [1, 2] -> Option C

4. Quick Check:

   Top 2 frequent = [1, 2] [OK]

Hint: Count frequencies, pick top K by frequency [OK]

Common Mistakes:

• Confusing element order in output
• Including less frequent elements
• Ignoring frequency counts

4. The following Go code snippet is intended to find the top 3 frequent elements but has a bug. What is the bug?

func topKFrequent(nums []int, k int) []int {
    freqMap := make(map[int]int)
    for _, num := range nums {
        freqMap[num]++
    }
    
    h := &IntHeap{}
    heap.Init(h)
    
    for num, freq := range freqMap {
        heap.Push(h, Pair{freq, num})
        if h.Len() > k {
            heap.Pop(h)
        }
    }
    
    res := make([]int, 0, k)
    for h.Len() > 0 {
        p := heap.Pop(h).(Pair)
        res = append(res, p.num)
    }
    return res
}

medium

A. Result list is in ascending frequency order, needs reversing

B. Heap is not initialized before use

C. Frequency map is not counting correctly

D. Heap size check should be < k, not > k

Solution

1. Step 1: Understand heap usage and result order

   The min-heap keeps smallest frequency on top, so popping elements gives ascending frequency order.

2. Step 2: Identify output order issue

   Appending popped elements directly results in ascending order, but top K frequent elements should be in descending order of frequency.

3. Final Answer:

   Result list is in ascending frequency order, needs reversing -> Option A

4. Quick Check:

   Output order issue = Result list is in ascending frequency order, needs reversing [OK]

Hint: Pop from min-heap gives ascending order; reverse result [OK]

Common Mistakes:

• Ignoring output order of popped elements
• Not initializing heap properly
• Incorrect frequency counting

5. Given a large list of integers where many elements have the same frequency, how should the Top K Frequent Elements Using Heap algorithm be adapted to return the top K elements sorted by frequency and then by element value ascending when frequencies tie?

hard

A. Use a map only without heap to track frequencies

B. Use a heap with custom comparison: first by frequency, then by element value ascending

C. Use a max-heap with frequency only, ignoring element value

D. Sort the entire list first, then pick first K elements

Solution

1. Step 1: Understand tie-breaking requirement

   When frequencies tie, elements should be ordered by their value ascending to maintain consistent order.

2. Step 2: Adapt heap comparison logic

   Implement a custom comparison in the heap that compares frequency first, and if equal, compares element values ascending.

3. Final Answer:

   Use a heap with custom comparison: first by frequency, then by element value ascending -> Option B

4. Quick Check:

   Custom heap comparison handles ties correctly [OK]

Hint: Add tie-breaker in heap comparison for stable ordering [OK]

Common Mistakes:

• Ignoring tie-breaker in heap comparison
• Sorting entire list unnecessarily
• Using max-heap without tie-break logic