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Let's formalize it precisely: **Formal Definition:** - **Input:** A collection A of n comparable elements and an integer K where 1 ≤ K ≤ n - **Output:** A set S containing exactly K elements from A such that every element in S is greater than or equal to every element in A − S (for Top-K largest) **Key Observations:** 1. **Order within the K elements may or may not matter.** Some problems ask for just the K elements (unordered), while others want them in sorted order. This affects the final step of your solution. 2. **The Kth largest element has special significance.** It serves as the "threshold"—any element greater than or equal to this value is in the Top-K set. 3. **K is typically much smaller than n.** Most real-world Top-K problems have K << n. If K approaches n, you're essentially sorting the entire collection. 4. **The elements don't need to be distinct.** Duplicates are handled naturally by the algorithms we'll explore.73:T96f,import heapq from typing import List def top_k_largest(arr: List[int], k: int) -> List[int]: """ Find the K largest elements using a min-heap. Time Complexity: O(n log K) - We process each of n elements exactly once - Each heap operation (insert/extract) is O(log K) - Since heap size never exceeds K, operations are O(log K), not O(log n) Space Complexity: O(K) - The heap stores at most K elements at any time Args: arr: Input array of n elements k: Number of largest elements to find Returns: List of K largest elements (not necessarily sorted) """ if k <= 0: return [] if k >= len(arr): return arr[:] # All elements are in Top-K # Python's heapq is a min-heap by default # We'll use it directly for finding K largest min_heap = [] for element in arr: if len(min_heap) < k: # Phase 1: Fill the heap until we have K elements heapq.heappush(min_heap, element) elif element > min_heap[0]: # Phase 2: New element beats our weakest candidate # heapreplace is more efficient than extractMin + insert heapq.heapreplace(min_heap, element) return min_heap def top_k_smallest(arr: List[int], k: int) -> List[int]: """ Find the K smallest elements using a max-heap. For K smallest, we use a MAX-heap of size K. The max element is our threshold—anything smaller must be in Top-K. Since Python only provides min-heap, we negate values. """ if k <= 0: return [] if k >= len(arr): return arr[:] # Negate values to simulate max-heap max_heap = [] for element in arr: if len(max_heap) < k: heapq.heappush(max_heap, -element) elif element < -max_heap[0]: # Compare with current max heapq.heapreplace(max_heap, -element) # Negate back to get original values return [-x for x in max_heap] # Example usage and verification if __name__ == "__main__": arr = [5, 2, 9, 1, 7, 6, 8] print(f"Array: {arr}") print(f"Top 3 largest: {sorted(top_k_largest(arr, 3), reverse=True)}") print(f"Top 3 smallest: {sorted(top_k_smallest(arr, 3))}") # Output: # Array: [5, 2, 9, 1, 7, 6, 8] # Top 3 largest: [9, 8, 7] # Top 3 smallest: [1, 2, 5]74:Tc32,/** * MinHeap implementation for Top-K operations. * Most production code would use a library, but understanding * the underlying structure is crucial for interviews and debugging. */ class MinHeap { private heap: number[] = []; get size(): number { return this.heap.length; } peek(): number | undefined { return this.heap[0]; } push(value: number): void { this.heap.push(value); this.bubbleUp(this.heap.length - 1); } pop(): number | undefined { if (this.heap.length === 0) return undefined; const min = this.heap[0]; const last = this.heap.pop()!; if (this.heap.length > 0) { this.heap[0] = last; this.bubbleDown(0); } return min; } // Replace root with new value (more efficient than pop + push) replace(value: number): number { const min = this.heap[0]; this.heap[0] = value; this.bubbleDown(0); return min; } private bubbleUp(index: number): void { while (index > 0) { const parentIndex = Math.floor((index - 1) / 2); if (this.heap[parentIndex] <= this.heap[index]) break; [this.heap[parentIndex], this.heap[index]] = [this.heap[index], this.heap[parentIndex]]; index = parentIndex; } } private bubbleDown(index: number): void { const length = this.heap.length; while (true) { const leftChild = 2 * index + 1; const rightChild = 2 * index + 2; let smallest = index; if (leftChild < length && this.heap[leftChild] < this.heap[smallest]) { smallest = leftChild; } if (rightChild < length && this.heap[rightChild] < this.heap[smallest]) { smallest = rightChild; } if (smallest === index) break; [this.heap[index], this.heap[smallest]] = [this.heap[smallest], this.heap[index]]; index = smallest; } } toArray(): number[] { return [...this.heap]; } } /** * Find the K largest elements using a min-heap. * * Time Complexity: O(n log K) * Space Complexity: O(K) */ function topKLargest(arr: number[], k: number): number[] { if (k <= 0) return []; if (k >= arr.length) return [...arr]; const minHeap = new MinHeap(); for (const element of arr) { if (minHeap.size < k) { // Phase 1: Fill the heap minHeap.push(element); } else if (element > minHeap.peek()!) { // Phase 2: Replace weakest candidate minHeap.replace(element); } } return minHeap.toArray(); } // Example usage const arr = [5, 2, 9, 1, 7, 6, 8]; console.log(`Array: ${arr}`); console.log(`Top 3 largest: ${topKLargest(arr, 3).sort((a, b) => b - a)}`); // Output: Top 3 largest: [9, 8, 7]75:T71f,The basic Top-K pattern extends naturally to several common variations. Understanding these helps you recognize Top-K problems in different disguises. **Variation 1: Kth Largest Element (Single Element)** Sometimes you don't need all K elements—just the Kth one: ```python def kth_largest(arr, k): """The Kth largest is the root of the min-heap after processing.""" min_heap = [] for element in arr: heapq.heappush(min_heap, element) if len(min_heap) > k: heapq.heappop(min_heap) # Evict smallest return min_heap[0] # Root is Kth largest ``` The min-heap root IS the Kth largest—no additional work needed. **Variation 2: Top-K Frequent Elements** Instead of comparing by value, compare by frequency: ```python def top_k_frequent(arr, k): """Find K most frequently occurring elements.""" # Step 1: Count frequencies - O(n) freq = Counter(arr) # Step 2: Use min-heap on frequencies - O(m log K) where m = unique elements min_heap = [] # (frequency, element) for element, count in freq.items(): heapq.heappush(min_heap, (count, element)) if len(min_heap) > k: heapq.heappop(min_heap) return [element for _, element in min_heap] ``` **Variation 3: Top-K with Custom Comparator** Real-world objects have multiple attributes. Use a comparison key: ```python def top_k_products_by_rating(products, k): """Find K highest-rated products, breaking ties by price (lower wins).""" min_heap = [] # (rating, -price, product) - negate price for tie-breaking for product in products: key = (product.rating, -product.price, product) heapq.heappush(min_heap, key) if len(min_heap) > k: heapq.heappop(min_heap) return [item[2] for item in min_heap] ```46:["$","$L71",null,{"owner":"anonymous","state":{"mutations":[],"queries":[{"dehydratedAt":1792296931973,"state":{"data":{"json":{"archivedAt":null,"id":"seed_a45eefd7ace053183db2aca078e8dfbc","slug":"data-structures-algorithms","title":"Data Structures & Algorithms","description":"Build strong algorithmic foundations, trace algorithms visually, solve progressive DSA problems, and apply invariants in real repository and code-review exercises.","image":null,"color":"#10B981","keyTopics":["Arrays & Strings","Linked Lists","Trees & Graphs","Sorting & Searching","Dynamic 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This pattern appears in coding interviews, system design, and production systems regularly.","variant":"info"},"type":"callout"}]},{"id":"defining-top-k-problem","title":"Defining the Top-K Problem","content":[{"data":{"content":"$72"},"type":"text"},{"data":{"icon":"Lightbulb","title":"The Kth Element as Threshold","content":"A crucial insight: finding the \"Kth largest element\" is equivalent to finding the threshold that separates the Top-K from the rest. Once you have this threshold, you can identify all elements in the Top-K set with a single pass. This connection is fundamental to efficient Top-K algorithms.","variant":"tip"},"type":"callout"},{"data":{"content":"**Variants of the Top-K Problem:**"},"type":"text"},{"data":{"rows":[["**Top-K Largest**","Find K elements with highest values","Highest-rated products, top-earning employees"],["**Top-K Smallest**","Find K elements with lowest values","Nearest neighbors, minimum costs"],["**Top-K Frequent**","Find K most frequently occurring elements","Most common words, trending hashtags"],["**Kth Largest/Smallest**","Find the single element at position K","Median (K = n/2), percentile calculations"],["**Top-K in Streaming**","Maintain Top-K as new elements arrive","Real-time leaderboards, live monitoring"]],"headers":["Variant","Description","Example Use Case"]},"type":"table"},{"data":{"content":"Each variant uses the same fundamental heap-based approach, with slight modifications. Mastering the core pattern enables you to solve all variants."},"type":"text"}],"titleType":"number","titleNumber":1},{"id":"why-not-just-sort","title":"Why Not Just Sort?","content":[{"data":{"content":"The most intuitive approach to Top-K is simple: sort the collection, then take the first K elements. Let's analyze why this isn't optimal.\n\n**The Sorting Approach:**\n```\nfunction topKBySorting(arr, k):\n sort(arr) // O(n log n)\n return arr[0...k-1] // O(k)\n```\n\n**Time Complexity:** O(n log n) — dominated by the sorting step\n**Space Complexity:** O(1) to O(n) depending on sorting algorithm\n\n**The Problem:**\n\nThe sorting approach does far more work than necessary. Consider the search engine example with n = 100,000,000 products and K = 10:\n\n- **Sorting approach:** ~2.66 billion comparisons (n log n ≈ 100M × 26.6)\n- **What we actually need:** Information about just 10 elements\n\nWe're using a sledgehammer to hang a picture frame. Sorting computes the *complete ordering* of all elements when we only need the *partial ordering*—specifically, which elements are in the top K."},"type":"text"},{"data":{"icon":"AlertCircle","title":"The Wasted Work of Full Sorting","content":"When K is small relative to n, full sorting wastes effort determining the relative order of elements outside the Top-K. Whether element 1,000 ranks higher than element 2,000 is irrelevant if both are outside the Top-10. This is the key insight that motivates the heap-based approach.","variant":"warning"},"type":"callout"},{"data":{"content":"**Alternative Approaches and Their Trade-offs:**"},"type":"text"},{"data":{"rows":[["**Full Sort**","O(n log n)","O(1)–O(n)","Simple but inefficient for small K"],["**Partial Sort**","O(n log K)","O(K)","Some languages offer this; same as heap"],["**Heap-based**","O(n log K)","O(K)","Optimal for small K; works with streams"],["**QuickSelect**","O(n) average, O(n²) worst","O(1)","Faster average case but modifies input"],["**Median of Medians + QuickSelect**","O(n) guaranteed","O(1)","Optimal worst-case but complex"]],"headers":["Approach","Time Complexity","Space Complexity","Notes"]},"type":"table"},{"data":{"content":"For most practical scenarios, the **heap-based approach** provides the best balance:\n- O(n log K) time complexity\n- O(K) space complexity \n- Works on streams (elements arriving one at a time)\n- Simple to implement and understand\n- Consistent performance (no worst-case degradation)\n\nWhen K is very small (say, K ≤ 100) and n is very large, the heap approach is almost always the right choice."},"type":"text"}],"titleType":"number","titleNumber":2},{"id":"heap-based-solution","title":"The Heap-Based Solution — The Core Pattern","content":[{"data":{"content":"Now we arrive at the heart of the Top-K pattern. The heap-based approach is elegant, efficient, and widely applicable. Here's the key insight:\n\n> **To find the K largest elements, maintain a min-heap of size K. The smallest element in the heap is our \"admission threshold\"—any element larger must be in the Top-K.**\n\nWait—a *min-heap* for finding the *largest* elements? This counterintuitive choice is precisely what makes the algorithm efficient. Let's break it down step by step."},"type":"text"},{"data":{"icon":"Sparkles","title":"The Min-Heap Paradox","content":"Using a min-heap to find the maximum elements seems backwards, but it's the key insight. The min-heap lets us efficiently identify and evict the WEAKEST candidate from our Top-K set. We always know which element would be \"first to go\" if a better candidate arrives—it's right there at the top of the heap.","variant":"note"},"type":"callout"},{"data":{"content":"**The Algorithm:**\n\n```\nfunction topKLargest(arr, k):\n minHeap = new MinHeap()\n \n for each element in arr:\n if minHeap.size() < k:\n // Phase 1: Fill the heap until we have K elements\n minHeap.insert(element)\n else if element > minHeap.peek():\n // Phase 2: New element beats our weakest candidate\n minHeap.extractMin() // Remove weakest\n minHeap.insert(element) // Add new champion\n \n return minHeap.elements()\n```\n\n**Step-by-Step Trace:**\n\nLet's trace through finding the Top-3 from `[5, 2, 9, 1, 7, 6, 8]`:"},"type":"text"},{"data":{"rows":[["1","5","[5]","5","Insert (heap not full)"],["2","2","[2, 5]","2","Insert (heap not full)"],["3","9","[2, 5, 9]","2","Insert (heap now full with K=3)"],["4","1","[2, 5, 9]","2","Skip (1 ≤ 2, not a top candidate)"],["5","7","[5, 7, 9]","5","7 > 2 → Extract 2, Insert 7"],["6","6","[6, 7, 9]","6","6 > 5 → Extract 5, Insert 6"],["7","8","[7, 8, 9]","7","8 > 6 → Extract 6, Insert 8"]],"headers":["Step","Element","Heap Contents","Heap Min","Action"]},"type":"table"},{"data":{"content":"**Result:** [7, 8, 9] — the three largest elements."},"type":"text"},{"data":{"fileName":"top_k_largest.py","languages":[{"code":"$73","label":"Python","value":"python"},{"code":"$74","label":"TypeScript","value":"typescript"}]},"type":"code"}],"titleType":"number","titleNumber":3},{"id":"why-min-heap-for-maximum","title":"Why Min-Heap for Finding Maximum Elements?","content":[{"data":{"content":"This is the most common point of confusion for engineers learning the Top-K pattern. Let's build a deep, intuitive understanding of why the heap choice seems \"backwards.\"\n\n**The Insight: Gatekeeping, Not Championing**\n\nThink of the heap as a **waiting room with limited capacity K**. We want to keep the K strongest candidates inside.\n\nThe crucial question isn't \"Who's the strongest?\" but rather **\"Who should we kick out if someone better arrives?\"**\n\nFor this gatekeeping role, the heap root tells us:\n- In a **min-heap**: Who is the *weakest* current occupant? (First to be evicted)\n- In a **max-heap**: Who is the *strongest* current occupant? (Not useful for eviction)\n\nWhen finding K largest elements, we need quick access to the weakest candidate—the one we'll evict when a better candidate arrives. That's what the min-heap root provides."},"type":"text"},{"data":{"left":[{"data":{"items":["Root = smallest in Top-K (threshold)","Root is our 'weakest link'","New element > root? Evict root, admit new element","New element ≤ root? Reject—can't beat the weakest","O(1) to check if element qualifies","O(log K) to perform replacement"],"title":{"icon":"CheckCircle","text":"Min-Heap for K Largest","type":"icon","color":"primary","variant":"outline-circle"},"variant":"accent"},"type":"list"}],"right":[{"data":{"items":["Root = largest in Top-K (champion)","But we don't need to evict the champion!","To find who to evict, must scan entire heap","Eviction becomes O(K) instead of O(log K)","Total complexity degrades to O(nK)","Defeats the purpose of using a heap"],"title":{"icon":"XCircle","text":"Max-Heap for K Largest (Wrong)","type":"icon","color":"destructive","variant":"outline-circle"},"variant":"accent"},"type":"list"}]},"type":"two-column"},{"data":{"icon":"Lightbulb","title":"The Golden Rule","content":"**For Top-K Largest → Use Min-Heap (quick access to weakest candidate)**\n**For Top-K Smallest → Use Max-Heap (quick access to strongest candidate)**\n\nThe heap type is OPPOSITE to what you're looking for because you need quick access to the element that would be EVICTED, not the element you want to keep.","variant":"tip"},"type":"callout"},{"data":{"content":"**Worked Example: Why Max-Heap Fails**\n\nSuppose we incorrectly use a max-heap to find the Top-3 largest from [5, 2, 9, 1, 7]:"},"type":"text"},{"data":{"rows":[["1","5","[5]","— (not full)"],["2","2","[5, 2]","— (not full)"],["3","9","[9, 5, 2]","— (now full)"],["4","1","[9, 5, 2]","Must scan all 3 to find min (2). O(K)"],["5","7","[9, 7, 5]","Must scan all 3 to find min (2), then restructure. O(K)"]],"headers":["Step","Element","Max-Heap","To find eviction candidate..."]},"type":"table"},{"data":{"content":"With a max-heap, every new element requires scanning the entire heap to find the minimum. For n elements, that's O(nK) total—worse than sorting when K is large!\n\nWith a min-heap, the minimum is always at the root—O(1) access, and O(log K) for the replacement. Total: O(n log K)."},"type":"text"}],"titleType":"number","titleNumber":4},{"id":"complexity-analysis","title":"Complexity Analysis — Understanding the Efficiency","content":[{"data":{"content":"Let's rigorously analyze the time and space complexity of the heap-based Top-K algorithm.\n\n**Time Complexity: O(n log K)**\n\nBreaking down the operations:\n\n1. **For each of n elements:**\n - Comparison with heap root: O(1)\n - If heap not full: Insert → O(log K)\n - If new element qualifies: Extract + Insert (or Replace) → O(log K)\n\n2. **Key insight: Heap size never exceeds K**\n - All heap operations are O(log K), not O(log n)\n - This is the source of efficiency when K << n\n\n3. **Worst case: Every element triggers insertion**\n - Happens when elements arrive in increasing order\n - Still O(n log K) because each insertion is O(log K)\n\n4. **Best case: After initial K elements, no replacements**\n - Happens when K largest elements come first\n - O(K log K) for initial build + O(n - K) for comparisons\n - Effectively O(n) when K << n"},"type":"text"},{"data":{"rows":[["Full Sort","O(n log n)","~2.66 billion ops","Wasteful for small K"],["Heap-Based","O(n log K)","~332 million ops","8x faster for this example"],["QuickSelect","O(n) average","~100 million ops","Fastest average, but worst case O(n²)"],["Median of Medians","O(n) guaranteed","~500 million ops","Larger constants, complex implementation"]],"caption":"Time Complexity Comparison for Top-K","headers":["Approach","Time Complexity","When n=10⁸, K=10","Notes"]},"type":"table"},{"data":{"content":"**Space Complexity: O(K)**\n\nThe heap maintains exactly K elements at any time. This is crucial for:\n- **Memory-constrained environments**: Can process billions of elements with tiny heap\n- **Stream processing**: Never need to store the full input\n- **Distributed systems**: Each node keeps local Top-K, merge at the end\n\n**Concrete Example:**\n- n = 1 billion elements (need ~8GB to store all)\n- K = 100 (need ~800 bytes for heap)\n- Memory reduction: 10,000,000x!\n\nThis space efficiency is what enables stream processing of massive datasets."},"type":"text"},{"data":{"icon":"Zap","title":"The Power of Bounded Space","content":"The O(K) space bound means you can find the Top-100 elements from an infinite stream using constant memory. This is impossible with sorting approaches that require storing all elements. This property makes heaps indispensable for real-time analytics and streaming systems.","variant":"success"},"type":"callout"}],"titleType":"number","titleNumber":5},{"id":"variations-extensions","title":"Variations and Extensions","content":[{"data":{"content":"$75"},"type":"text"},{"data":{"icon":"Info","title":"Sorted Output Requirement","content":"If the problem requires the Top-K elements in sorted order, add a final O(K log K) sorting step. The heap gives you the K elements but not in sorted order. For K = 10, this adds negligible overhead. For larger K, consider whether sorted output is truly necessary.","variant":"note"},"type":"callout"},{"data":{"content":"**Variation 4: Top-K by Key/Score**\n\nVery common in recommendation systems and search engines:\n\n```python\ndef top_k_by_score(items: List[Tuple[str, float]], k: int) -> List[str]:\n \"\"\"\n Given items with scores, return K items with highest scores.\n \n items: List of (item_id, score) tuples\n Returns: List of item_ids for Top-K items\n \"\"\"\n min_heap = [] # (score, item_id)\n \n for item_id, score in items:\n if len(min_heap) < k:\n heapq.heappush(min_heap, (score, item_id))\n elif score > min_heap[0][0]:\n heapq.heapreplace(min_heap, (score, item_id))\n \n # Return in descending score order\n return [item_id for _, item_id in sorted(min_heap, reverse=True)]\n```\n\nThis pattern appears in:\n- Search result ranking\n- Product recommendations \n- Feed personalization\n- Fraud score prioritization"},"type":"text"}],"titleType":"number","titleNumber":6},{"id":"common-mistakes","title":"Common Mistakes and Pitfalls","content":[{"data":{"content":"The Top-K pattern is simple in concept but has several common implementation pitfalls. Being aware of these will save you debugging time."},"type":"text"},{"data":{"items":["**Wrong heap type:** Using max-heap for K largest (should be min-heap). Remember: heap type is OPPOSITE to what you're finding.","**Forgetting the K bound:** Not limiting heap size leads to O(n log n) complexity—same as sorting!","**Off-by-one in heap size:** Should evict when size > K, not when size >= K.","**Incorrect comparison:** For Top-K largest, new element must be STRICTLY greater than heap root to qualify.","**Forgetting edge cases:** K = 0, K >= n, empty input array.","**Tie-breaking issues:** When values are equal, order may matter. Define consistent tie-breaking rules.","**Modifying input:** Some implementations modify the input array. Document and handle appropriately.","**Heap pollution:** In languages with type erasure (Java), mixing types causes subtle bugs."],"title":{"icon":"AlertCircle","text":"Common Pitfalls to Avoid","type":"icon","color":"destructive","variant":"outline-circle"},"variant":"glass"},"type":"list"},{"data":{"fileName":"top_k_edge_cases.py","languages":[{"code":"def top_k_largest_robust(arr: List[int], k: int) -> List[int]:\n \"\"\"\n Robust Top-K implementation handling all edge cases.\n \"\"\"\n # Edge case 1: Invalid K\n if k <= 0:\n return []\n \n # Edge case 2: K >= n (return all elements)\n if k >= len(arr):\n return list(arr) # Return copy, not reference\n \n # Edge case 3: Empty array\n if not arr:\n return []\n \n min_heap = []\n \n for element in arr:\n if len(min_heap) < k:\n heapq.heappush(min_heap, element)\n elif element > min_heap[0]: # STRICTLY greater\n heapq.heapreplace(min_heap, element)\n \n return min_heap\n\n\n# Test edge cases\nassert top_k_largest_robust([], 5) == []\nassert top_k_largest_robust([1, 2, 3], 0) == []\nassert top_k_largest_robust([1, 2, 3], 5) == [1, 2, 3]\nassert top_k_largest_robust([1, 1, 1], 2) == [1, 1] # Duplicates OK\nprint(\"All edge cases passed!\")","label":"Python","value":"python"}]},"type":"code"}],"titleType":"number","titleNumber":7},{"id":"summary","title":"Summary: The Top-K Pattern","content":[{"data":{"content":"We've explored the Top-K pattern in depth—one of the most practical applications of the heap data structure. Let's consolidate the key insights:"},"type":"text"},{"data":{"type":"ordered","items":["**The Top-K problem is ubiquitous**—finding K largest/smallest elements appears in search, recommendations, analytics, and countless other systems.","**Full sorting is wasteful** when K << n. Why compute the complete ordering when you only need K elements?","**Use a min-heap for Top-K largest** (and max-heap for smallest). The heap gives O(1) access to the eviction candidate.","**Time complexity is O(n log K)**, which is a significant improvement over O(n log n) sorting when K is small.","**Space complexity is O(K)**—enabling processing of massive streams with bounded memory.","**The pattern extends naturally** to Kth element, Top-K frequent, and custom comparators.","**Watch for common pitfalls**: wrong heap type, missing bound enforcement, and edge cases."],"title":{"icon":"CheckCircle","text":"Key Takeaways","type":"icon","color":"primary","variant":"outline-circle"},"variant":"accent"},"type":"list"},{"data":{"content":"**What's Next:**\n\nIn the next page, we'll explore **space-efficient K element tracking**—how to maintain a Top-K set that can be dynamically updated as elements are added or removed, and techniques for reducing memory overhead even further."},"type":"text"},{"data":{"icon":"CheckCircle","title":"Pattern Mastered","content":"You now understand the core Top-K pattern with heaps. This single pattern solves a wide variety of interview problems and real-world engineering challenges. In the upcoming pages, we'll build on this foundation to tackle more advanced scenarios including streaming data and real-world applications.","variant":"success"},"type":"callout"}],"titleType":"number","titleNumber":8}],"isLocked":false},{"id":"seed_171c22c90d30b054d6f2cd383305cb46","title":"Space-Efficient K Element Tracking","order":1,"content":null,"isLocked":true},{"id":"seed_3df052493ce09444cb0b3cfd127d96a1","title":"Stream Processing with Heaps","order":2,"content":null,"isLocked":true},{"id":"seed_c17876cf27520936b0b99c920c6ddef1","title":"Real-World Applications","order":3,"content":null,"isLocked":true}]}},"dataUpdateCount":1,"dataUpdatedAt":1792296931947,"error":null,"errorUpdateCount":0,"errorUpdatedAt":0,"fetchFailureCount":0,"fetchFailureReason":null,"fetchMeta":null,"isInvalidated":false,"status":"success","fetchStatus":"idle"},"queryKey":[["learningContent","getModule"],{"input":{"slug":"top-k-problems-and-heap-applications"},"type":"query"}],"queryHash":"[[\"learningContent\",\"getModule\"],{\"input\":{\"slug\":\"top-k-problems-and-heap-applications\"},\"type\":\"query\"}]"},{"dehydratedAt":1792296931995,"state":{"data":{"json":null},"dataUpdateCount":1,"dataUpdatedAt":1792296931949,"error":null,"errorUpdateCount":0,"errorUpdatedAt":0,"fetchFailureCount":0,"fetchFailureReason":null,"fetchMeta":null,"isInvalidated":false,"status":"success","fetchStatus":"idle"},"queryKey":[["learningContent","getProgress"],{"input":{"moduleId":"seed_218c2dcb4053779f26e6206e0a5dd00d"},"type":"query"}],"queryHash":"[[\"learningContent\",\"getProgress\"],{\"input\":{\"moduleId\":\"seed_218c2dcb4053779f26e6206e0a5dd00d\"},\"type\":\"query\"}]"},{"dehydratedAt":1792296931995,"state":{"data":{"json":null},"dataUpdateCount":1,"dataUpdatedAt":1792296931949,"error":null,"errorUpdateCount":0,"errorUpdatedAt":0,"fetchFailureCount":0,"fetchFailureReason":null,"fetchMeta":null,"isInvalidated":false,"status":"success","fetchStatus":"idle"},"queryKey":[["feedback","get"],{"input":{"contentType":"LEARNING_PAGE","contentId":"seed_c17876cf27520936b0b99c920c6ddef1"},"type":"query"}],"queryHash":"[[\"feedback\",\"get\"],{\"input\":{\"contentId\":\"seed_c17876cf27520936b0b99c920c6ddef1\",\"contentType\":\"LEARNING_PAGE\"},\"type\":\"query\"}]"},{"dehydratedAt":1792296931995,"state":{"data":{"json":null},"dataUpdateCount":1,"dataUpdatedAt":1792296931949,"error":null,"errorUpdateCount":0,"errorUpdatedAt":0,"fetchFailureCount":0,"fetchFailureReason":null,"fetchMeta":null,"isInvalidated":false,"status":"success","fetchStatus":"idle"},"queryKey":[["feedback","getUserLike"],{"input":{"contentType":"LEARNING_PAGE","contentId":"seed_c17876cf27520936b0b99c920c6ddef1"},"type":"query"}],"queryHash":"[[\"feedback\",\"getUserLike\"],{\"input\":{\"contentId\":\"seed_c17876cf27520936b0b99c920c6ddef1\",\"contentType\":\"LEARNING_PAGE\"},\"type\":\"query\"}]"},{"dehydratedAt":1792296931995,"state":{"data":{"json":[]},"dataUpdateCount":1,"dataUpdatedAt":1792296931949,"error":null,"errorUpdateCount":0,"errorUpdatedAt":0,"fetchFailureCount":0,"fetchFailureReason":null,"fetchMeta":null,"isInvalidated":false,"status":"success","fetchStatus":"idle"},"queryKey":[["highlights","getHighlights"],{"input":{"contentType":"LEARNING_PAGE","contentId":"seed_c17876cf27520936b0b99c920c6ddef1"},"type":"query"}],"queryHash":"[[\"highlights\",\"getHighlights\"],{\"input\":{\"contentId\":\"seed_c17876cf27520936b0b99c920c6ddef1\",\"contentType\":\"LEARNING_PAGE\"},\"type\":\"query\"}]"},{"dehydratedAt":1792296931995,"state":{"data":"$undefined","dataUpdateCount":0,"dataUpdatedAt":0,"error":null,"errorUpdateCount":0,"errorUpdatedAt":0,"fetchFailureCount":0,"fetchFailureReason":null,"fetchMeta":null,"isInvalidated":false,"status":"pending","fetchStatus":"fetching"},"queryKey":[["highlights","getPopularHighlights"],{"input":{"contentType":"LEARNING_PAGE","contentId":"seed_c17876cf27520936b0b99c920c6ddef1","minCount":2},"type":"query"}],"queryHash":"[[\"highlights\",\"getPopularHighlights\"],{\"input\":{\"contentId\":\"seed_c17876cf27520936b0b99c920c6ddef1\",\"contentType\":\"LEARNING_PAGE\",\"minCount\":2},\"type\":\"query\"}]","promise":"$@76"}]},"children":"$L77"}]