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graph where nodes are words, edges are single-letter changes function ladderLength(beginWord: string, endWord: string, wordList: string[]): number { const wordSet = new Set(wordList); if (!wordSet.has(endWord)) return 0; // BFS on implicit graph const queue: [string, number][] = [[beginWord, 1]]; const visited = new Set([beginWord]); while (queue.length > 0) { const [word, distance] = queue.shift()!; if (word === endWord) return distance; // Generate all neighbors (words differing by one letter) for (let i = 0; i < word.length; i++) { for (let c = 97; c <= 122; c++) { // 'a' to 'z' const newWord = word.slice(0, i) + String.fromCharCode(c) + word.slice(i + 1); if (wordSet.has(newWord) && !visited.has(newWord)) { visited.add(newWord); queue.push([newWord, distance + 1]); } } } } return 0; // No path exists }74:T400,// Problem: Count ways to climb n stairs, taking 1 to k steps at a time // Classic counting problem with overlapping subproblems function climbStairs(n: number, k: number): 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Structures & Algorithms","topic":"Identifying Problem Patterns","title":"Identifying Problem Patterns","description":"Master the art of recognizing problem patterns—the critical skill that separates expert problem solvers from those who struggle. Learn to categorize problems, map them to data structures and algorithms, and build an intuition that accelerates your problem-solving ability.","difficulty":"ADVANCED","estimatedMinutes":90,"pages":[{"id":"seed_6a7a20e99baf31c70e162e92d8f3e725","title":"Recognizing Problem Categories","order":0,"content":[{"id":"opening-hook","title":"The Pattern Recognition Advantage","content":[{"data":{"content":"Consider two engineers facing the same algorithmic challenge. The first spends 45 minutes exploring dead ends, trying various approaches that don't quite fit, eventually arriving at a solution through trial and error. The second glances at the problem, recognizes its fundamental structure within seconds, and confidently implements a solution in 15 minutes.\n\nWhat separates these two engineers isn't raw intelligence or years of experience alone—it's **pattern recognition**: the ability to see beneath the surface details of a problem and identify its fundamental category. This skill transforms problem-solving from a creative struggle into a structured exercise of recognition and application.\n\nIn this page, we'll develop the definitive framework for recognizing problem categories—the taxonomy that underlies virtually every algorithmic challenge you'll encounter in interviews, competitions, and production systems."},"type":"text"},{"data":{"icon":"Target","title":"What You Will Learn","content":"By the end of this page, you will understand the major categories of algorithmic problems, recognize the distinguishing characteristics of each category, and develop a systematic approach to classification that accelerates your problem-solving ability from the very first glance at a problem statement.","variant":"info"},"type":"callout"}]},{"id":"meta-skill","title":"The Meta-Skill of Problem-Solving","content":[{"data":{"content":"Before diving into specific problem categories, we need to understand why categorization itself is so powerful—and why it's often the missing piece in a developer's problem-solving toolkit.\n\n**The cognitive science of expertise:**\n\nResearch in cognitive psychology consistently demonstrates that expert performance in any domain—chess, medicine, software engineering—relies heavily on **chunking**: the ability to recognize complex patterns as single units. A chess grandmaster doesn't see 32 individual pieces; they see familiar configurations, attack patterns, and strategic structures.\n\nSimilarly, an expert algorithmist doesn't see a problem as a unique puzzle. They see it as an instance of a known category—a variation of the longest increasing subsequence, a graph coloring problem in disguise, or a classic two-pointer scenario with a twist. This recognition immediately narrows the solution space from infinite possibilities to a handful of known approaches."},"type":"text"},{"data":{"icon":"Lightbulb","title":"The Expert's Internal Process","content":"When experts solve problems quickly, they're not computing faster—they're **recognizing** rather than **computing**. They've seen this pattern before (or a close variant), and the solution approach comes as retrieval rather than invention. Your goal is to build this same library of recognizable patterns.","variant":"tip"},"type":"callout"},{"data":{"content":"**Why ad-hoc problem-solving fails at scale:**\n\nWithout a categorical framework, every problem feels novel. You reinvent approaches, miss obvious connections to solved problems, and waste mental energy on structural questions that should be automatic. This approach might work for simple problems, but it becomes exhausting and error-prone as complexity increases.\n\nConsider the difference:\n\n- **Without categorization:** \"This problem asks me to find some kind of optimal path through choices... maybe I should try recursion? Or perhaps dynamic programming? Let me try both and see what works.\"\n\n- **With categorization:** \"This is a shortest-path problem on an implicit graph where states are game configurations and edges are valid moves. Standard BFS will work since all edges have equal weight.\"\n\nThe second engineer isn't smarter—they've simply learned to see the problem's category, which immediately suggests the appropriate technique."},"type":"text"},{"data":{"items":["**Reduced cognitive load** — Once you recognize the category, you stop considering irrelevant solution approaches and focus only on techniques that apply","**Faster convergence** — Category recognition narrows the solution space immediately, reducing exploration time from exponential to linear","**Higher confidence** — When you recognize a known pattern, you can be confident your approach will work before writing code","**Better communication** — Categorical vocabulary lets you discuss problem structure precisely with other engineers","**Transferable intuition** — Solving problems in one category builds intuition that transfers to all problems in that category"],"title":{"icon":"Brain","text":"Benefits of Categorical Thinking","type":"icon","color":"primary","variant":"outline-circle"},"variant":"accent"},"type":"list"}],"titleType":"number","titleNumber":1},{"id":"master-taxonomy","title":"The Master Problem Taxonomy","content":[{"data":{"content":"While problems can be categorized in many ways, the most practical taxonomy organizes problems by their **fundamental computational structure**—the underlying abstract operations that define how solutions must work. This taxonomy cuts across application domains: whether a problem comes from finance, biology, gaming, or pure mathematics, its computational structure determines its category.\n\nHere is the master taxonomy of algorithmic problem categories, organized from most common to specialized:"},"type":"text"},{"data":{"rows":[["Search & Lookup","Find an element or verify existence","Binary search, hash tables, BST, two-pointer","Very High"],["Traversal & Exploration","Visit all elements or states systematically","BFS, DFS, recursion, iteration","Very High"],["Optimization","Find the best solution among many","DP, greedy, binary search on answer","High"],["Counting & Enumeration","Count valid configurations or list all","DP counting, combinatorics, backtracking","High"],["Transformation & Construction","Build or modify a structure","In-place algorithms, constructive proofs","Medium"],["Aggregation & Query","Compute aggregate values over ranges","Prefix sums, segment trees, BIT","Medium"],["Partitioning & Grouping","Divide elements into valid groups","Union-Find, graph coloring, DFS/BFS","Medium"],["Ordering & Arrangement","Find or verify a valid ordering","Topological sort, sorting, permutation check","Medium"],["Matching & Pairing","Find optimal assignments between sets","Bipartite matching, greedy pairing","Lower"],["Simulation & State Machine","Model step-by-step state transitions","Direct simulation, automata","Lower"]],"caption":"Master Problem Category Taxonomy","headers":["Category","Core Question","Typical Techniques","Frequency"]},"type":"table"},{"data":{"content":"**The hierarchical nature of categories:**\n\nThese categories aren't mutually exclusive; they often nest within each other. An optimization problem might require traversal to explore the solution space. A counting problem might embed search subproblems. Understanding both the primary category and secondary elements is crucial for selecting the right approach.\n\nLet's explore each major category in depth, understanding its defining characteristics and how to recognize it in the wild."},"type":"text"}],"titleType":"number","titleNumber":2},{"id":"search-lookup","title":"Category 1: Search & Lookup Problems","content":[{"data":{"content":"**Defining question:** Does a specific element exist, and if so, where?\n\nSearch problems are the most fundamental algorithmic category—finding whether something exists in a collection or locating its position. Despite their simplicity, search problems appear everywhere and form the building blocks of more complex categories."},"type":"text"},{"data":{"items":["**Keywords:** \"find\", \"locate\", \"exists\", \"contains\", \"search for\", \"lookup\"","**Structure:** A collection (array, tree, graph) and a target element or property","**Output type:** Boolean (yes/no), index position, or the element itself","**Implicit searches:** Many problems hide search as a subproblem—\"find the minimum that satisfies...\" is optimization + search"],"title":{"icon":"Search","text":"Recognition Signals for Search Problems","type":"icon","color":"secondary","variant":"outline-circle"},"variant":"accent"},"type":"list"},{"data":{"content":"**Subcategories of search problems:**"},"type":"text"},{"data":{"left":[{"data":{"items":["**Sequential scan** — Check elements one by one when no ordering exists","**First/last occurrence** — Find the first or last element matching a condition","**Conditional search** — Find element satisfying a complex predicate","**Multi-target search** — Find multiple elements in one pass"],"title":"Linear Search Variants","variant":"glass"},"type":"list"}],"right":[{"data":{"items":["**Classic binary search** — Find exact match in sorted array","**Lower/upper bound** — Find insertion point or first/last match","**Binary search on answer** — Search solution space for optimal value","**Rotated/modified arrays** — Binary search with structural variations"],"title":"Binary Search Variants","variant":"glass"},"type":"list"}]},"type":"two-column"},{"data":{"icon":"Info","title":"The Binary Search Recognition Pattern","content":"Binary search applies whenever you have a **monotonic predicate**—a condition that transitions from false to true (or vice versa) at a single point across an ordered space. If you can answer \"given value X, is the answer at least X?\" and the answer changes from 'no' to 'yes' at some threshold, binary search applies. This insight unlocks binary search for optimization problems, not just sorted array lookups.","variant":"note"},"type":"callout"},{"data":{"code":"$72","title":"Binary Search on Answer: Classic Pattern","language":"typescript"},"type":"code"}],"titleType":"number","titleNumber":3},{"id":"traversal-exploration","title":"Category 2: Traversal & Exploration Problems","content":[{"data":{"content":"**Defining question:** How do we visit all relevant elements or explore all possible states?\n\nTraversal problems require systematically visiting elements in a collection—whether it's tree nodes, graph vertices, matrix cells, or abstract state spaces. The key insight is that traversal problems are about **coverage**: ensuring you reach everything that needs to be processed."},"type":"text"},{"data":{"items":["**Keywords:** \"visit all\", \"explore\", \"traverse\", \"reach all\", \"path from X to Y\"","**Structure:** Graph-like data (explicit graphs, grids, trees, state machines)","**Output type:** Path, whether something is reachable, visited node count, or transformed structure","**Constraint patterns:** \"connected components\", \"flood fill\", \"shortest path in unweighted graph\""],"title":{"icon":"Route","text":"Recognition Signals for Traversal Problems","type":"icon","color":"secondary","variant":"outline-circle"},"variant":"accent"},"type":"list"},{"data":{"content":"**The BFS vs DFS decision:**\n\nThe choice between Breadth-First Search and Depth-First Search is one of the most common decisions in traversal problems. Here's a comprehensive guide:"},"type":"text"},{"data":{"rows":[["Shortest path (unweighted)","✓ Optimal—first path found is shortest","✗ May find longer paths first"],["Memory-constrained large graphs","✗ Stores entire frontier (O(width))","✓ Stack only holds current path (O(depth))"],["Finding any path quickly","Depends","✓ Often faster for sparse graphs"],["Level-order processing","✓ Natural level-by-level structure","✗ Mixes levels"],["Cycle detection in directed graphs","Possible but awkward","✓ Natural with back-edge detection"],["Topological sorting","✓ Kahn's algorithm","✓ Reverse postorder"],["State space exploration","✓ When solution is shallow","✓ When solution is deep"],["Maze solving / path finding","✓ Guarantees shortest path","✓ Faster for existence check"]],"caption":"BFS vs DFS: When to Use Each","headers":["Use Case","BFS","DFS"]},"type":"table"},{"data":{"icon":"Lightbulb","title":"The Implicit Graph Pattern","content":"Many traversal problems don't have explicit graphs. Instead, they define states and transitions: a chess position with possible moves, a string with allowed edits, a number with allowed operations. Recognizing these **implicit graphs** is crucial—once you see the graph structure, standard BFS/DFS applies directly.","variant":"tip"},"type":"callout"},{"data":{"code":"$73","title":"Implicit Graph: Word Ladder via BFS","language":"typescript"},"type":"code"}],"titleType":"number","titleNumber":4},{"id":"optimization","title":"Category 3: Optimization Problems","content":[{"data":{"content":"**Defining question:** Among all valid solutions, which is the best according to some criterion?\n\nOptimization problems ask you to find maximum, minimum, or optimal values. They're among the most common interview problems because they naturally test both algorithmic knowledge and the ability to analyze tradeoffs."},"type":"text"},{"data":{"items":["**Keywords:** \"maximum\", \"minimum\", \"optimal\", \"best\", \"least cost\", \"most profit\"","**Structure:** A set of choices/options with associated values or costs","**Output type:** A single optimal value, or the configuration that achieves it","**Constraint patterns:** \"subject to constraints\", \"without exceeding\", \"at least K\""],"title":{"icon":"TrendingUp","text":"Recognition Signals for Optimization Problems","type":"icon","color":"secondary","variant":"outline-circle"},"variant":"accent"},"type":"list"},{"data":{"content":"**The optimization technique decision tree:**\n\nChoosing the right optimization technique depends on problem structure. Here's a systematic approach:"},"type":"text"},{"data":{"code":"Is there optimal substructure? (Optimal solution contains optimal sub-solutions)\n├── NO → Consider exhaustive search, branch & bound, or approximation\n└── YES → Does making locally optimal choices lead to global optimum?\n ├── YES → Use GREEDY algorithm\n │ Examples: Activity selection, Huffman coding, Dijkstra's\n └── NO → Are there overlapping subproblems?\n ├── YES → Use DYNAMIC PROGRAMMING\n │ Examples: Knapsack, LCS, Edit distance, Coin change\n └── NO → Use DIVIDE AND CONQUER\n Examples: Merge sort, Binary search, Closest pair\n\nSpecial case: Can you binary search on the answer?\n├── YES (monotonic feasibility) → BINARY SEARCH ON ANSWER\n│ Examples: Capacity to ship, Minimum speed to arrive\n└── NO → Proceed with above decision tree","title":"Optimization Technique Decision Tree","language":"text"},"type":"code"},{"data":{"icon":"AlertCircle","title":"The Greedy Trap","content":"Many optimization problems *look* greedy but aren't. The 0/1 Knapsack problem is a classic example: taking the highest value-to-weight ratio items doesn't guarantee the optimal solution. Always verify that greedy works (ideally with a proof or exchange argument) before committing to it. When in doubt, DP is safer.","variant":"warning"},"type":"callout"},{"data":{"left":[{"data":{"items":["Greedy choice property holds: local optimal leads to global optimal","You can prove exchange argument: swapping choices doesn't improve","Problem has matroid structure (mathematical condition)","Items can be fractionally selected (fractional knapsack)"],"title":"Greedy Works When...","variant":"glass"},"type":"list"}],"right":[{"data":{"items":["Choices interact: taking one affects what others are worth","Problem has overlapping subproblems","You need to consider combinations, not just individual selections","Counter-examples exist for greedy approaches"],"title":"DP Needed When...","variant":"glass"},"type":"list"}]},"type":"two-column"}],"titleType":"number","titleNumber":5},{"id":"counting-enumeration","title":"Category 4: Counting & Enumeration Problems","content":[{"data":{"content":"**Defining question:** How many valid configurations exist, or what are all valid configurations?\n\nCounting problems ask for the number of ways to achieve something. Enumeration problems ask you to list all valid solutions. These categories are closely related—enumeration is counting where you must produce each item, while counting can often use mathematical shortcuts."},"type":"text"},{"data":{"items":["**Keywords:** \"how many\", \"count the number of\", \"in how many ways\", \"number of paths\"","**Structure:** A set of choices where order or selection matters","**Output type:** A single count (often modulo 10^9+7), or a list of all items","**Constraint patterns:** \"subject to rules\", \"valid combinations\", \"distinct arrangements\""],"title":{"icon":"Hash","text":"Recognition Signals for Counting Problems","type":"icon","color":"secondary","variant":"outline-circle"},"variant":"accent"},"type":"list"},{"data":{"content":"**The counting technique decision:**\n\n- **Combinatorics formulas:** When structure is regular and mathematical formulas apply (permutations, combinations, Catalan numbers)\n- **DP counting:** When structure requires tracking state across choices\n- **Backtracking:** When you need to enumerate all items, not just count them\n- **Inclusion-exclusion:** When counting by complement is easier than direct counting"},"type":"text"},{"data":{"code":"$74","title":"DP Counting: Ways to Climb Stairs with Variable Steps","language":"typescript"},"type":"code"},{"data":{"icon":"Lightbulb","title":"The Modulo Signal","content":"When a problem asks for the count \"modulo 10^9+7\" or similar, it's almost certainly a DP counting problem. The modulo is needed because the true count grows exponentially—too large for standard integers. This constraint is a strong category signal.","variant":"tip"},"type":"callout"}],"titleType":"number","titleNumber":6},{"id":"additional-categories","title":"Additional Problem Categories","content":[{"data":{"content":"Beyond the four major categories above, several specialized categories appear regularly. Here's a brief overview of each with key recognition signals:"},"type":"text"},{"data":{"items":["**Question:** Build X from Y, or convert X into valid form","**Signals:** \"construct\", \"rearrange\", \"transform\", \"make valid\"","**Techniques:** Constructive algorithms, greedy building, simulation","**Example:** Build a valid parentheses string from given characters"],"title":"Transformation & Construction","variant":"accent"},"type":"list"},{"data":{"items":["**Question:** Compute aggregate values efficiently, often with updates","**Signals:** \"range sum\", \"range minimum\", \"update and query\", \"k-th element\"","**Techniques:** Prefix sums, segment trees, Fenwick trees, sparse tables","**Example:** Answer 10^5 range sum queries with point updates"],"title":"Aggregation & Query","variant":"accent"},"type":"list"},{"data":{"items":["**Question:** Divide elements into groups satisfying constraints","**Signals:** \"group\", \"partition\", \"clusters\", \"connected components\"","**Techniques:** Union-Find, graph traversal, DFS forest","**Example:** Find minimum groups such that no two elements in a group conflict"],"title":"Partitioning & Grouping","variant":"accent"},"type":"list"},{"data":{"items":["**Question:** Find a valid ordering or check if ordering is possible","**Signals:** \"dependencies\", \"before/after\", \"prerequisites\", \"topological\"","**Techniques:** Topological sort, sorting with custom comparators","**Example:** Find order to take courses given prerequisite constraints"],"title":"Ordering & Arrangement","variant":"accent"},"type":"list"},{"data":{"items":["**Question:** Find optimal pairing between two sets","**Signals:** \"match\", \"assign\", \"pair\", \"bipartite\"","**Techniques:** Bipartite matching, Hungarian algorithm, greedy pairing","**Example:** Assign students to projects maximizing total preference"],"title":"Matching & Pairing","variant":"accent"},"type":"list"},{"data":{"items":["**Question:** Model a process step by step through defined transitions","**Signals:** \"simulate\", \"after K steps\", \"state transitions\", \"rules\"","**Techniques:** Direct simulation, cycle detection, matrix exponentiation","**Example:** Simulate a game for 10^9 moves (requires cycle detection)"],"title":"Simulation & State Machine","variant":"accent"},"type":"list"}],"titleType":"number","titleNumber":7},{"id":"cross-category","title":"Cross-Category Patterns","content":[{"data":{"content":"Real problems rarely fit cleanly into a single category. Expert problem-solvers recognize when problems combine categories and apply hybrid approaches. Here are the most common combinations:"},"type":"text"},{"data":{"rows":[["Optimization","Search","Find minimum K such that X is possible","Binary search on answer + feasibility check"],["Optimization","Traversal","Shortest path in weighted graph","Dijkstra's algorithm (BFS + priority queue)"],["Counting","Optimization","Count paths with maximum score","DP with both count and max tracking"],["Enumeration","Optimization","Find all optimal solutions","Backtracking with pruning at optimal value"],["Traversal","Aggregation","Sum values from root to each node","DFS with running aggregate"],["Partitioning","Ordering","Divide into groups, order within each","Union-Find + topological sort per group"]],"caption":"Common Category Combinations","headers":["Primary Category","Combined With","Example","Technique"]},"type":"table"},{"data":{"icon":"Info","title":"The Reduction Insight","content":"Many advanced problems are solved by **reducing** them to known problems in different categories. \"If I model X as a graph, this becomes shortest path.\" \"If I think of states as nodes, this is BFS.\" Learning to see problems through multiple categorical lenses enables these powerful reductions.","variant":"note"},"type":"callout"}],"titleType":"number","titleNumber":8},{"id":"recognition-framework","title":"Practical Recognition Framework","content":[{"data":{"content":"Here's a systematic approach to categorize any problem you encounter. Follow these steps to quickly narrow down the applicable category:"},"type":"text"},{"data":{"type":"ordered","items":["**Read the question being asked:** What does the problem actually want? A single value? A path? A count? All valid configurations? This immediately suggests a category.","**Identify the input structure:** Is it a sequence (array, string)? A tree? A graph? A grid? The structure constrains which techniques apply.","**Note the constraints:** Problem constraints encode hints. n ≤ 20 suggests exponential. n ≤ 10^5 suggests O(n log n). Modulo outputs suggest counting DP.","**Look for keywords:** The vocabulary table above maps keywords to categories. \"Maximum\", \"minimum\" → optimization. \"Count\", \"how many\" → counting.","**Ask what happens as input scales:** If finding one thing → search. If visiting everything → traversal. If picking from options → optimization/counting."],"title":{"icon":"ListChecks","text":"5-Step Category Recognition Process","type":"icon","color":"primary","variant":"outline-circle"},"variant":"accent"},"type":"list"},{"data":{"code":"SEARCH & LOOKUP:\n \"find\", \"exists\", \"contains\", \"locate\", \"search\", \"target\"\n\nTRAVERSAL & EXPLORATION:\n \"visit\", \"reach\", \"path to\", \"connected\", \"reachable\", \"explore\"\n\nOPTIMIZATION:\n \"maximum\", \"minimum\", \"optimal\", \"best\", \"largest\", \"smallest\", \"most\", \"least\"\n\nCOUNTING & ENUMERATION:\n \"how many\", \"count\", \"number of ways\", \"all possible\", \"generate all\"\n\nTRANSFORMATION:\n \"convert\", \"transform\", \"rearrange\", \"build\", \"construct\"\n\nAGGREGATION:\n \"range query\", \"sum between\", \"update and query\", \"k-th\"\n\nPARTITIONING:\n \"group\", \"divide\", \"partition\", \"cluster\", \"components\"\n\nORDERING:\n \"valid order\", \"prerequisites\", \"dependencies\", \"sequence\", \"topological\"\n\nMATCHING:\n \"pair\", \"match\", \"assign\", \"bipartite\"\n\nSIMULATION:\n \"simulate\", \"after K steps\", \"evolve\", \"state machine\"","title":"Quick Reference: Keyword to Category Mapping","language":"text"},"type":"code"}],"titleType":"number","titleNumber":9},{"id":"summary","title":"Summary: Recognizing Problem Categories","content":[{"data":{"content":"We've established the foundational framework for recognizing problem categories—the first and most critical step in systematic problem-solving. Let's consolidate the key insights:"},"type":"text"},{"data":{"type":"ordered","items":["**Categorization is the meta-skill** — Recognizing a problem's category immediately narrows the solution space and suggests appropriate techniques","**Ten major categories** — Search, Traversal, Optimization, Counting, Transformation, Aggregation, Partitioning, Ordering, Matching, and Simulation cover virtually all problems","**Categories combine** — Real problems often blend multiple categories; recognize both primary and secondary elements","**Keywords are signals** — Problem vocabulary provides strong hints about category","**Constraints encode hints** — Input size constraints suggest required time complexity, which suggests techniques","**Practice builds recognition** — Each problem you solve adds to your pattern library, accelerating future recognition"],"title":{"icon":"CheckCircle","text":"Key Takeaways","type":"icon","color":"primary","variant":"outline-circle"},"variant":"accent"},"type":"list"},{"data":{"content":"**What's next:**\n\nNow that we can recognize problem categories, the next page explores how to map these categories to appropriate data structures. The right data structure often makes the difference between an elegant O(n) solution and a struggling O(n²) attempt."},"type":"text"},{"data":{"icon":"CheckCircle","title":"Page Complete","content":"You now have a systematic framework for categorizing algorithmic problems. Practice applying this framework to new problems—within a few weeks of consistent practice, category recognition will become automatic.","variant":"success"},"type":"callout"}],"titleType":"number","titleNumber":10}],"isLocked":false},{"id":"seed_8b47c8bc4653d39f40e829ab825bbac1","title":"Mapping Problems to Data Structures","order":1,"content":null,"isLocked":true},{"id":"seed_fae5f16f4d497562dccf8770bf5adb18","title":"Mapping Problems to Algorithms","order":2,"content":null,"isLocked":true},{"id":"seed_4e8c0933c971358f97f65c21e707e217","title":"Building a Pattern Recognition Muscle","order":3,"content":null,"isLocked":true}]}},"dataUpdateCount":1,"dataUpdatedAt":1792296611472,"error":null,"errorUpdateCount":0,"errorUpdatedAt":0,"fetchFailureCount":0,"fetchFailureReason":null,"fetchMeta":null,"isInvalidated":false,"status":"success","fetchStatus":"idle"},"queryKey":[["learningContent","getModule"],{"input":{"slug":"identifying-problem-patterns"},"type":"query"}],"queryHash":"[[\"learningContent\",\"getModule\"],{\"input\":{\"slug\":\"identifying-problem-patterns\"},\"type\":\"query\"}]"},{"dehydratedAt":1792296611531,"state":{"data":{"json":null},"dataUpdateCount":1,"dataUpdatedAt":1792296611472,"error":null,"errorUpdateCount":0,"errorUpdatedAt":0,"fetchFailureCount":0,"fetchFailureReason":null,"fetchMeta":null,"isInvalidated":false,"status":"success","fetchStatus":"idle"},"queryKey":[["learningContent","getProgress"],{"input":{"moduleId":"seed_34a7d902db97e7fc25360b5f31a1a703"},"type":"query"}],"queryHash":"[[\"learningContent\",\"getProgress\"],{\"input\":{\"moduleId\":\"seed_34a7d902db97e7fc25360b5f31a1a703\"},\"type\":\"query\"}]"},{"dehydratedAt":1792296611531,"state":{"data":{"json":null},"dataUpdateCount":1,"dataUpdatedAt":1792296611472,"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_fae5f16f4d497562dccf8770bf5adb18"},"type":"query"}],"queryHash":"[[\"feedback\",\"get\"],{\"input\":{\"contentId\":\"seed_fae5f16f4d497562dccf8770bf5adb18\",\"contentType\":\"LEARNING_PAGE\"},\"type\":\"query\"}]"},{"dehydratedAt":1792296611531,"state":{"data":{"json":null},"dataUpdateCount":1,"dataUpdatedAt":1792296611472,"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_fae5f16f4d497562dccf8770bf5adb18"},"type":"query"}],"queryHash":"[[\"feedback\",\"getUserLike\"],{\"input\":{\"contentId\":\"seed_fae5f16f4d497562dccf8770bf5adb18\",\"contentType\":\"LEARNING_PAGE\"},\"type\":\"query\"}]"},{"dehydratedAt":1792296611531,"state":{"data":{"json":[]},"dataUpdateCount":1,"dataUpdatedAt":1792296611472,"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_fae5f16f4d497562dccf8770bf5adb18"},"type":"query"}],"queryHash":"[[\"highlights\",\"getHighlights\"],{\"input\":{\"contentId\":\"seed_fae5f16f4d497562dccf8770bf5adb18\",\"contentType\":\"LEARNING_PAGE\"},\"type\":\"query\"}]"},{"dehydratedAt":1792296611531,"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_fae5f16f4d497562dccf8770bf5adb18","minCount":2},"type":"query"}],"queryHash":"[[\"highlights\",\"getPopularHighlights\"],{\"input\":{\"contentId\":\"seed_fae5f16f4d497562dccf8770bf5adb18\",\"contentType\":\"LEARNING_PAGE\",\"minCount\":2},\"type\":\"query\"}]","promise":"$@75"}]},"children":"$L76"}]