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Algorithms
Learn Algorithms as a connected topic across chapters, concepts, simulations, and interview reasoning.
AlgorithmsMental ModelTradeoffsFailure ModesInterview ReasoningHyperLogLog
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HyperLogLog gives you the cleanest entry point before branching into constraints, failures, and related systems.
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Algorithms
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HyperLogLog Cardinality Estimation
Hash values route into registers, leading-zero runs update maxima, and the harmonic mean estimates unique cardinality with bounded error.
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1HyperLogLog Explained: Counting Billions of Unique Items with 12 KBTLDR: HyperLogLog estimates the number of distinct elements in a dataset using ~12 KB of memory regardless of cardinality — with ±0.81% error. The insight: if you hash every element to a random bit st18 min2Count-Min Sketch Explained: Frequency Estimation at Streaming ScaleTLDR: Count-Min Sketch (CMS) is a fixed-size d × w counter matrix that estimates how often any element has appeared in a stream. Insert: hash the element with each of the d hash functions to get one c22 min3Bloom Filters Explained: Membership Testing with Zero False NegativesTLDR: A Bloom filter is a bit array of m bits + k independent hash functions that sets k bits on insert and checks those same k bits on lookup. If any checked bit is 0, the element is definitely not i19 min4Big O Notation Explained: Time Complexity, Space Complexity, and Why They Matter in InterviewsTLDR: Big O notation describes how an algorithm's resource usage grows as input size grows — not how fast it runs on your laptop. Learn to identify the 7 complexity classes (O(1) through O(n!)), deriv34 min5Probabilistic Data Structures: A Practical Guide to Bloom Filters, HyperLogLog, and Count-Min SketchTLDR: Probabilistic data structures trade a small, bounded probability of being wrong for orders-of-magnitude better memory efficiency and O(1) speed. Bloom Filters answer "definitely not in this set"14 min6Two Pointer Technique: Solving Pair and Partition Problems in O(n)TLDR: Place one pointer at the start and one at the end of a sorted array. Move them toward each other based on a comparison condition. Every classic pair/partition problem that naively runs in O(n²) 16 min7Tries (Prefix Trees): The Data Structure Behind AutocompleteTLDR: A Trie stores strings character by character in a tree, so every string sharing a common prefix shares those nodes. Insert and search are O(L) where L is the word length. Tries beat HashMaps on 17 min8Sliding Window Technique: From O(n·k) Scans to O(n) in One PassTLDR: Instead of recomputing a subarray aggregate from scratch on every shift, maintain it incrementally — add the incoming element, remove the outgoing element. For a fixed window this costs O(1) per16 min9Merge Intervals Pattern: Solve Scheduling Problems with Sort and SweepTLDR: Sort intervals by start time, then sweep left-to-right and merge any interval whose start ≤ the current running end. O(n log n) time, O(n) space. One pattern — three interview problems solved.
13 min10In-Place Reversal of a Linked List: The 3-Pointer Dance Every Interviewer ExpectsTLDR: Reversing a linked list in O(1) space requires three pointers — prev, curr, and next. Each step: save next, flip curr.next to point backward, advance both prev and curr. Learn this once and you 16 min11Fast and Slow Pointer: Floyd's Cycle Detection Algorithm ExplainedTLDR: Move a slow pointer one step and a fast pointer two steps through a linked structure. If they ever meet, a cycle exists. Then reset one pointer to the head and advance both one step at a time — 17 min12DFS — Depth-First Search: Go Deep Before Going WideTLDR: DFS explores a graph by diving as deep as possible along each path before backtracking, using a call stack (recursion) or an explicit stack. It is the go-to algorithm for cycle detection, path f15 min
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