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LEARNING PATH · Foundations

Advanced Algorithms & Data Structures

For when the interview basics aren’t enough.

Advanced ~3h 15m13 lessons13 steps

The specialized machinery behind real systems — range-query trees, string automata, network flow, and probabilistic sketches — each played as an interactive visualization, in a coherent order.

  • Reach for the right advanced structure: segment / Fenwick trees, B-trees, skip lists
  • Match many patterns and query trees in linear or logarithmic time
  • Model problems as max-flow and estimate at scale with probabilistic sketches
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  1. AlgorithmNext up

    The Segment Tree

    Range queries and updates in O(log n).

  2. Algorithm

    Bits Do the Walking: Fenwick Tree

    The leaner prefix-sum tree — same power, less code.

  3. Algorithm

    How Databases Stay Balanced: B-Trees

    How database indexes stay balanced and shallow on disk.

  4. Algorithm

    Express Lanes: The Skip List

    Balance by coin flips instead of rotations.

  5. Algorithm

    Two Nodes, Climbing to Meet: LCA with Binary Lifting

    Jump up a tree in powers of two.

  6. Algorithm

    The Non-Backtracker: KMP

    Single-pattern matching with no backtracking.

  7. Algorithm

    One Pass, Every Word: Aho-Corasick

    A whole dictionary matched in one pass.

  8. Algorithm

    Cycles Into Components: Tarjan’s SCC

    Strongly connected components in one DFS.

  9. Algorithm

    Pushing Water Through Pipes: Dinic’s Max-Flow

    Max-flow / min-cut, the fast way.

  10. Algorithm

    Fibonacci Fast-Forwarded: Matrix Exponentiation

    Linear recurrences in O(log n).

  11. Algorithm

    Halving the Exponential: Meet in the Middle

    Halve the exponent on brute force.

  12. Algorithm

    Counting a Crowd in Kilobytes: HyperLogLog

    Count billions of distinct items in kilobytes.

  13. Algorithm

    The Fair Draw: Reservoir Sampling

    Sample a stream of unknown length in one pass.

This path picks up where the coding-interview basics stop. It walks the heavier tools engineers actually reach for — the trees that answer range queries in logarithmic time, the automata that scan text for a whole dictionary at once, the flow networks behind matching and scheduling, and the sketches that count billions of items in kilobytes. Each step is an interactive page you can step through, so the mechanism is something you watch rather than memorize. Work top to bottom, or drop into whichever tool you need next.
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