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HomeConcept libraryComputer ScienceAlgorithms and Search Foundations

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Follow the authored sequence, or switch to recap mode for a faster review of the same path.

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Starter track6 concepts2 checkpointsComputer Science138 min

Algorithms and Search Foundations

Not started

Start with visible list work, reuse that search language for binary search, and then carry the branch into one live graph bench for adjacency, BFS, DFS, and visited-state behavior.

Use this track when the computer-science slice should stay compact and simulation-first, but still grow beyond the original list-only pilot. The path starts with sorting as a visible process, carries that same bounded search language into binary search, and then reuses one shared graph bench so adjacency, frontier order, and cycle bookkeeping all stay honest instead of becoming syntax lessons.

Visible sorting workComparisons and writesOrdered-data searchHalving the intervalGraph frontiersBFS vs DFS

Entry diagnostic

Decide where to enter this path without opening a second testing system.

Reuse the sorting quick test and the binary-search challenge to decide whether to start from visible sorting work or jump ahead to the shared graph bench.

Start from beginning0 / 2 probes ready

Check the list-to-search bridge first

Start from beginning

No saved diagnostic checks are available yet, so the opening concept is still the best place to start.

Uses the same local-first quick tests, checkpoint challenges, and track history already saved in this browser.

Begin with Sorting and Algorithmic Trade-offs
  2. ChallengeNot started7 checks

    Binary-search checkpoint

    Use the halving challenge to verify that ordered data and shrinking intervals already feel concrete before you skip the opening concept.

    No saved checkpoint attempt yet.

    Binary search
    Open Find a far-right target fast

Why this order

The sequence is authored to keep the model honest.

Sorting and Algorithmic Trade-offs comes first because it turns the list itself into a live object with visible cost and disorder. Binary Search / Halving the Search Space then reuses that list language while ordered data, low-mid-high markers, and interval shrinking explain why binary search is fast. Graph Representation and Adjacency Intuition widens the branch from lists into neighborhoods, Breadth-First Search and Layered Frontiers keeps that bench shallow and queue-based, Depth-First Search and Backtracking Paths gives the same graph a stack-based contrast, and Frontier and Visited State on Graphs closes by showing how cycles become manageable through clean bookkeeping.

Shared concept pages

Each step opens the same simulation-first framework.

Compare mode, prediction mode, quick test, worked examples, guided overlays, challenge mode, and read-next cues stay on the concept pages. The track only decides the guided order and the next recommended stop.

Guided path

Follow the concepts and checkpoint moments in order.

Checkpoint cards reuse the authored challenge entries already living on the concept pages.

  1. 1Not startedMastery: NewStart here

    Sorting and Algorithmic Trade-offs

    Watch sorting as visible work on a live list so input order, comparisons, and writes stay concrete instead of collapsing into one final answer.

    Start here before moving into Binary Search / Halving the Search Space.

    Algorithms and SearchIntro24 min
    Start concept
  2. Checkpoint 1LockedNot started

    Sorting trade-off checkpoint

    Pause once the list and the counters make it clear why a nearly sorted case can reward insertion differently from a heavier bubble run.

    Finish Sorting and Algorithmic Trade-offs first. This checkpoint ties together Sorting trade-offs through Use insertion where it pays off.

    Pause here after Sorting and Algorithmic Trade-offs before moving into Binary Search / Halving the Search Space.

    Sorting trade-offs7 checksCoreGraph-linkedGuided start
    Return to Sorting trade-offsOpen concept
  3. 2Not startedMastery: New

    Binary Search / Halving the Search Space

    Keep an ordered list, the low-mid-high markers, and the shrinking interval visible together so binary search feels visual instead of procedural.

    Builds on Sorting and Algorithmic Trade-offs before setting up Graph Representation and Adjacency Intuition.

    Algorithms and SearchIntro22 min
    Open concept
  4. Checkpoint 2LockedNot started

    Binary-search checkpoint

    Finish by finding a far-right target quickly enough that halving the interval feels different from scanning one by one.

    Finish Binary Search / Halving the Search Space first. This checkpoint ties together Sorting trade-offs and Binary search through Find a far-right target fast.

    Pause here after Binary Search / Halving the Search Space before moving into Graph Representation and Adjacency Intuition.

    Sorting trade-offsBinary search7 checksCoreGraph-linkedGuided start
    Return to Binary searchOpen concept
  5. 3Not startedMastery: New

    Graph Representation and Adjacency Intuition

    Keep one live graph, one local neighborhood, and one frontier cue visible together so graph structure feels readable before traversal rules get formal.

    Builds on Binary Search / Halving the Search Space before setting up Breadth-First Search and Layered Frontiers.

    Algorithms and SearchIntro22 min
    Open concept
  6. 4Not startedMastery: New

    Breadth-First Search and Layered Frontiers

    Keep the queue frontier, visited count, and graph layers visible together so breadth-first search reads as a layered process instead of a procedure list.

    Builds on Graph Representation and Adjacency Intuition before setting up Depth-First Search and Backtracking Paths.

    Algorithms and SearchIntro24 min
    Open concept
  7. 5Not startedMastery: New

    Depth-First Search and Backtracking Paths

    Keep the stack frontier, current depth, and branch order visible together so depth-first search feels like disciplined backtracking instead of random wandering.

    Builds on Breadth-First Search and Layered Frontiers before setting up Frontier and Visited State on Graphs.

    Algorithms and SearchIntro24 min
    Open concept
  8. 6Not startedMastery: New

    Frontier and Visited State on Graphs

    Keep repeat skips, waiting frontier nodes, and already-expanded nodes visible together so cycle handling feels like honest bookkeeping on one graph bench.

    Capstone step after Depth-First Search and Backtracking Paths.

    Algorithms and SearchIntro22 min
    Open concept