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Class 10 · DSA · Enrichment

Union–find / disjoint sets

Interactive explanation Gamified quiz, feedback & rewards

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DSA enrichment · Learning goals & preparation

By the end, you can…

  • Explain An edge whose endpoints already share a root closes a cycle in this edge-insertion setting.
  • Trace a small input and connect each operation to the algorithm’s rule.
  • Explain the implementation’s time and space cost and solve its mission.

Useful preparation: Reading arrays, indexing from zero and following step-by-step instructions. Suggested previous stop: Topological sorting.

DSA uses suggested Foundation (Class 8), Builder (Class 9) and Advanced (Class 10) levels. It is an enrichment pathway.

Graphs · Advanced

Union–find / disjoint sets

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Ready. Step through the algorithm and explain each change.

  1. initialise each vertex as its own parent
  2. find(x): compress path to root
  3. for each edge (u,v)
  4. if roots match: edge closes a cycle
  5. else union roots by rank

Example: 6 vertices, undirected edges

A small fixed example keeps the mechanics easy to inspect.

A deliberate practice loop

Don’t just watch it move

  1. 1Before stepping, predict the next comparison, pointer move or state update.
  2. 2Read the explanation and identify the invariant that remains true.
  3. 3Change the input, then solve the concept quest without guessing.
About this pathway

From foundations to advanced patterns

The library covers core DSA techniques with bounded teaching examples. Foundation, Builder and Advanced describe learning progression, rather than a school-class syllabus. Snapshots are stored for playback and are excluded from algorithm-space labels.

Further study: MIT Introduction to Algorithms ↗