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Class 10 · DSA · Enrichment

Coin change / minimum coins

Interactive explanation Gamified quiz, feedback & rewards

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DSA enrichment · Learning goals & preparation

By the end, you can…

  • Explain Each reachable amount extends a smaller reachable amount by one coin.
  • 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: Longest common subsequence.

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

Dynamic programming · Advanced

Coin change / minimum coins

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Step to initialise the table.

Ready. Step through the algorithm and explain each change.

  1. dp[0] = 0; others = ∞
  2. for amount = 1 to target
  3. for each usable coin
  4. dp[amount] = min(dp[amount], 1+dp[amount−coin])
  5. return dp[target]

Up to 12 integers. Apply input to rebuild the trace and restart this topic’s quest.

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 ↗