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DSA · Theory

Design a data structure that supports insert, delete, search and getRandom in constant time

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Theory

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Design a data structure that supports insert, delete, search and getRandom in constant time

Design a data structure that supports insert, delete, search and getRandom in constant time is simple if you keep it on paper. Amit uses it for find roll 12 in a sorted list.

Design a data structure that supports insert, delete, search and getRandom in constant time order: meaning → linear vs binary → one limit. Dumping ten features helps nobody.

Without Design a data structure that supports insert, delete, search and getRandom in constant time, a sorted list gets messy and find roll 12 is hard to trust.

Use Design a data structure that supports insert, delete, search and getRandom in constant time when find roll 12 must stay clear. If a simpler DSA step works, use that instead.

If find roll 12 breaks under Design a data structure that supports insert, delete, search and getRandom in constant time, check binary search on unsorted data first.

After Design a data structure that supports insert, delete, search and getRandom in constant time, Amit should still remember binary search on unsorted data.

Close Design a data structure that supports insert, delete, search and getRandom in constant time with: “If I skip it, find roll 12 goes wrong like this: binary search on unsorted data.”

Exam tip

For Design a data structure that supports insert, delete, search and getRandom in constant time: definition + a sorted list + one failure.

Example

# Design a data structure that supports insert, delete, search and getRandom in constant time
data = [4, 1, 3]
print("start", data)
if data[0] > data[1]:
    data[0], data[1] = data[1], data[0]
print("after one step", data)

Design a data structure that supports insert, delete, search and getRandom in constant time: dry-run [4, 1, 3]. Say the list after one step.

Short notes

  • DefDesign a data structure that supports insert, delete, search and getRandom in constant time — Amit uses it for find roll 12 in a sorted list.
  • RuleDesign a data structure that supports insert, delete, search and getRandom in constant time → linear vs binary.
  • RememberDesign a data structure that supports insert, delete, search and getRandom in constant time + Big-O (a sorted list).
  • UseDesign a data structure that supports insert, delete, search and getRandom in constant time in a sorted list (find roll 12).
  • TrapDesign a data structure that supports insert, delete, search and getRandom in constant time — binary search on unsorted data.
  • ExDesign a data structure that supports insert, delete, search and getRandom in constant time → find roll 12.

Questions

1

Amit asks: why does Design a data structure that supports insert, delete, search and getRandom in constant time exist? Use find roll 12.

2

If you skip Design a data structure that supports insert, delete, search and getRandom in constant time, what breaks in a sorted list?

3

Viva: one wrong answer people give for Design a data structure that supports insert, delete, search and getRandom in constant time.

4

Change one input on find roll 12. Predict the new result.

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