DSA · Theory

Asymptotic Notation

Theory

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Asymptotic Notation

Ananya only reaches for Asymptotic Notation when Ananya walking through Asymptotic Notation has to stay correct in a small live site.

Asymptotic Notation on the board: one Asymptotic Notation step Ananya can write from memory. Then say what Ananya walking through Asymptotic Notation looks like after.

Without Asymptotic Notation, a small live site gets messy and Ananya walking through Asymptotic Notation is hard to trust.

Ananya ships Asymptotic Notation in a small live site. That is the use case worth saying.

If Ananya walking through Asymptotic Notation breaks under Asymptotic Notation, check copy-pasting Asymptotic Notation without a dry-run first.

After Asymptotic Notation, Ananya should still remember copy-pasting Asymptotic Notation without a dry-run.

Close Asymptotic Notation with: “If I skip it, Ananya walking through Asymptotic Notation goes wrong like this: copy-pasting Asymptotic Notation without a dry-run.”

Exam tip

For Asymptotic Notation: definition + a small live site + one failure.

Example

def demo(n):
    # O(1)
    x = n + 1
    # O(n)
    total = sum(range(n))
    # O(n^2)
    pairs = 0
    for i in range(n):
        for j in range(n):
            pairs += 1
    return x, total, pairs

print(demo(3))

Asymptotic Notation — big-O describes how work grows with input size — ignore constants.

Short notes

DefAsymptotic Notation — Ananya uses it for Ananya walking through Asymptotic Notation in a small live site.
RuleAsymptotic Notation → one Asymptotic Notation step Ananya can write from memory.
RememberAsymptotic Notation + a dry-run table (a small live site).
UseAsymptotic Notation in a small live site (Ananya walking through Asymptotic Notation).
TrapAsymptotic Notation — copy-pasting Asymptotic Notation without a dry-run.
ExAsymptotic Notation → Ananya walking through Asymptotic Notation.

def demo(n): # O(1) x = n + 1 # O(n) total = sum(range(n)) # O(n^2) pairs = 0 for i in range(n): for j in range(n): pairs += 1 return x, total, pairs print(demo(3))

Asymptotic Notation

Example

Short notes

Questions

Asymptotic Notation

Example

Short notes

Questions