Four lines on one chart

Comparing the Curves

The analogy

🧸 ELI5⚙ Tech

Put all four growth shapes on one chart and drag the data size. At ten items they are almost indistinguishable — which is exactly why bad choices survive testing. Drag to a thousand and the quadratic curve leaves the chart entirely.

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Four shapes of growth

step 1 / 6

One curve to start: O(n). Straight line — twice the data, twice the work.O(n): the honest baseline

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PythonJavaScriptHow devs thinkWhere it's used

import math

for n in (10, 100, 1000):
    print(n,
          1,                      # O(1)
          round(math.log2(n)),    # O(log n)
          n,                      # O(n)
          round(n * math.log2(n)),# O(n log n)
          n * n)                  # O(n^2)

Check yourself

At n = 10, an O(n²) algorithm is…