Big-O & growth rates

Big-O bounds asymptotic growth. Explicit count models show why linear, quadratic and exponential algorithms scale differently.

Remember: Growth class is not a stopwatch.

Example: At n=8: n is 8, n² is 64, and 2ⁿ is 256.

Time: Model comparison. Auxiliary space: Model comparison.

Formula: 1; floor(log₂ n)+1; n; n(floor(log₂ n)+1); n²; 2ⁿ

Choose n from 1 to 12. Explicit operation-count models illustrate growth classes; they are not benchmark timings. Logarithmic count models a halving loop. Big-O is an asymptotic upper bound; constants and lower-order terms still matter at small inputs. Vertical chart axis: log₂(1 + count).

Complexities describe the underlying algorithm; tutorial snapshots and rendering can use additional resources.

The interactive workspace loads here when JavaScript is available. You can still browse the learning notes and links above without it.