bigo-time 0.1.2

Auto Time Complexity Estimator — empirically measure Big-O with one line

bigo-time — Auto Time Complexity Estimator

One function call. Instant Big-O estimate. No static analysis, no AST tricks — pure empirical measurement.

from bigo_time import analyze

analyze(my_function)

────────────────────────────────────────────────────
  bigo analysis  ·  my_function()
────────────────────────────────────────────────────
  🟡  Estimated complexity : O(n log n)  (Linearithmic)
     R² fit score         : 0.9994  [high confidence]
     Data points used     : 14

           n      avg time   inner loops
  ──────────  ────────────  ────────────
          10    0.0014 ms        10,000
          16    0.0023 ms        10,000
          ...
      32,768    1.4821 ms             1
────────────────────────────────────────────────────

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How it works

Instead of analysing source code (which is hard and often wrong), bigo-time:

1. Generates inputs of geometrically-increasing sizes (n ≈ 10 → 50 000)
2. Measures runtime for each size — intelligently averaging out noise
3. Fits known curves (O(1), O(log n), O(n), O(n log n), O(n²), O(n³), O(2ⁿ)) via least-squares
4. Returns the best fit with an R² confidence score

Problems solved

Problem	Solution
CPU noise & variance	Average 7 independent runs; trim min/max outliers
Small-n bias	15 log-spaced sizes up to ~50 000
Functions too fast to time	Auto-repeat in inner loop; divide elapsed by count
Exponential blowup (2ⁿ)	Per-run and total wall-clock budget; early stop

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Installation

pip install bigo-time

No dependencies — pure Python stdlib.

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Usage

Basic

from bigo_time import analyze

def my_sort(lst):
    return sorted(lst)

result = analyze(my_sort)

Custom input generator

# Default: list of n ints. Override for your data shape:
analyze(my_sort, input_generator=lambda n: list(range(n, 0, -1)))

# Dict-based function
def count_values(d: dict):
    return len(set(d.values()))

analyze(count_values, input_generator=lambda n: {i: i % 100 for i in range(n)})

Custom sizes

# Probe specific sizes
analyze(my_sort, sizes=[100, 500, 1000, 5000, 10000])

Programmatic access

result = analyze(my_sort, print_result=False)

print(result.complexity.notation)   # "O(n log n)"
print(result.complexity.name)       # "Linearithmic"
print(result.r_squared)             # 0.9994
print(result.confidence)            # "high"
print(result.input_sizes)           # [10, 16, 25, ...]
print(result.runtimes)              # [1.4e-6, 2.3e-6, ...]

Verbose mode

analyze(my_sort, verbose=True)
# → n=      10  inner=10,000  avg=  0.0014 ms  stdev=0.0001 ms
# → n=      16  inner=10,000  avg=  0.0023 ms  stdev=0.0002 ms
# ...

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API reference

analyze(func, *, ...)

Parameter	Type	Default	Description
func	Callable	—	Function to analyse
input_generator	Callable[[int], Any]	auto-detected	f(n) → input of size n
sizes	List[int]	log-spaced 10→50k	Input sizes to probe
repeat	int	7	Outer timing repeats per size
time_budget	float	3.0	Per-run abort threshold (seconds)
total_budget	float	30.0	Total wall-clock limit (seconds)
verbose	bool	False	Print live timing lines
print_result	bool	True	Print summary table

Returns AnalysisResult.

AnalysisResult

Attribute	Type	Description
.func_name	str	Name of analysed function
.complexity	ComplexityClass	Best-fit complexity class
.complexity.notation	str	e.g. "O(n log n)"
.complexity.name	str	e.g. "Linearithmic"
.r_squared	float	Goodness-of-fit (0–1)
.confidence	str	"high" / "medium" / "low"
.input_sizes	List[int]	n values measured
.runtimes	List[float]	Per-call averages (seconds)

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Caveats

• Empirical estimation is probabilistic, not exact. Noise, JIT caching, and branch prediction can affect results.
• O(1) and O(log n) are hard to distinguish — both run very fast.
• Results reflect average-case behaviour on the default input shape. Adversarial inputs may show different complexity.
• For O(2ⁿ) functions the early-stop kicks in — you'll get a partial result but the trend is unmistakable.

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License

MIT