a.py

"""
Sample output:

```
range: 19.7 → 30.9
mean:  25.06

19.6   (0.0%)
20.0   (0.1%)
20.4 █  (0.1%)
20.8 ███  (0.4%)
21.2 ████  (0.6%)
21.6 ████████  (1.2%)
22.0 █████████████  (2.0%)
22.4 ████████████████████  (2.9%)
22.8 ████████████████████████████  (4.1%)
23.2 ████████████████████████████████████████  (5.8%)
23.6 ████████████████████████████████████████████████  (7.0%)
24.0 ████████████████████████████████████████████████████████████  (8.7%)
24.4 ███████████████████████████████████████████████████████████████████  (9.8%)
24.8 ██████████████████████████████████████████████████████████████████████  (10.2%)
25.2 ████████████████████████████████████████████████████████████████  (9.4%)
25.6 █████████████████████████████████████████████████████████████  (8.9%)
26.0 ███████████████████████████████████████████████████████  (8.0%)
26.4 ████████████████████████████████████████████  (6.4%)
26.8 ████████████████████████████████████  (5.3%)
27.2 ███████████████████████  (3.4%)
27.6 █████████████████  (2.4%)
28.0 ██████████  (1.5%)
28.4 ██████  (0.9%)
28.8 ████  (0.6%)
29.2 ██  (0.3%)
29.6 █  (0.1%)
30.0   (0.0%)
30.4   (0.0%)
30.8   (0.0%)

Questions: 0.1/0.1, 0.1/0.3, 0.1/0.7, 0.1/0.9, 0.2/0.2, 0.2/0.5, 0.2/0.6, 0.2/0.8, 0.4/0.5, 0.1/0.3/1.0, 0.1/0.6/0.9, 0.2/0.3/0.5, 0.2/0.3/0.8, 0.3/0.4/0.5, 0.3/0.4/0.9, 0.3/0.5/0.9, 0.3/0.7/0.8, 0.3/0.8/1.0, 0.4/0.5/0.7, 0.4/0.7/0.8, 0.4/0.8/0.9, 0.5/0.7/0.8, 0.5/0.9/1.0, 0.6/0.6/1.0, 0.9/0.9/0.9, 0.2/0.2/0.9/0.9, 0.2/0.3/0.5/0.7, 0.2/0.4/0.7/0.7, 0.2/0.5/0.5/0.6, 0.2/0.5/0.7/0.7, 0.3/0.3/0.4/0.9, 0.3/0.4/0.9/1.0, 0.6/0.6/0.7/0.8, 0.6/0.6/0.7/1.0, 0.1/0.1/0.4/0.6/0.9, 0.1/0.2/0.3/0.6/1.0, 0.1/0.5/0.6/0.8/1.0, 0.1/0.6/0.7/0.8/0.9, 0.1/0.7/0.7/0.9/0.9, 0.2/0.2/0.4/0.7/0.9, 0.2/0.3/0.3/0.4/0.8, 0.2/0.5/0.9/1.0/1.0, 0.3/0.3/0.6/0.6/0.9, 0.3/0.5/0.5/0.6/0.8, 0.4/0.4/0.4/0.7/1.0, 0.5/0.6/0.7/0.9/1.0, 0.7/0.7/0.7/0.8/0.8
```
"""

import random
import math
import collections


QUESTIONS = [
    (0.3, 0.5, 0.5, 0.6, 0.8),
    (0.3, 0.4, 0.9, 1.0),
    (0.4, 0.7, 0.8),
    (0.6, 0.6, 0.7, 1.0),
    (0.4, 0.8, 0.9),
    (0.2, 0.5, 0.5, 0.6),
    (0.5, 0.9, 1.0),
    (0.2, 0.2, 0.9, 0.9),
    (0.7, 0.7, 0.7, 0.8, 0.8),
    (0.3, 0.3, 0.4, 0.9),
    (0.3, 0.8, 1.0),
    (0.2, 0.5, 0.9, 1.0, 1.0),
    (0.6, 0.6, 0.7, 0.8),
    (0.6, 0.6, 1.0),
    (0.2, 0.3, 0.3, 0.4, 0.8),
    (0.1, 0.3, 1.0),
    (0.2, 0.8),
    (0.9, 0.9, 0.9),
    (0.3, 0.3, 0.6, 0.6, 0.9),
    (0.5, 0.6, 0.7, 0.9, 1.0),
    (0.2, 0.5, 0.7, 0.7),
    (0.2, 0.3, 0.8),
    (0.3, 0.4, 0.5),
    (0.2, 0.2),
    (0.1, 0.6, 0.9),
    (0.1, 0.7),
    (0.4, 0.5),
    (0.1, 0.1),
    (0.5, 0.7, 0.8),
    (0.1, 0.9),
    (0.2, 0.2, 0.4, 0.7, 0.9),
    (0.1, 0.2, 0.3, 0.6, 1.0),
    (0.3, 0.5, 0.9),
    (0.3, 0.7, 0.8),
    (0.3, 0.4, 0.9),
    (0.1, 0.7, 0.7, 0.9, 0.9),
    (0.2, 0.4, 0.7, 0.7),
    (0.2, 0.5),
    (0.2, 0.6),
    (0.4, 0.4, 0.4, 0.7, 1.0),
    (0.4, 0.5, 0.7),
    (0.1, 0.3),
    (0.2, 0.3, 0.5, 0.7),
    (0.1, 0.6, 0.7, 0.8, 0.9),
    (0.2, 0.3, 0.5),
    (0.1, 0.1, 0.4, 0.6, 0.9),
    (0.1, 0.5, 0.6, 0.8, 1.0),
]


def generateQuestions(rng):
    questions = []
    for i in range(rng.randint(20, 50)):
        n = rng.randint(2, 5)
        answerWeights = [round(mix(0.1, 1, rng.random()), 1) for j in range(n)]
        question = tuple(sorted(answerWeights))
        questions.append(question)
    return questions


def sampleSurvey(questions: list[tuple[float]], rng) -> int:
    total: int = 0
    for answerWeights in questions:
        weight = rng.choice(answerWeights)
        score = fixedWidth(weight)
        total += score
    return total


def sampleSurveys(questions, n, rng) -> list[float]:
    samples = []
    for i in range(n):
        sample = sampleSurvey(questions, rng)
        samples.append(sample)
    return samples


def printHistogram(samples, approxLines=20):
    p0 = min(samples)
    p100 = max(samples)
    mean = round(sum(samples) / len(samples), 1)

    print(
        f"range: {coFixedWidth(p0)} → {coFixedWidth(p100)}\nmean:  {coFixedWidth(mean)}\n"
    )

    bucketWidth = sigfig((p100 - p0) / approxLines, 1)
    counts = collections.Counter(quantize(bucketWidth, x) for x in samples)
    largest = counts.most_common(1)[0][1]
    maxBarLength = 70
    for bucket, count in sorted(counts.items()):
        barLength = round(mix(0, maxBarLength, coMix(0, largest, count)))
        print(
            coFixedWidth(bucket),
            "█" * barLength,
            f" ({round(100 * count / len(samples), 1)}%)",
        )


def fixedWidth(x: float) -> int:
    return int(x * 1000)


def coFixedWidth(x: int) -> int:
    return round(x / 1000, 2)


def mix(e0, e1, x):
    return x * (e1 - e0) + e0


def coMix(e0, e1, y):
    return (y - e0) / (e1 - e0)


def sigfig(x, sig=2):
    return round(x, sig - int(math.floor(math.log10(abs(x)))) - 1)


def quantize(quantum, x):
    return math.trunc(x / quantum) * quantum


def main():
    rng = random.Random(0)

    if False:
        questions = generateQuestions(rng)
        print(questions)
    else:
        questions = QUESTIONS

    samples = sampleSurveys(questions, 10000, rng)
    printHistogram(samples, 30)
    print("\nQuestions: ", end="")
    print(
        ", ".join(
            sorted(
                ["/".join(str(y) for y in x) for x in questions],
                key=lambda z: (len(z), z),
            )
        )
    )


if __name__ == "__main__":
    main()