import json import math from pathlib import Path import random import statistics import matplotlib matplotlib.use("Agg") import matplotlib.pyplot as plt from matplotlib import font_manager from matplotlib.ticker import FuncFormatter OUT = Path(__file__).resolve().parent N = 10 TRIALS = 10_000 SEED = 20260915 LANGUAGE = 'hi' def completion_cdf(n, max_draws): p = [1.0] + [0.0] * n cdf = [p[n]] for _ in range(max_draws): p = [ p[k] * k / n + (p[k - 1] * (n - k + 1) / n if k else 0) for k in range(n + 1) ] assert math.isclose(sum(p), 1.0, abs_tol=1e-12) cdf.append(p[n]) return cdf def collect_all(n, rng): collected = set() draws = 0 while len(collected) < n: collected.add(rng.randrange(n)) draws += 1 return draws def number(value, digits): value = f"{value:.{digits}f}" return value def finish_svg(path): import xml.etree.ElementTree as ET svg_ns = "http://www.w3.org/2000/svg" ET.register_namespace("", svg_ns) ET.register_namespace("xlink", "http://www.w3.org/1999/xlink") tree = ET.parse(path) root = tree.getroot() root.set("{http://www.w3.org/XML/1998/namespace}lang", LANGUAGE) for element in root.iter("{" + svg_ns + "}text"): text = "".join(element.itertext()) style = element.get("style", "") if LANGUAGE == "ar" and any("\u0600" <= c <= "\u06ff" for c in text): if "text-anchor: start" in style: style = style.replace("text-anchor: start", "text-anchor: end") elif "text-anchor: end" in style: style = style.replace("text-anchor: end", "text-anchor: start") elif "text-anchor:" not in style: style += "; text-anchor: end" style += "; direction: rtl; unicode-bidi: plaintext" element.set("style", style) tree.write(path, encoding="utf-8", xml_declaration=True) def main(): fonts = {f.name for f in font_manager.fontManager.ttflist} candidates = ['Nirmala UI'] font = next((f for f in candidates if f in fonts), None) if font is None: raise RuntimeError("ग्राफ़ की भाषा का समर्थन करने वाला फ़ॉन्ट स्थापित करें।") plt.rcParams.update({ "font.family": font, "font.size": 13, "axes.titlesize": 17, "svg.fonttype": "none", "figure.constrained_layout.h_pad": 0.2, "figure.constrained_layout.w_pad": 0.2, "axes.labelsize": 14, "axes.spines.top": False, "axes.spines.right": False, "axes.edgecolor": "#8b96a6", "text.color": "#18263c", "axes.labelcolor": "#18263c", "xtick.color": "#34445b", "ytick.color": "#34445b", "savefig.facecolor": "white", }) cyan, orange = "#007c91", "#c95b16" cdf = completion_cdf(N, 250) mean = N * sum(1 / j for j in range(1, N + 1)) variance = N * N * sum(1 / j**2 for j in range(1, N + 1)) - mean quantiles = {str(a): next(m for m, p in enumerate(cdf) if p >= a) for a in [0.5, 0.9, 0.95, 0.99]} rng = random.Random(SEED) results = [collect_all(N, rng) for _ in range(TRIALS)] fig, ax = plt.subplots(figsize=(10, 5.8), layout="constrained") waiting = [N / (N - k) for k in range(N)] ax.bar(range(N), waiting, color=[cyan] * 9 + [orange], width=0.65) for k, w in enumerate(waiting): ax.text(k, w + 0.18, number(w, 2).rstrip("0").rstrip(".,"), ha="center") ax.set(title="अंतिम प्रकार के लिए ही औसतन 10 बार चुनना पड़ता है", xlabel="पहले से मिले प्रकारों की संख्या (कुल 10)", ylabel="अगला नया प्रकार मिलने तक औसत चयन संख्या", ylim=(0, 11.7), xticks=range(N)) ax.set_axisbelow(True) ax.grid(axis="y", alpha=0.18) fig.savefig(OUT / "stage-waiting.hi.svg", dpi=160) finish_svg(OUT / "stage-waiting.hi.svg") plt.close(fig) fig, ax = plt.subplots(figsize=(10, 5.8), layout="constrained") ax.plot(range(101), cdf[:101], color=cyan, linewidth=2.8) for m, offset in [(30, (8, -40)), (51, (-105, -60)), (66, (10, -35))]: ax.scatter([m], [cdf[m]], color=orange, zorder=4) ax.annotate('{m} चयन: {p}'.format(m=m, p=number(cdf[m] * 100, 1) + "%"), (m, cdf[m]), xytext=offset, textcoords="offset points", fontsize=13, arrowprops={"arrowstyle": "-", "color": "#65758b"}) ax.axvline(mean, color="#69778b", linestyle="--", linewidth=1.2, label='औसत: {v} चयन'.format(v=number(mean, 2))) ax.set(title="30 चयन के बाद भी पूरा होने की संभावना लगभग 63%", xlabel="चयन की संख्या m (10 प्रकार)", ylabel="m चयन तक संग्रह पूरा होने की संभावना", xlim=(0, 100), ylim=(0, 1.06)) ax.yaxis.set_major_formatter(FuncFormatter(lambda value, _: number(value * 100, 0) + "%")) ax.grid(alpha=0.18) ax.legend(loc="lower right", frameon=False) fig.savefig(OUT / "completion-probability.hi.svg", dpi=160) finish_svg(OUT / "completion-probability.hi.svg") plt.close(fig) lows = list(range(10, 100, 5)) + [100] empirical = [sum(lo <= t < lo + 5 for t in results) / TRIALS for lo in lows[:-1]] empirical.append(sum(t >= 100 for t in results) / TRIALS) exact = [cdf[lo + 4] - cdf[lo - 1] for lo in lows[:-1]] exact.append(1 - cdf[99]) assert math.isclose(sum(empirical), 1.0, abs_tol=1e-12) assert math.isclose(sum(exact), 1.0, abs_tol=1e-12) fig, ax = plt.subplots(figsize=(11, 6), layout="constrained") x = list(range(len(lows))) ax.bar(x, empirical, color=cyan, alpha=0.8, width=0.78, label="सिमुलेशन (10,000 संग्रह)") ax.plot(x, exact, color=orange, marker="o", markersize=4, linewidth=1.6, label="उन्हीं अंतरालों की सैद्धांतिक संभावना") ax.set_xticks(x, [f"{lo}–{lo+4}" for lo in lows[:-1]] + ["100 या अधिक"], rotation=55, ha="right", fontsize=10) ax.set(title="कुछ संग्रह जल्दी पूरे होते हैं, कुछ में अधिक समय लगता है", xlabel="पूरा होने तक चयन (5 के अंतराल; अंतिम: 100 या अधिक)", ylabel="हर अंतराल में आने वाला अनुपात", ylim=(0, max(exact + empirical) * 1.22)) ax.yaxis.set_major_formatter(FuncFormatter(lambda value, _: number(value * 100, 0) + "%")) ax.set_axisbelow(True) ax.grid(axis="y", alpha=0.18) ax.legend(frameon=False) fig.savefig(OUT / "simulation-distribution.hi.svg", dpi=160) finish_svg(OUT / "simulation-distribution.hi.svg") plt.close(fig) report = { "model": "प्रतिस्थापन के साथ स्वतंत्र और समान संभाव्यता वाले चयन", "n": N, "seed": SEED, "trials": TRIALS, "theory_mean": mean, "theory_stddev": math.sqrt(variance), "simulation_mean": statistics.mean(results), "simulation_median": statistics.median(results), "simulation_completion_by_30": sum(t <= 30 for t in results) / TRIALS, "simulation_max": max(results), "quantiles": quantiles, "completion_cdf": {str(m): cdf[m] for m in range(101)}, "histogram": {"lower_bounds": lows, "empirical": empirical, "theory": exact}, } (OUT / "calculation-results.hi.json").write_text(json.dumps(report, indent=2) + "\n", encoding="utf-8") print(json.dumps({k: v for k, v in report.items() if k not in ["completion_cdf", "histogram"]}, indent=2)) if __name__ == "__main__": main()