mathtool2/lib/tools/hypergeometric_distribution.dart

// tools/hypergeometric_distribution.dart
import 'package:fl_chart/fl_chart.dart';
import 'package:flutter/material.dart';

import 'tool_kit.dart';

/// 超几何分布。
///
///   期望 EX = n·M/N
///   方差 DX = n·M·(N-M)·(N-n) / (N²·(N-1))
///   P(X = k) = C(M,k)·C(N-M,n-k) / C(N,n)，k = max(0, n-(N-M)) … min(n, M)
///
/// Symja 里 `N` 是内置名（数值近似），所以表达式里的变量一律换成 nn/mm/kk。
class HypergeometricDistributionPage extends StatefulWidget {
  const HypergeometricDistributionPage({super.key});

  @override
  State<HypergeometricDistributionPage> createState() =>
      _HypergeometricDistributionPageState();
}

class _HypergeometricDistributionPageState
    extends State<HypergeometricDistributionPage> {
  final _total = ToolField('总数 N', hint: '整数，如 10');
  final _good = ToolField('满足条件数 M', hint: '整数，如 4');
  final _draw = ToolField('抽取数 n', hint: '整数，如 3');

  @override
  Widget build(BuildContext context) => ToolScaffold(
        title: '超几何分布',
        fields: [_total, _good, _draw],
        compute: (session) async {
          final total = int.tryParse(_total.text);
          final good = int.tryParse(_good.text);
          final draw = int.tryParse(_draw.text);
          if (total == null || good == null || draw == null) {
            throw Exception('总数 N、满足条件数 M、抽取数 n 都必须是整数');
          }
          if (total <= 1) {
            throw Exception('总数 N 必须大于 1（方差公式要除以 N-1）');
          }
          if (good < 0 || good > total) {
            throw Exception('满足条件数 M 必须在 0 到 N 之间（现在是 $good，N = $total）');
          }
          if (draw < 0 || draw > total) {
            throw Exception('抽取数 n 必须在 0 到 N 之间（现在是 $draw，N = $total）');
          }

          // nn=N，mm=M，kk=n（避开内置名 N）。
          final wrap = 'With[{nn=$total,mm=$good,kk=$draw},';

          final outputs = <ToolOutput>[
            ...await exactAndApprox(session, '期望 EX', '$wrap kk*mm/nn]'),
            ...await exactAndApprox(
                session,
                '方差 DX',
                '$wrap kk*mm*(nn-mm)*(nn-kk)/(nn^2*(nn-1))]'),
          ];

          // 表格里的 k 从 max(0, n-(N-M)) 起，是个偏移量。让 Symja 单独算一次，
          // 拿到起点后才能把第 j 项标成真实的 k。
          final startRes =
              await session.compute('$wrap Max[0,kk-(nn-mm)]]');
          final start = int.tryParse(startRes.text.trim());
          if (start == null) {
            throw Exception('无法确定 k 的起始值：${startRes.text}');
          }

          final exact = await session.compute(
            '$wrap Table[Binomial[mm,j]*Binomial[nn-mm,kk-j]/Binomial[nn,kk], '
            '{j, Max[0,kk-(nn-mm)], Min[kk,mm]}]]',
          );
          final probs = parseSymjaList(exact.text);
          for (var i = 0; i < probs.length; i++) {
            outputs.add(ToolText('P(X = ${start + i})', '${probs[i]}'));
          }

          final numeric = await session.compute(
            '$wrap N[Table[Binomial[mm,j]*Binomial[nn-mm,kk-j]/Binomial[nn,kk], '
            '{j, Max[0,kk-(nn-mm)], Min[kk,mm]}], 8]]',
          );
          final values = parseSymjaList(numeric.text)
              .map(asNumber)
              .whereType<double>()
              .toList(growable: false);
          if (values.length == probs.length) {
            outputs.add(ToolChart('概率分布', _barChart(start, values)));
          }
          return outputs;
        },
      );

  /// 柱状图：最高的那一段（可能并排几个）涂红，左边蓝、右边绿 —— 和原来一样的规则。
  Widget _barChart(int start, List<double> probs) {
    var maxProb = 0.0;
    for (final v in probs) {
      if (v > maxProb) maxProb = v;
    }
    var firstMax = -1, lastMax = -1;
    for (var i = 0; i < probs.length; i++) {
      if (probs[i] == maxProb) {
        if (firstMax < 0) firstMax = i;
        lastMax = i;
      }
    }
    Color colorAt(int i) {
      if (i >= firstMax && i <= lastMax) return Colors.red;
      return i < firstMax ? Colors.blue.shade300 : Colors.green.shade300;
    }

    return SizedBox(
      height: 300,
      child: BarChart(
        BarChartData(
          barTouchData: BarTouchData(enabled: false),
          alignment: BarChartAlignment.spaceAround,
          maxY: maxProb == 0 ? 1.0 : maxProb * 1.1,
          borderData: FlBorderData(show: true),
          gridData: FlGridData(show: true),
          titlesData: FlTitlesData(
            bottomTitles: AxisTitles(
              sideTitles: SideTitles(
                showTitles: true,
                reservedSize: 30,
                getTitlesWidget: (value, meta) => Padding(
                  padding: const EdgeInsets.only(top: 8),
                  child: Text('${value.toInt()}',
                      style: const TextStyle(fontSize: 10)),
                ),
              ),
            ),
            leftTitles: AxisTitles(
              sideTitles: SideTitles(
                showTitles: true,
                reservedSize: 40,
                getTitlesWidget: (value, meta) => value % 0.1 == 0
                    ? Text(value.toStringAsFixed(1),
                        style: const TextStyle(fontSize: 10))
                    : const Text(''),
              ),
            ),
            topTitles: AxisTitles(sideTitles: SideTitles(showTitles: false)),
            rightTitles: AxisTitles(sideTitles: SideTitles(showTitles: false)),
          ),
          barGroups: [
            for (var i = 0; i < probs.length; i++)
              BarChartGroupData(
                x: start + i,
                barRods: [
                  BarChartRodData(
                    toY: probs[i],
                    color: colorAt(i),
                    width: 16,
                    borderRadius: BorderRadius.circular(4),
                  ),
                ],
              ),
          ],
        ),
      ),
    );
  }
}