mathtool2/lib/tools/hypergeometric_distribution.dart

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

class HypergeometricDistributionPage extends StatefulWidget {
  @override
  _HypergeometricDistributionPageState createState() => _HypergeometricDistributionPageState();
}

class _HypergeometricDistributionPageState extends State<HypergeometricDistributionPage> {
  final TextEditingController nController = TextEditingController(); // 抽取数
  final TextEditingController NController = TextEditingController(); // 总数
  final TextEditingController MController = TextEditingController(); // 满足条件数

  String expectation = '';
  String variance = '';
  List<String> probabilities = [];
  List<BarChartGroupData> barGroups = [];

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(title: Text('超几何分布')),
      body: SingleChildScrollView( // 添加滚动支持
        child: Padding(
          padding: EdgeInsets.all(16),
          child: Column(
            children: [
              _buildInputField('总数 N', NController),
              _buildInputField('满足条件数 M', MController),
              _buildInputField('抽取数 n', nController),
              SizedBox(height: 20),
              ElevatedButton(
                onPressed: _calculate,
                child: Text('计算'),
              ),
              SizedBox(height: 20),
              if (expectation.isNotEmpty) ...[
                _buildResultCard('期望', expectation),
                _buildResultCard('方差', variance),
                SizedBox(height: 10),
                Text('概率分布:', style: TextStyle(fontWeight: FontWeight.bold)),
                if (barGroups.isNotEmpty) ...[
                  SizedBox(height: 10),
                  Container(
                    height: 300,
                    child: BarChart(
                      BarChartData(
                        barTouchData: BarTouchData(
                          enabled: false,
                        ),
                        titlesData: FlTitlesData(
                          show: true,
                          bottomTitles: AxisTitles(
                            sideTitles: SideTitles(
                              showTitles: true,
                              getTitlesWidget: (value, meta) {
                                return Padding(
                                  padding: const EdgeInsets.only(top: 8.0),
                                  child: Text(
                                    value.toInt().toString(),
                                    style: TextStyle(fontSize: 10),
                                  ),
                                );
                              },
                              reservedSize: 30,
                            ),
                          ),
                          leftTitles: AxisTitles(
                            sideTitles: SideTitles(
                              showTitles: true,
                              getTitlesWidget: (value, meta) {
                                if (value % 0.1 == 0) {
                                  return Text(
                                    value.toStringAsFixed(1),
                                    style: TextStyle(fontSize: 10),
                                  );
                                }
                                return Text('');
                              },
                              reservedSize: 40,
                            ),
                          ),
                          topTitles: AxisTitles(
                            sideTitles: SideTitles(showTitles: false),
                          ),
                          rightTitles: AxisTitles(
                            sideTitles: SideTitles(showTitles: false),
                          ),
                        ),
                        borderData: FlBorderData(show: true),
                        barGroups: barGroups,
                        gridData: FlGridData(show: true),
                        alignment: BarChartAlignment.spaceAround,
                        maxY: _getMaxY(),
                      ),
                    ),
                  ),
                  SizedBox(height: 10),
                ],
                // 移除 Expanded 和 ListView.builder，改用简单的 Column
                Column(
                  children: probabilities.map((prob) => 
                    Card(
                      child: ListTile(
                        title: Text(prob),
                      ),
                    )
                  ).toList(),
                ),
              ],
            ],
          ),
        ),
      ),
    );
  }

  double _getMaxY() {
    if (barGroups.isEmpty) return 1.0;
    double maxY = 0.0;
    for (var group in barGroups) {
      for (var rod in group.barRods) {
        if (rod.toY > maxY) maxY = rod.toY;
      }
    }
    return maxY * 1.1;
  }

  Widget _buildInputField(String label, TextEditingController controller) {
    return Padding(
      padding: EdgeInsets.symmetric(vertical: 8),
      child: TextField(
        controller: controller,
        keyboardType: TextInputType.numberWithOptions(signed: true, decimal: true),
        decoration: InputDecoration(
          labelText: label,
          border: OutlineInputBorder(),
        ),
      ),
    );
  }

  Widget _buildResultCard(String title, String value) {
    return Card(
      child: ListTile(
        title: Text(title),
        subtitle: Text(value),
      ),
    );
  }

  Rational _combination(int n, int k) {
    if (k < 0 || k > n) return Rational.zero;
    if (k == 0 || k == n) return Rational.one;

    BigInt result = BigInt.one;
    for (int i = 1; i <= k; i++) {
      result = result * BigInt.from(n - i + 1) ~/ BigInt.from(i);
    }
    return Rational(result);
  }

  void _calculate() {
    try {
      final N = int.parse(NController.text);
      final M = int.parse(MController.text);
      final n = int.parse(nController.text);

      final m = n - (N - M) > 0 ? n - (N - M) : 0;
      final r = n < M ? n : M;

      final EX = MathUtils.fromInt(n * M) / MathUtils.fromInt(N);
      final DX = MathUtils.fromInt(n * M * (N - M) * (N - n)) /
      (MathUtils.fromInt(N) * MathUtils.fromInt(N) * MathUtils.fromInt(N - 1));

      final probs = <String>[];
      final barGroupsData = <BarChartGroupData>[];

      // 首先计算所有概率并找到最大值
      List<double> probValues = [];
      double maxProb = 0.0;
      
      for (int k = m; k <= r; k++) {
        final combMk = _combination(M, k);
        final combNM_nk = _combination(N - M, n - k);
        final combNn = _combination(N, n);
        final prob = combMk * combNM_nk / combNn;
        final probDouble = prob.toDouble();
        
        probValues.add(probDouble);
        if (probDouble > maxProb) {
          maxProb = probDouble;
        }
        
        probs.add('P(X = $k) = ${MathUtils.rationalToString(prob)}');
      }

      // 找到所有具有最大概率的k值
      List<int> maxProbIndices = [];
      for (int i = 0; i < probValues.length; i++) {
        if (probValues[i] == maxProb) {
          maxProbIndices.add(m + i);
        }
      }

      // 确定最高组的范围
      int minMaxIndex = maxProbIndices.reduce((a, b) => a < b ? a : b);
      int maxMaxIndex = maxProbIndices.reduce((a, b) => a > b ? a : b);

      // 构建柱状图数据
      for (int i = 0; i <= r - m; i++) {
        int k = m + i;
        double probDouble = probValues[i];
        
        barGroupsData.add(
          BarChartGroupData(
            x: k,
            barRods: [
              BarChartRodData(
                toY: probDouble,
                color: _getBarColor(k, minMaxIndex, maxMaxIndex),
                width: 16,
                borderRadius: BorderRadius.circular(4),
              ),
            ],
          ),
        );
      }

      setState(() {
        expectation = 'EX = ${MathUtils.rationalToString(EX)}';
        variance = 'DX = ${MathUtils.rationalToString(DX)}';
        probabilities = probs;
        barGroups = barGroupsData;
      });
    } catch (e) {
      setState(() {
        expectation = '错误: $e';
        variance = '';
        probabilities = [];
        barGroups = [];
      });
    }
  }

  Color _getBarColor(int x, int minMaxIndex, int maxMaxIndex) {
    if (x >= minMaxIndex && x <= maxMaxIndex) {
      // 最高组（可能有多组）
      return Colors.red;
    } else if (x < minMaxIndex) {
      // 最高组左边的组
      return Colors.blue.shade300;
    } else {
      // 最高组右边的组
      return Colors.green.shade300;
    }
  }

  @override
  void dispose() {
    nController.dispose();
    NController.dispose();
    MController.dispose();
    super.dispose();
  }
}