mathtool2/lib/tools/binomial_distribution.dart

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

import 'tool_kit.dart';

/// 二项分布 B(n, p)。
///
///   期望 EX = n·p
///   方差 DX = n·p·(1-p)
///   P(X = i) = C(n,i)·p^i·(1-p)^(n-i)，i = 0…n
///
/// 算式全部交给 Symja：p 允许写 `1/3` 这样的分数，精确概率就原样给分数。
/// 只有画图要 double，才另跑一份数值版表达式（绘图是唯一允许在 Dart 侧碰数的地方）。
class BinomialDistributionPage extends StatefulWidget {
  const BinomialDistributionPage({super.key});

  @override
  State<BinomialDistributionPage> createState() =>
      _BinomialDistributionPageState();
}

class _BinomialDistributionPageState extends State<BinomialDistributionPage> {
  final _n = ToolField('n (试验次数)', hint: '整数，如 4');
  final _p = ToolField('p (成功概率)', hint: '分数或小数，如 1/3');

  @override
  Widget build(BuildContext context) => ToolScaffold(
    title: '二项分布',
    fields: [_n, _p],
    compute: (session) async {
      // n 只用来数个数、定循环范围，取整数是记账不是算数；
      // p 原样交给 Symja 解析（1/3 这种分数不能被 Dart 折成小数）。
      final n = int.tryParse(_n.text);
      if (n == null || n < 0) {
        throw Exception('试验次数 n 必须是非负整数，现在是「${_n.text}」');
      }
      final p = _p.text;
      if (p.isEmpty) throw Exception('请填写成功概率 p');

      final outputs = <ToolOutput>[
        ...await exactAndApprox(session, '期望 EX', 'With[{n=$n,p=$p}, n*p]'),
        ...await exactAndApprox(
          session,
          '方差 DX',
          'With[{n=$n,p=$p}, n*p*(1-p)]',
        ),
      ];

      // 每个 i 的概率：整列一次算出来，再拆成一条一条，这样每条都能单独复制。
      // 精确列走 Rationalize（p 填小数时也能给成分数），数值列给图表用。
      final exact = await session.compute(
        'Rationalize[With[{n=$n,p=$p}, '
        'Table[Binomial[n,i]*p^i*(1-p)^(n-i), {i,0,n}]]]',
      );
      final numeric = await session.compute(
        'With[{n=$n,p=$p}, N[Table[Binomial[n,i]*p^i*(1-p)^(n-i), {i,0,n}], '
        '${session.approximateDigits}]]',
      );
      final probs = parseSymjaList(exact.text);
      final nums = parseSymjaList(numeric.text);
      for (var i = 0; i < probs.length; i++) {
        outputs.add(
          ToolText(
            'P(X = $i)',
            withApprox('${probs[i]}', i < nums.length ? '${nums[i]}' : ''),
          ),
        );
      }

      final values = nums
          .map(asNumber)
          .whereType<double>()
          .toList(growable: false);
      if (values.length == probs.length) {
        outputs.add(ToolChart('概率分布', _barChart(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 —— 保留原来的配色规则。
  Widget _barChart(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: i,
                barRods: [
                  BarChartRodData(
                    toY: probs[i],
                    color: colorAt(i),
                    width: 16,
                    borderRadius: BorderRadius.circular(4),
                  ),
                ],
              ),
          ],
        ),
      ),
    );
  }
}