mathtool2/lib/tools/cycle_coloring.dart

import 'package:flutter/material.dart';

import 'tool_kit.dart';

/// n 边形染色：用 k 种颜色给 n 边形的 n 个顶点染色，相邻顶点不同色。
///
/// 圈图 Cₙ 的色多项式是 (k−1)ⁿ + (−1)ⁿ(k−1)。
class CycleColoringPage extends StatefulWidget {
  const CycleColoringPage({super.key});

  @override
  State<CycleColoringPage> createState() => _CycleColoringPageState();
}

class _CycleColoringPageState extends State<CycleColoringPage> {
  final _n = ToolField('n (边数)', hint: '不小于 3 的整数',
      keyboard: TextInputType.number);
  final _k = ToolField('k (颜色数)', hint: '正整数', keyboard: TextInputType.number);

  @override
  Widget build(BuildContext context) => ToolScaffold(
        title: 'n 边形染色',
        fields: [_n, _k],
        intro: const Text('用 k 种颜色给 n 边形的顶点染色，相邻顶点不同色\n'
            '方案数 = (k−1)ⁿ + (k−1)·(−1)ⁿ'),
        compute: (session) async {
          final n = int.tryParse(_n.text);
          final k = int.tryParse(_k.text);
          if (n == null || n < 3) throw Exception('n 要填一个不小于 3 的整数');
          if (k == null || k < 1) throw Exception('k 要填一个正整数');

          return exactAndApprox(
            session,
            '染色方案数',
            '($k-1)^$n + ($k-1)*(-1)^$n',
          );
        },
      );
}