From 4d468494268ba589afbaa20c02fd7aa575d0415e Mon Sep 17 00:00:00 2001 From: LittleSheep Date: Sat, 13 Sep 2025 22:02:13 +0800 Subject: [PATCH] =?UTF-8?q?:lipstick:=20=F0=9F=A4=94?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- lib/solver.dart | 149 +++++++++++++++++++++++++++++++++++++++++++----- 1 file changed, 136 insertions(+), 13 deletions(-) diff --git a/lib/solver.dart b/lib/solver.dart index 27d507f..8085e2a 100644 --- a/lib/solver.dart +++ b/lib/solver.dart @@ -59,15 +59,24 @@ class SolverService { stepNumber: 1, title: '表达式求值', explanation: '这是一个标准的数学表达式，我们将直接计算其结果。', - formula: input, + formula: '\$\$$input\$\$', ), ); - GrammarParser p = GrammarParser(); - Expression exp = p.parse(input); - final result = RealEvaluator().evaluate(exp); + // 预处理平方根符号 + final processedInput = _preprocessSqrt(input); - return CalculationResult(steps: steps, finalAnswer: result.toString()); + GrammarParser p = GrammarParser(); + Expression exp = p.parse(processedInput); + final result = RealEvaluator().evaluate(exp).toDouble(); + + // 尝试将结果格式化为几倍根号的形式 + final formattedResult = _formatSqrtResult(result); + + return CalculationResult( + steps: steps, + finalAnswer: '\$\$$formattedResult\$\$', + ); } /// 2. 求解一元一次方程 @@ -422,6 +431,81 @@ ${b1}y &= ${c1 - a1 * x} /// ---- 辅助函数 ---- + /// 将数值结果格式化为几倍根号的形式 + String _formatSqrtResult(double result) { + // 处理负数 + if (result < 0) { + return '-${_formatSqrtResult(-result)}'; + } + + // 处理零 + if (result == 0) return '0'; + + // 检查是否接近整数 + final rounded = result.round(); + if ((result - rounded).abs() < 1e-10) { + return rounded.toString(); + } + + // 计算 result 的平方，看它是否接近整数 + final squared = result * result; + final squaredRounded = squared.round(); + + // 如果 squared 接近整数，说明 result 是某个数的平方根 + if ((squared - squaredRounded).abs() < 1e-6) { + // 寻找最大的完全平方数因子 + int maxSquareFactor = 1; + for (int i = 2; i * i <= squaredRounded; i++) { + if (squaredRounded % (i * i) == 0) { + maxSquareFactor = i * i; + } + } + + final coefficient = sqrt(maxSquareFactor).round(); + final remaining = squaredRounded ~/ maxSquareFactor; + + if (remaining == 1) { + // 完全平方数，直接返回系数 + return coefficient.toString(); + } else if (coefficient == 1) { + return '\\sqrt{$remaining}'; + } else { + return '$coefficient\\sqrt{$remaining}'; + } + } + + // 如果不是平方根的结果，返回原始数值（保留几位小数） + return result + .toStringAsFixed(6) + .replaceAll(RegExp(r'\.0+$'), '') + .replaceAll(RegExp(r'\.$'), ''); + } + + /// 预处理平方根表示法，将 \sqrt{expr} 转换为 sqrt(expr) + String _preprocessSqrt(String input) { + // 使用正则表达式替换 \sqrt{expr} 为 sqrt(expr) + // 处理嵌套的情况，使用循环直到没有更多匹配 + String result = input; + int maxIterations = 10; // 防止无限循环 + int iterationCount = 0; + + while (iterationCount < maxIterations) { + String oldResult = result; + result = result.replaceAllMapped( + RegExp(r'\\sqrt\{([^}]+)\}'), + (match) => 'sqrt(${match.group(1)})', + ); + if (result == oldResult) break; + iterationCount++; + } + + if (iterationCount >= maxIterations) { + throw Exception('平方根表达式过于复杂，请简化输入。'); + } + + return result; + } + String _expandExpressions(String input) { String result = input; int maxIterations = 10; // Prevent infinite loops @@ -544,29 +628,68 @@ ${b1}y &= ${c1 - a1 * x} Map _parsePolynomial(String side) { final coeffs = {}; + // 扩展模式以支持 sqrt 函数 final pattern = RegExp( - r'([+-]?(?:\d*\.?\d*)?)x(?:\^(\d+))?|([+-]?\d*\.?\d+)', + r'([+-]?(?:\d*\.?\d*|sqrt\(\d+\)))x(?:\^(\d+))?|([+-]?(?:\d*\.?\d*|sqrt\(\d+\)))', ); var s = side.startsWith('+') || side.startsWith('-') ? side : '+$side'; for (final match in pattern.allMatches(s)) { if (match.group(3) != null) { - coeffs[0] = (coeffs[0] ?? 0) + double.parse(match.group(3)!); + // 常数项 + final constStr = match.group(3)!; + final constValue = _parseCoefficientWithSqrt(constStr); + coeffs[0] = (coeffs[0] ?? 0) + constValue; } else { + // x 的幂次项 int power = match.group(2) != null ? int.parse(match.group(2)!) : 1; String coeffStr = match.group(1) ?? '+'; - double coeff = 1.0; - if (coeffStr.isNotEmpty && coeffStr != '+') { - coeff = coeffStr == '-' ? -1.0 : double.parse(coeffStr); - } else if (coeffStr == '-') { - coeff = -1.0; - } + final coeff = _parseCoefficientWithSqrt(coeffStr); coeffs[power] = (coeffs[power] ?? 0) + coeff; } } return coeffs; } + /// 解析包含 sqrt 函数的系数 + double _parseCoefficientWithSqrt(String coeffStr) { + if (coeffStr.isEmpty || coeffStr == '+') return 1.0; + if (coeffStr == '-') return -1.0; + + // 检查是否包含 sqrt 函数 + final sqrtMatch = RegExp(r'sqrt\((\d+)\)').firstMatch(coeffStr); + if (sqrtMatch != null) { + final innerValue = int.parse(sqrtMatch.group(1)!); + + // 对于完全平方数，直接返回整数结果 + final sqrtValue = sqrt(innerValue.toDouble()); + final rounded = sqrtValue.round(); + if ((sqrtValue - rounded).abs() < 1e-10) { + // 检查是否有系数 + final coeffPart = coeffStr.replaceFirst(sqrtMatch.group(0)!, ''); + if (coeffPart.isEmpty) return rounded.toDouble(); + if (coeffPart == '-') return -rounded.toDouble(); + + final coeff = double.parse(coeffPart); + return coeff * rounded; + } + + // 对于非完全平方数，计算数值但保持高精度 + final nonPerfectSqrtValue = sqrt(innerValue.toDouble()); + + // 检查是否有系数 + final coeffPart = coeffStr.replaceFirst(sqrtMatch.group(0)!, ''); + if (coeffPart.isEmpty) return nonPerfectSqrtValue; + if (coeffPart == '-') return -nonPerfectSqrtValue; + + final coeff = double.parse(coeffPart); + return coeff * nonPerfectSqrtValue; + } + + // 普通数值 + return double.parse(coeffStr); + } + List _parseTwoVariableLinear(String equation) { final parts = equation.split('='); if (parts.length != 2) throw Exception("方程 $equation 格式错误");