From 1b80702bbe7915cc61888135fce6af60d50aac0a Mon Sep 17 00:00:00 2001 From: LittleSheep Date: Tue, 16 Sep 2025 22:17:57 +0800 Subject: [PATCH] :wastebasket: Clean up code --- lib/solver.dart | 205 ++++++++++++++++++++++++++++++++++++++---------- 1 file changed, 162 insertions(+), 43 deletions(-) diff --git a/lib/solver.dart b/lib/solver.dart index 9ba1ee6..cd1e06c 100644 --- a/lib/solver.dart +++ b/lib/solver.dart @@ -24,37 +24,43 @@ class SolverService { return formatted; } - /// 获取整数的所有因数（包括正负） - List _getAllDivisors(int n) { - List divisors = []; - int absN = n.abs(); - for (int i = 1; i <= absN; i++) { - if (absN % i == 0) { - divisors.add(i); - if (i != absN) divisors.add(-i); - } - } - return divisors; - } - /// 尝试对二次方程进行因式分解 String? _tryFactorQuadratic(double a, double b, double c) { if (a != a.round() || b != b.round() || c != c.round()) return null; int aa = a.round(), bb = b.round(), cc = c.round(); if (aa == 0) return null; // 不是二次方程 - var divisorsA = _getAllDivisors(aa); - var divisorsC = _getAllDivisors(cc); - for (int p in divisorsA) { - int r = aa ~/ p; - for (int q in divisorsC) { - int s = cc ~/ q; - if (p * s + q * r == bb) { - String factor1 = _formatFactorTerm(p, q); - String factor2 = _formatFactorTerm(r, s); - return '($factor1)($factor2)'; + + // 简单情况：如果 a=1，尝试简单的因式分解 + if (aa == 1) { + // 寻找两个因式 (x + m)(x + n) = x^2 + (m+n)x + mn + // 需要满足 m+n = -b, mn = c + for (int m = -100; m <= 100; m++) { + for (int n = -100; n <= 100; n++) { + if (m + n == -bb && m * n == cc) { + String factor1 = _formatFactorTerm(1, -m); + String factor2 = _formatFactorTerm(1, -n); + return '($factor1)($factor2)'; + } } } } + + // 简单情况：如果 a=-1，尝试简单的因式分解 + if (aa == -1) { + // 寻找两个因式 -(x + m)(x + n) = -x^2 - (m+n)x - mn + // 需要满足 m+n = b, mn = -c + for (int m = -100; m <= 100; m++) { + for (int n = -100; n <= 100; n++) { + if (m + n == bb && m * n == -cc) { + String factor1 = _formatFactorTerm(1, m); + String factor2 = _formatFactorTerm(1, n); + return '-($factor1)($factor2)'; + } + } + } + } + + // 对于更复杂的情况，暂时不进行因式分解 return null; } @@ -407,13 +413,9 @@ class SolverService { formula: '\$\$$factored = 0\$\$', ), ); - final discriminant = b * b - 4 * a * c; - final roots = _calculateSymbolicRoots( - a, - b, - discriminant, - _getSymbolicSquareRoot(discriminant), - ); + + // Parse the factored form to find the roots + final roots = _calculateRootsFromFactoredForm(factored); steps.add( CalculationStep( stepNumber: 4, @@ -1732,6 +1734,94 @@ ${b1}y &= ${c1 - a1 * x.toDouble()} return '\\frac{${r.numerator}}{${r.denominator}}'; } + /// 从因式分解形式计算二次方程的根 + ({String formula, String finalAnswer}) _calculateRootsFromFactoredForm( + String factored, + ) { + // 解析因式分解形式，如 "(2x + 4)(x - 3)" 或 "(x - 1)(x - 1)" + final factorMatch = RegExp(r'\(([^)]+)\)\(([^)]+)\)').firstMatch(factored); + if (factorMatch == null) { + return (formula: '\$\$无法解析因式形式\$\$', finalAnswer: '\$\$无法解析因式形式\$\$'); + } + + final factor1 = factorMatch.group(1)!; + final factor2 = factorMatch.group(2)!; + + // 简化解析：直接从字符串中提取系数 + double a1 = 1, b1 = 0; + double a2 = 1, b2 = 0; + + // 解析第一个因式 + final f1 = factor1.replaceAll(' ', ''); + if (f1.contains('x')) { + final parts = f1.split('x'); + if (parts[0].isEmpty || parts[0] == '+') { + a1 = 1; + } else if (parts[0] == '-') { + a1 = -1; + } else { + a1 = double.parse(parts[0]); + } + + if (parts.length > 1 && parts[1].isNotEmpty) { + b1 = double.parse(parts[1]); + } + } else { + // 常数项 + b1 = double.parse(f1); + a1 = 0; + } + + // 解析第二个因式 + final f2 = factor2.replaceAll(' ', ''); + if (f2.contains('x')) { + final parts = f2.split('x'); + if (parts[0].isEmpty || parts[0] == '+') { + a2 = 1; + } else if (parts[0] == '-') { + a2 = -1; + } else { + a2 = double.parse(parts[0]); + } + + if (parts.length > 1 && parts[1].isNotEmpty) { + b2 = double.parse(parts[1]); + } + } else { + // 常数项 + b2 = double.parse(f2); + a2 = 0; + } + + // 计算根：x = -b/a 对于每个因式 + String root1, root2; + + if (a1 != 0) { + final root1Rat = _rationalFromDouble(-b1 / a1); + root1 = _formatRational(root1Rat); + } else { + root1 = 'undefined'; + } + + if (a2 != 0) { + final root2Rat = _rationalFromDouble(-b2 / a2); + root2 = _formatRational(root2Rat); + } else { + root2 = 'undefined'; + } + + // 检查是否为重根 + final formula = root1 == root2 + ? '\$\$x_1 = x_2 = $root1\$\$' + : '\$\$x_1 = $root1, \\quad x_2 = $root2\$\$'; + + final finalAnswer = root1 == root2 + ? '\$\$x_1 = x_2 = $root1\$\$' + : '\$\$x_1 = $root1, \\quad x_2 = $root2\$\$'; + + return (formula: formula, finalAnswer: finalAnswer); + } + /// 使用公式法求解一元二次方程 CalculationResult _solveQuadraticByFormula( double a, @@ -1747,7 +1837,7 @@ ${b1}y &= ${c1 - a1 * x.toDouble()} title: '计算判别式', explanation: '判别式 Δ = b² - 4ac，用于判断方程根的情况。', formula: - '\$\$\\Delta = b^2 - 4ac = ${b}^2 - 4 \\cdot ${a} \\cdot ${c} = $discriminant\$\$', + '\$\$\\Delta = b^2 - 4ac = $b^2 - 4 \\cdot $a \\cdot $c = $discriminant\$\$', ), ); @@ -1759,28 +1849,57 @@ ${b1}y &= ${c1 - a1 * x.toDouble()} String finalAnswer; if (discriminant > 0) { - // 两个实数根 + // 两个实数根 - 使用有理数计算并化简 final x1 = (-b + sqrtDiscriminant) / denominator; final x2 = (-b - sqrtDiscriminant) / denominator; - formula = - '\$\$x = \\frac{-b \\pm \\sqrt{\\Delta}}{2a} = \\frac{${-b} \\pm \\sqrt{$discriminant}}{${denominator}}\$\$'; - finalAnswer = '\$\$x_1 = ${x1}, \\quad x_2 = ${x2}\$\$'; - } else if (discriminant == 0) { - // 一个实数根（重根） - final x = -b / denominator; + // 尝试使用有理数精确计算 + final aRat = _rationalFromDouble(a); + final bRat = _rationalFromDouble(b); + final cRat = _rationalFromDouble(c); + final discriminantRat = + bRat * bRat - Rational(BigInt.from(4)) * aRat * cRat; + final sqrtRat = sqrtRational(discriminantRat); - formula = '\$\$x = \\frac{-b}{2a} = \\frac{${-b}}{${denominator}}\$\$'; - finalAnswer = '\$\$x = ${x}\$\$'; + if (sqrtRat != null) { + // 使用精确有理数计算 + final x1Rat = (-bRat + sqrtRat) / (Rational(BigInt.from(2)) * aRat); + final x2Rat = (-bRat - sqrtRat) / (Rational(BigInt.from(2)) * aRat); + final x1Str = _formatRational(x1Rat); + final x2Str = _formatRational(x2Rat); + + formula = + '\$\$x = \\frac{-b \\pm \\sqrt{\\Delta}}{2a} = \\frac{${-b} \\pm \\sqrt{$discriminant}}{$denominator}\$\$'; + finalAnswer = '\$\$x_1 = $x1Str, \\quad x_2 = $x2Str\$\$'; + } else { + // 回退到数值计算 + formula = + '\$\$x = \\frac{-b \\pm \\sqrt{\\Delta}}{2a} = \\frac{${-b} \\pm \\sqrt{$discriminant}}{$denominator}\$\$'; + finalAnswer = '\$\$x_1 = $x1, \\quad x_2 = $x2\$\$'; + } + } else if (discriminant == 0) { + // 尝试使用有理数计算 + final aRat = _rationalFromDouble(a); + final bRat = _rationalFromDouble(b); + final xRat = -bRat / (Rational(BigInt.from(2)) * aRat); + final xStr = _formatRational(xRat); + + formula = '\$\$x = \\frac{-b}{2a} = \\frac{${-b}}{$denominator}\$\$'; + finalAnswer = '\$\$x = $xStr\$\$'; } else { // 两个虚数根 - final realPart = -b / denominator; final imagPart = sqrtDiscriminant / denominator.abs(); + // 尝试使用有理数计算实部 + final aRat = _rationalFromDouble(a); + final bRat = _rationalFromDouble(b); + final realPartRat = -bRat / (Rational(BigInt.from(2)) * aRat); + final realPartStr = _formatRational(realPartRat); + formula = - '\$\$x = \\frac{-b \\pm \\sqrt{\\Delta}}{2a} = \\frac{${-b} \\pm \\sqrt{${discriminant}}}{${denominator}}\$\$'; + '\$\$x = \\frac{-b \\pm \\sqrt{\\Delta}}{2a} = \\frac{${-b} \\pm \\sqrt{$discriminant}}{$denominator}\$\$'; finalAnswer = - '\$\$x_1 = ${realPart} + ${imagPart}i, \\quad x_2 = ${realPart} - ${imagPart}i\$\$'; + '\$\$x_1 = $realPartStr + ${imagPart}i, \\quad x_2 = $realPartStr - ${imagPart}i\$\$'; } steps.add(