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🗑️ Clean up code

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LittleSheep
2025-09-16 22:17:57 +08:00
parent ac101a2f0e
commit 1b80702bbe
1 changed files with 162 additions and 43 deletions
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205
lib/solver.dart
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@@ -24,37 +24,43 @@ class SolverService {
return formatted;
}
/// 获取整数的所有因数（包括正负）
List<int> _getAllDivisors(int n) {
List<int> 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(