//hys专属水印
////hys专属水印
//方程/不等式计算器 v2.0 (支持一元一次、二元一次、一元二次、一元一次不等式组)
#include <bits/stdc++.h>
using namespace std;
// ==================== 版本信息 ====================
const string VERSION = "v2.0";
const string UPDATE_DATE = "2026-07-26";
// ==================== 颜色高亮（必须先定义） ====================
#ifdef _WIN32
#include <windows.h>
void setColor(int color) {
HANDLE hConsole = GetStdHandle(STD_OUTPUT_HANDLE);
SetConsoleTextAttribute(hConsole, color);
}
#define COLOR_RESET 7
#define COLOR_GREEN 10
#define COLOR_RED 12
#define COLOR_YELLOW 14
#define COLOR_CYAN 11
#define COLOR_WHITE 15
#else
#define COLOR_RESET "\033[0m"
#define COLOR_GREEN "\033[1;32m"
#define COLOR_RED "\033[1;31m"
#define COLOR_YELLOW "\033[1;33m"
#define COLOR_CYAN "\033[1;36m"
#define COLOR_WHITE "\033[1;37m"
void setColor(int color) {}
#endif
// 颜色输出函数（必须在 printVersionInfo 之前定义）
void printGreen(const string& s) { setColor(COLOR_GREEN); cout << s; setColor(COLOR_RESET); }
void printRed(const string& s) { setColor(COLOR_RED); cout << s; setColor(COLOR_RESET); }
void printYellow(const string& s) { setColor(COLOR_YELLOW); cout << s; setColor(COLOR_RESET); }
void printCyan(const string& s) { setColor(COLOR_CYAN); cout << s; setColor(COLOR_RESET); }
void printWhite(const string& s) { setColor(COLOR_WHITE); cout << s; setColor(COLOR_RESET); }
// ==================== 版本信息显示 ====================
void printVersionInfo() {
cout << "\n";
printCyan("╔═══════════════════════════════════════════════════════════════╗\n");
printCyan("║");
printWhite(" 方程/不等式计算器 " + VERSION + " 更新说明");
printCyan(" ║\n");
printCyan("╠═══════════════════════════════════════════════════════════════╣\n");
printCyan("║");
printGreen(" 新增功能:");
printCyan(" ║\n");
printCyan("║ 一元一次不等式组求解 (支持2-4个不等式) ║\n");
printCyan("║ 智能识别方程/不等式/方程组类型 ║\n");
printCyan("║ 更完善的错误提示和边界检测 ║\n");
printCyan("║ ║\n");
printCyan("║");
printGreen(" 已有功能:");
printCyan(" ║\n");
printCyan("║ 一元一次方程 一元一次不等式 ║\n");
printCyan("║ 一元二次方程 二元一次方程组 ║\n");
printCyan("║ 常数方程识别 高次项检测 ║\n");
printCyan("║ 自定义变量名 隐式乘法支持 ║\n");
printCyan("║ 分数形式输出 彩色高亮显示 ║\n");
printCyan("║ ║\n");
printCyan("╚═══════════════════════════════════════════════════════════════╝\n");
}
// ==================== 表达式解析器 ====================
class ExpressionParser {
private:
string expr;
size_t pos;
map<char, double> vars;
double parseAddSub();
double parseMulDiv();
double parseFactor();
void skipSpaces() { while (pos < expr.size() && isspace(expr[pos])) pos++; }
public:
ExpressionParser(const string& s) : expr(s), pos(0) {}
void setVar(char name, double value) { vars[name] = value; }
double eval();
};
double ExpressionParser::eval() { pos = 0; return parseAddSub(); }
double ExpressionParser::parseAddSub() {
double result = parseMulDiv();
while (true) {
skipSpaces();
if (pos >= expr.size()) break;
char op = expr[pos];
if (op == '+' || op == '-') { pos++; double val = parseMulDiv(); result += (op == '+') ? val : -val; }
else break;
}
return result;
}
double ExpressionParser::parseMulDiv() {
double result = parseFactor();
while (true) {
skipSpaces();
if (pos >= expr.size()) break;
char op = expr[pos];
if (op == '*' || op == '/') { pos++; double val = parseFactor(); if (op == '*') result *= val; else { if (fabs(val) < 1e-12) throw runtime_error("除以零"); result /= val; } }
else { if (pos < expr.size() && (isalpha(expr[pos]) || expr[pos] == '(')) { double val = parseFactor(); result *= val; } else break; }
}
return result;
}
double ExpressionParser::parseFactor() {
skipSpaces();
if (pos >= expr.size()) throw runtime_error("表达式意外结束");
char ch = expr[pos];
if (ch == '+' || ch == '-') { pos++; double val = parseFactor(); return (ch == '-') ? -val : val; }
if (ch == '(') { pos++; double val = parseAddSub(); skipSpaces(); if (pos >= expr.size() || expr[pos] != ')') throw runtime_error("括号不匹配"); pos++; return val; }
if (isalpha(ch)) { pos++; if (vars.find(ch) != vars.end()) return vars[ch]; throw runtime_error(string("未知变量: ") + ch); }
if (isdigit(ch) || ch == '.') {
string num;
while (pos < expr.size() && (isdigit(expr[pos]) || expr[pos] == '.')) num += expr[pos++];
if (pos < expr.size() && (expr[pos] == 'e' || expr[pos] == 'E')) {
num += expr[pos++];
if (pos < expr.size() && (expr[pos] == '+' || expr[pos] == '-')) num += expr[pos++];
while (pos < expr.size() && isdigit(expr[pos])) num += expr[pos++];
}
try { return stod(num); } catch (...) { throw runtime_error(string("无效数字: ") + num); }
}
throw runtime_error(string("非法字符: ") + ch);
}
string removeSpaces(const string& s) { string r; for (char c : s) if (!isspace(c)) r += c; return r; }
// ==================== 方程类型检测 ====================
bool isInequality(const string& eq) {
string s = removeSpaces(eq);
return s.find('<') != string::npos || s.find('>') != string::npos;
}
struct InequalityInfo {
char sign;
size_t pos;
string signStr;
};
InequalityInfo getInequalitySign(const string& eq) {
string s = removeSpaces(eq);
InequalityInfo info;
info.pos = string::npos;
info.sign = '=';
info.signStr = "";
if (s.find("<=") != string::npos) {
info.pos = s.find("<=");
info.sign = 'l';
info.signStr = "<=";
} else if (s.find(">=") != string::npos) {
info.pos = s.find(">=");
info.sign = 'g';
info.signStr = ">=";
} else if (s.find('<') != string::npos) {
info.pos = s.find('<');
info.sign = '<';
info.signStr = "<";
} else if (s.find('>') != string::npos) {
info.pos = s.find('>');
info.sign = '>';
info.signStr = ">";
}
return info;
}
bool isQuadraticEquation(const string& eq) {
string s = removeSpaces(eq);
for (size_t i = 0; i < s.size(); i++) {
if (s[i] == 'x' || s[i] == 'X') {
if (i + 2 < s.size() && s[i + 1] == '^' && s[i + 2] == '2') return true;
if (i + 2 < s.size() && s[i + 1] == '*' && (s[i + 2] == 'x' || s[i + 2] == 'X')) return true;
if (i + 1 < s.size() && (s[i + 1] == 'x' || s[i + 1] == 'X')) return true;
}
}
return false;
}
bool hasHigherDegree(const string& eq) {
string s = removeSpaces(eq);
for (size_t i = 0; i < s.size(); i++) {
if ((s[i] == 'x' || s[i] == 'X') && i + 2 < s.size() && s[i + 1] == '^') {
if (s[i + 2] >= '3' && s[i + 2] <= '9') return true;
}
}
return false;
}
bool hasVariable(const string& eq) {
string s = removeSpaces(eq);
for (char c : s) {
if (isalpha(c) && c != 'e' && c != 'E') return true;
}
return false;
}
bool isLinearEquation(const string& eq) {
string s = removeSpaces(eq);
size_t pos = s.find('^');
if (pos != string::npos) {
size_t p = pos + 1;
while (p < s.size() && isspace(s[p])) p++;
if (p < s.size() && s[p] == '1') {
if (p + 1 < s.size() && isdigit(s[p + 1])) return false;
return true;
}
return false;
}
for (size_t i = 0; i < s.size(); i++) {
if (isalpha(s[i]) && s[i] != 'e' && s[i] != 'E') {
if (i + 2 < s.size() && s[i + 1] == '*' && isalpha(s[i + 2]) && s[i + 2] != 'e' && s[i + 2] != 'E') return false;
if (i + 1 < s.size() && isalpha(s[i + 1]) && s[i + 1] != 'e' && s[i + 1] != 'E') return false;
}
}
return true;
}
vector<char> extractVariables(const string& eq) {
string s = removeSpaces(eq);
vector<char> vars;
set<char> found;
for (char c : s) {
if (isalpha(c) && c != 'e' && c != 'E') found.insert(c);
}
for (char c : found) vars.push_back(c);
return vars;
}
// ==================== 解析函数 ====================
long long gcdll(long long a, long long b) { a = abs(a); b = abs(b); while (b) { long long t = a % b; a = b; b = t; } return a; }
string doubleToFraction(double val) {
const double EPS = 1e-9;
if (fabs(val - round(val)) < EPS) {
long long n = (long long)round(val);
return to_string(n);
}
long long num = (long long)round(val * 1000000);
long long den = 1000000;
long long g = gcdll(num, den);
num /= g; den /= g;
if (den < 0) { num = -num; den = -den; }
if (den == 1) return to_string(num);
return to_string(num) + "/" + to_string(den);
}
bool parseLinearEquation(const string& eq, double& a, double& b, double& c, string& errorMsg) {
errorMsg = "";
string s = removeSpaces(eq);
if (isInequality(eq)) {
InequalityInfo info = getInequalitySign(s);
if (info.sign == '=') { errorMsg = "无法识别不等号"; return false; }
string left = s.substr(0, info.pos);
string right = s.substr(info.pos + info.signStr.length());
string eqStr = left + "-(" + right + ")=0";
return parseLinearEquation(eqStr, a, b, c, errorMsg);
}
size_t eqPos = s.find('=');
string left, right;
if (eqPos == string::npos) { left = s; right = "0"; }
else { left = s.substr(0, eqPos); right = s.substr(eqPos + 1); }
if (left.empty()) { errorMsg = "方程左边不能为空"; return false; }
vector<char> vars = extractVariables(eq);
if (vars.empty()) {
try {
ExpressionParser p(left);
double f = p.eval();
ExpressionParser rp(right);
double rv = rp.eval();
a = 0; b = 0; c = rv - f;
return true;
} catch (const exception& e) {
errorMsg = string("常数方程解析错误: ") + e.what();
return false;
}
}
char var1 = vars[0];
char var2 = (vars.size() > 1) ? vars[1] : 'y';
try {
ExpressionParser p00(left);
p00.setVar(var1, 0.0);
p00.setVar(var2, 0.0);
double f00_left = p00.eval();
ExpressionParser r00(right);
r00.setVar(var1, 0.0);
r00.setVar(var2, 0.0);
double f00_right = r00.eval();
double F00 = f00_left - f00_right;
ExpressionParser p10(left);
p10.setVar(var1, 1.0);
p10.setVar(var2, 0.0);
double f10_left = p10.eval();
ExpressionParser r10(right);
r10.setVar(var1, 1.0);
r10.setVar(var2, 0.0);
double f10_right = r10.eval();
double F10 = f10_left - f10_right;
ExpressionParser p01(left);
p01.setVar(var1, 0.0);
p01.setVar(var2, 1.0);
double f01_left = p01.eval();
ExpressionParser r01(right);
r01.setVar(var1, 0.0);
r01.setVar(var2, 1.0);
double f01_right = r01.eval();
double F01 = f01_left - f01_right;
double C = F00;
double A = F10 - F00;
double B = F01 - F00;
a = A;
b = B;
c = C;
return true;
} catch (const exception& e) {
errorMsg = string("表达式解析错误: ") + e.what();
return false;
}
}
bool parseQuadraticEquation(const string& eq, double& a, double& b, double& c, string& errorMsg) {
errorMsg = "";
string s = removeSpaces(eq);
size_t eqPos = s.find('=');
string left, right;
if (eqPos == string::npos) { left = s; right = "0"; }
else { left = s.substr(0, eqPos); right = s.substr(eqPos + 1); }
if (left.empty()) { errorMsg = "方程左边不能为空"; return false; }
try {
double x0 = 0, x1 = 1, x2 = 2;
ExpressionParser p0(left);
p0.setVar('x', x0);
double f0_left = p0.eval();
ExpressionParser r0(right);
r0.setVar('x', x0);
double f0_right = r0.eval();
double F0 = f0_left - f0_right;
ExpressionParser p1(left);
p1.setVar('x', x1);
double f1_left = p1.eval();
ExpressionParser r1(right);
r1.setVar('x', x1);
double f1_right = r1.eval();
double F1 = f1_left - f1_right;
ExpressionParser p2(left);
p2.setVar('x', x2);
double f2_left = p2.eval();
ExpressionParser r2(right);
r2.setVar('x', x2);
double f2_right = r2.eval();
double F2 = f2_left - f2_right;
double c0 = F0;
double A = (F2 - 2*F1 + F0) / 2;
double B = F1 - F0 - A;
a = A;
b = B;
c = c0;
return true;
} catch (const exception& e) {
errorMsg = string("方程解析错误: ") + e.what();
return false;
}
}
// ==================== 高亮显示 ====================
void highlightResult(const string& label, const string& value, bool isSuccess = true) {
cout << "\n";
printCyan("╔══════════════════════════════════════════════════════════╗\n");
printCyan("║ ");
printWhite("求解结果");
printCyan(" ║\n");
printCyan("╠══════════════════════════════════════════════════════════╣\n");
printCyan("║ ");
cout << label;
int padding = 56 - label.length() - value.length();
if (padding < 0) padding = 0;
if (isSuccess) {
printGreen(value);
} else {
printRed(value);
}
for (int i = 0; i < padding; i++) cout << " ";
cout << " ║\n";
printCyan("╚══════════════════════════════════════════════════════════╝\n");
setColor(COLOR_RESET);
}
void highlightSimple(const string& msg, bool isSuccess = true) {
cout << "\n";
printCyan("╔══════════════════════════════════════════════════════════╗\n");
printCyan("║ ");
if (isSuccess) {
printGreen(msg);
} else {
printRed(msg);
}
int padding = 56 - msg.length();
if (padding < 0) padding = 0;
for (int i = 0; i < padding; i++) cout << " ";
cout << " ║\n";
printCyan("╚══════════════════════════════════════════════════════════╝\n");
setColor(COLOR_RESET);
}
// ==================== 不等式组求解 ====================
struct InequalityResult {
string var;
double bound;
bool isUpper;
bool isStrict;
bool isValid;
string error;
};
InequalityResult solveSingleInequality(const string& ineq, char var) {
InequalityResult result;
result.isValid = false;
string s = removeSpaces(ineq);
InequalityInfo info = getInequalitySign(s);
if (info.sign == '=') {
result.error = "无法识别不等号";
return result;
}
string left = s.substr(0, info.pos);
string right = s.substr(info.pos + info.signStr.length());
string eq = left + "-(" + right + ")=0";
double a, b, c; string error;
if (!parseLinearEquation(eq, a, b, c, error)) {
result.error = error;
return result;
}
if (fabs(a) < 1e-12) {
bool isTrue;
if (info.sign == '<') isTrue = (c < 0);
else if (info.sign == 'l') isTrue = (c <= 0);
else if (info.sign == '>') isTrue = (c > 0);
else isTrue = (c >= 0);
if (isTrue) {
result.error = "恒成立";
} else {
result.error = "恒不成立";
}
return result;
}
double solution = -c / a;
bool reverseSign = (a < 0);
result.var = var;
result.bound = solution;
result.isValid = true;
if (info.sign == '<') {
result.isUpper = !reverseSign;
result.isStrict = true;
} else if (info.sign == 'l') {
result.isUpper = !reverseSign;
result.isStrict = false;
} else if (info.sign == '>') {
result.isUpper = reverseSign;
result.isStrict = true;
} else {
result.isUpper = reverseSign;
result.isStrict = false;
}
return result;
}
void solveInequalitySystem(const vector<string>& inequalities) {
if (inequalities.empty()) {
printRed("错误: 没有输入不等式\n");
return;
}
vector<char> allVars;
for (const string& ineq : inequalities) {
vector<char> vars = extractVariables(ineq);
for (char v : vars) {
if (find(allVars.begin(), allVars.end(), v) == allVars.end()) {
allVars.push_back(v);
}
}
}
if (allVars.empty()) {
printRed("错误: 没有检测到变量\n");
return;
}
char var = allVars[0];
if (allVars.size() > 1) {
printYellow("警告: 检测到多个变量，仅使用第一个变量 " + string(1, var) + "\n");
}
cout << "\n变量: " << var << "\n";
cout << "不等式组:\n";
for (size_t i = 0; i < inequalities.size(); i++) {
cout << " " << (i+1) << ". " << inequalities[i] << "\n";
}
cout << "\n";
vector<InequalityResult> results;
double lowerBound = -1e100, upperBound = 1e100;
bool hasLower = false, hasUpper = false;
bool lowerStrict = false, upperStrict = false;
bool hasConflict = false;
for (const string& ineq : inequalities) {
InequalityResult r = solveSingleInequality(ineq, var);
if (!r.isValid) {
if (r.error == "恒成立") {
cout << " " << ineq << " 恒成立 ?\n";
continue;
} else if (r.error == "恒不成立") {
cout << " " << ineq << " 恒不成立 ?\n";
hasConflict = true;
break;
} else {
printRed("错误: " + r.error + "\n");
return;
}
}
results.push_back(r);
cout << " " << ineq << " → " << var;
if (r.isUpper) {
cout << (r.isStrict ? " < " : " ≤ ");
if (r.bound < upperBound) {
upperBound = r.bound;
upperStrict = r.isStrict;
hasUpper = true;
}
} else {
cout << (r.isStrict ? " > " : " ≥ ");
if (r.bound > lowerBound) {
lowerBound = r.bound;
lowerStrict = r.isStrict;
hasLower = true;
}
}
cout << doubleToFraction(r.bound) << "\n";
}
if (hasConflict) {
highlightSimple("不等式组无解（存在矛盾不等式）", false);
return;
}
if (hasLower && hasUpper) {
if (lowerBound > upperBound || (fabs(lowerBound - upperBound) < 1e-12 && (lowerStrict || upperStrict))) {
highlightSimple("不等式组无解（上下界矛盾）", false);
return;
}
}
string result;
if (!hasLower && !hasUpper) {
result = string(1, var) + " ∈ R （全体实数）";
} else if (hasLower && hasUpper) {
result = string(1, var);
if (lowerStrict) result += " > ";
else result += " ≥ ";
result += doubleToFraction(lowerBound);
result += " 且 ";
result += string(1, var);
if (upperStrict) result += " < ";
else result += " ≤ ";
result += doubleToFraction(upperBound);
} else if (hasLower) {
result = string(1, var);
if (lowerStrict) result += " > ";
else result += " ≥ ";
result += doubleToFraction(lowerBound);
} else {
result = string(1, var);
if (upperStrict) result += " < ";
else result += " ≤ ";
result += doubleToFraction(upperBound);
}
highlightResult("解集: ", result, true);
}
// ==================== 各类求解函数 ====================
void solveInequality(const string& ineq) {
string s = removeSpaces(ineq);
cout << "输入不等式: " << ineq << "\n";
InequalityInfo info = getInequalitySign(s);
if (info.sign == '=') {
cout << "这不是不等式，请使用方程求解\n";
return;
}
string left = s.substr(0, info.pos);
string right = s.substr(info.pos + info.signStr.length());
string eq = left + "-(" + right + ")=0";
double a, b, c; string error;
if (!parseLinearEquation(eq, a, b, c, error)) {
printRed("错误: " + error + "\n");
return;
}
vector<char> vars = extractVariables(ineq);
char var = (vars.empty()) ? 'x' : vars[0];
if (vars.empty()) {
bool isTrue;
if (info.sign == '<') isTrue = (c < 0);
else if (info.sign == 'l') isTrue = (c <= 0);
else if (info.sign == '>') isTrue = (c > 0);
else isTrue = (c >= 0);
if (isTrue) highlightSimple("不等式恒成立", true);
else highlightSimple("不等式恒不成立", false);
return;
}
if (fabs(a) < 1e-12) {
bool isTrue;
if (info.sign == '<') isTrue = (c < 0);
else if (info.sign == 'l') isTrue = (c <= 0);
else if (info.sign == '>') isTrue = (c > 0);
else isTrue = (c >= 0);
if (isTrue) highlightSimple("不等式恒成立", true);
else highlightSimple("不等式恒不成立", false);
return;
}
double solution = -c / a;
string solStr = doubleToFraction(solution);
string result;
bool reverseSign = (a < 0);
if (info.sign == '<') result = string(1, var) + (reverseSign ? " > " : " < ") + solStr;
else if (info.sign == 'l') result = string(1, var) + (reverseSign ? " ≥ " : " ≤ ") + solStr;
else if (info.sign == '>') result = string(1, var) + (reverseSign ? " < " : " > ") + solStr;
else result = string(1, var) + (reverseSign ? " ≤ " : " ≥ ") + solStr;
cout << "化简为: " << a << var << " + " << c << " " << info.signStr << " 0\n";
cout << "解集: ";
highlightResult("", result, true);
}
void solveQuadratic(const string& eq) {
double a, b, c; string error;
cout << "输入方程: " << eq << "\n";
if (!parseQuadraticEquation(eq, a, b, c, error)) {
printRed("错误: " + error + "\n");
return;
}
if (!hasVariable(eq)) {
if (fabs(c) < 1e-12) {
cout << "化简为: 0 = 0 (常数方程)\n";
highlightSimple("方程恒成立，任意 x 都是解", true);
} else {
cout << "化简为: 0 = " << c << " (常数方程)\n";
highlightSimple("方程恒不成立，无解", false);
}
return;
}
string eqStr = "";
if (fabs(a) > 1e-12) {
if (fabs(a - 1) < 1e-12) eqStr += "x^2";
else if (fabs(a + 1) < 1e-12) eqStr += "-x^2";
else eqStr += doubleToFraction(a) + "x^2";
}
if (fabs(b) > 1e-12) {
if (!eqStr.empty() && b > 0) eqStr += " + ";
else if (!eqStr.empty() && b < 0) eqStr += " - ";
else if (b < 0) eqStr += "-";
if (fabs(fabs(b) - 1) > 1e-12) eqStr += doubleToFraction(fabs(b));
eqStr += "x";
}
if (fabs(c) > 1e-12) {
if (!eqStr.empty() && c > 0) eqStr += " + ";
else if (!eqStr.empty() && c < 0) eqStr += " - ";
else if (c < 0) eqStr += "-";
eqStr += doubleToFraction(fabs(c));
}
if (eqStr.empty()) eqStr = "0";
eqStr += " = 0";
cout << "化简为: " << eqStr << "\n";
const double EPS = 1e-12;
if (fabs(a) < EPS) {
if (fabs(b) < EPS) {
if (fabs(c) < EPS) highlightSimple("方程有无数解 (0 = 0)", true);
else highlightSimple("方程无解 (常数项不为0)", false);
} else {
double x = -c / b;
string result = "x = " + doubleToFraction(x);
highlightResult("解: ", result, true);
cout << " 小数形式: " << setprecision(12) << x << "\n";
}
return;
}
double discriminant = b * b - 4 * a * c;
if (fabs(discriminant) < EPS) {
double x = -b / (2 * a);
string result = "x = " + doubleToFraction(x) + " (重根)";
highlightResult("解: ", result, true);
cout << " 小数形式: " << setprecision(12) << x << "\n";
} else if (discriminant > 0) {
double sqrtD = sqrt(discriminant);
double x1 = (-b + sqrtD) / (2 * a);
double x2 = (-b - sqrtD) / (2 * a);
string result = "x? = " + doubleToFraction(x1) + ", x? = " + doubleToFraction(x2);
highlightResult("解: ", result, true);
cout << " 小数形式: x? = " << setprecision(12) << x1 << ", x? = " << setprecision(12) << x2 << "\n";
} else {
double realPart = -b / (2 * a);
double imagPart = sqrt(-discriminant) / (2 * a);
string realStr = doubleToFraction(realPart);
string imagStr = doubleToFraction(imagPart);
if (realStr == "0") realStr = "0";
if (imagStr == "1") imagStr = "";
else if (imagStr == "-1") imagStr = "-";
string result = "x? = " + realStr + " + " + imagStr + "i, x? = " + realStr + " - " + imagStr + "i";
highlightResult("解: ", result, true);
cout << " 小数形式: x? = " << setprecision(12) << realPart << " + " << imagPart << "i, "
<< "x? = " << realPart << " - " << imagPart << "i\n";
}
}
void solveLinear(const string& eq) {
double a, b, c; string error;
cout << "输入方程: " << eq << "\n";
if (!parseLinearEquation(eq, a, b, c, error)) {
printRed("错误: " + error + "\n");
return;
}
vector<char> vars = extractVariables(eq);
char var = (vars.empty()) ? 'x' : vars[0];
if (vars.empty()) {
if (fabs(c) < 1e-12) {
cout << "化简为: 0 = 0 (常数方程)\n";
highlightSimple("方程恒成立，任意 " + string(1, var) + " 都是解", true);
} else {
cout << "化简为: 0 = " << c << " (常数方程)\n";
highlightSimple("方程恒不成立，无解", false);
}
return;
}
if (fabs(b) > 1e-9 && vars.size() > 1) {
cout << "警告: 此方程包含多个变量 (" << vars[0];
if (vars.size() > 1) cout << ", " << vars[1];
cout << ")，将忽略其他变量，仅解 " << var << "。\n";
}
cout << "化简为: " << a << var << " + " << c << " = 0\n";
cout << "即: " << a << var << " = " << -c << "\n";
const double EPS = 1e-12;
if (fabs(a) < EPS) {
if (fabs(c) < EPS) highlightSimple("方程有无数解 (0 = 0)", true);
else highlightSimple("方程无解 (0 = " + to_string(-c) + ")", false);
} else {
double x = -c / a;
string result = string(1, var) + " = " + doubleToFraction(x);
highlightResult("解: ", result, true);
cout << " 小数形式: " << setprecision(12) << x << "\n";
}
}
void solveSystem(const string& eq1, const string& eq2) {
double a1, b1, c1, a2, b2, c2; string error;
vector<char> vars1 = extractVariables(eq1);
vector<char> vars2 = extractVariables(eq2);
set<char> allVars;
for (char c : vars1) allVars.insert(c);
for (char c : vars2) allVars.insert(c);
vector<char> varList(allVars.begin(), allVars.end());
if (varList.size() == 0) {
printRed("错误: 方程中没有变量\n");
return;
}
char var1 = varList[0];
char var2 = (varList.size() > 1) ? varList[1] : 'y';
cout << "变量: " << var1;
if (varList.size() > 1) cout << ", " << var2;
cout << "\n";
cout << "方程1: " << eq1 << "\n";
if (!parseLinearEquation(eq1, a1, b1, c1, error)) {
printRed("错误 (方程1): " + error + "\n");
return;
}
cout << "方程2: " << eq2 << "\n";
if (!parseLinearEquation(eq2, a2, b2, c2, error)) {
printRed("错误 (方程2): " + error + "\n");
return;
}
cout << "\n解析结果:\n";
cout << " 方程1: " << a1 << var1 << " + " << b1 << var2 << " + " << c1 << " = 0\n";
cout << " 方程2: " << a2 << var1 << " + " << b2 << var2 << " + " << c2 << " = 0\n";
const double EPS = 1e-12;
double D = a1 * b2 - a2 * b1;
double Dx = (-c1) * b2 - (-c2) * b1;
double Dy = a1 * (-c2) - a2 * (-c1);
bool const1 = (fabs(a1) < EPS && fabs(b1) < EPS), const2 = (fabs(a2) < EPS && fabs(b2) < EPS);
if (const1 && const2) {
if (fabs(c1 - c2) < EPS) highlightSimple("方程组有无数解 (两个常数方程相同)", true);
else highlightSimple("方程组无解 (两个常数方程矛盾)", false);
return;
}
if (const1) {
if (fabs(c1) > EPS) {
highlightSimple("方程组无解 (方程1矛盾: 0 = " + to_string(-c1) + ")", false);
return;
}
if (fabs(a2) < EPS && fabs(b2) < EPS) {
if (fabs(c2) < EPS) highlightSimple("方程组有无数解", true);
else highlightSimple("方程组无解", false);
return;
}
if (fabs(a2) < EPS) {
double y = -c2 / b2;
string result = string(1, var1) + " 任意, " + string(1, var2) + " = " + doubleToFraction(y);
highlightResult("解: ", result, true);
cout << " 小数形式: " << setprecision(12) << y << "\n";
} else if (fabs(b2) < EPS) {
double x = -c2 / a2;
string result = string(1, var1) + " = " + doubleToFraction(x) + ", " + string(1, var2) + " 任意";
highlightResult("解: ", result, true);
cout << " 小数形式: " << setprecision(12) << x << "\n";
} else {
string msg = "方程组有无数解 (一个方程约束)\n 关系: " + to_string(a2) + string(1, var1) + " + " + to_string(b2) + string(1, var2) + " + " + to_string(c2) + " = 0";
highlightSimple(msg, true);
}
return;
}
if (const2) {
if (fabs(c2) > EPS) {
highlightSimple("方程组无解 (方程2矛盾: 0 = " + to_string(-c2) + ")", false);
return;
}
if (fabs(a1) < EPS && fabs(b1) < EPS) {
if (fabs(c1) < EPS) highlightSimple("方程组有无数解", true);
else highlightSimple("方程组无解", false);
return;
}
if (fabs(a1) < EPS) {
double y = -c1 / b1;
string result = string(1, var1) + " 任意, " + string(1, var2) + " = " + doubleToFraction(y);
highlightResult("解: ", result, true);
cout << " 小数形式: " << setprecision(12) << y << "\n";
} else if (fabs(b1) < EPS) {
double x = -c1 / a1;
string result = string(1, var1) + " = " + doubleToFraction(x) + ", " + string(1, var2) + " 任意";
highlightResult("解: ", result, true);
cout << " 小数形式: " << setprecision(12) << x << "\n";
} else {
string msg = "方程组有无数解 (一个方程约束)\n 关系: " + to_string(a1) + string(1, var1) + " + " + to_string(b1) + string(1, var2) + " + " + to_string(c1) + " = 0";
highlightSimple(msg, true);
}
return;
}
if (fabs(D) < EPS) {
if (fabs(Dx) < EPS && fabs(Dy) < EPS) {
bool proportional = true;
if (fabs(a1) > EPS && fabs(a2) > EPS) {
double ratio = a1 / a2;
if (fabs(b1 - b2 * ratio) > EPS * 100 || fabs(c1 - c2 * ratio) > EPS * 100) proportional = false;
} else if (fabs(b1) > EPS && fabs(b2) > EPS) {
double ratio = b1 / b2;
if (fabs(a1 - a2 * ratio) > EPS * 100 || fabs(c1 - c2 * ratio) > EPS * 100) proportional = false;
} else proportional = true;
if (proportional) {
string msg = "方程组有无数解 (两个方程成比例)\n 关系: " + to_string(a1) + string(1, var1) + " + " + to_string(b1) + string(1, var2) + " + " + to_string(c1) + " = 0";
highlightSimple(msg, true);
} else {
highlightSimple("方程组有无数解 (方程线性相关)", true);
}
} else {
highlightSimple("方程组无解 (矛盾)", false);
}
} else {
double x = Dx / D, y = Dy / D;
string result = string(1, var1) + " = " + doubleToFraction(x) + ", " +
string(1, var2) + " = " + doubleToFraction(y);
highlightResult("解: ", result, true);
cout << " 小数形式: " << var1 << " = " << setprecision(12) << x << ", " << var2 << " = " << setprecision(12) << y << "\n";
double v1 = a1 * x + b1 * y + c1, v2 = a2 * x + b2 * y + c2;
cout << "验证: " << v1 << " = 0, " << v2 << " = 0\n";
}
}
void solveEquation(const string& eq) {
string s = removeSpaces(eq);
if (isInequality(eq)) {
solveInequality(eq);
return;
}
if (hasHigherDegree(s)) {
printRed("错误: 此方程包含超过2次的高次项，本程序暂不支持\n");
return;
}
if (isQuadraticEquation(eq)) {
vector<char> vars = extractVariables(eq);
if (vars.size() == 1 && (vars[0] == 'x' || vars[0] == 'X')) {
solveQuadratic(eq);
return;
} else {
printRed("错误: 一元二次方程只能包含一个变量 x\n");
return;
}
}
if (isLinearEquation(s)) {
vector<char> vars = extractVariables(eq);
if (vars.size() <= 1) {
solveLinear(eq);
} else {
printRed("错误: 检测到多个变量，请使用二元方程组模式(选项2)\n");
}
return;
}
printRed("错误: 无法识别的方程类型\n");
}
// ==================== 主程序 ====================
int main() {
int choice;
string input;
vector<string> inequalities;
#ifdef _WIN32
system("color 0F");
#endif
cout << "==============================================\n";
printCyan(" 方程/不等式计算器 " + VERSION);
cout << "\n";
printYellow(" " + UPDATE_DATE + " 更新");
cout << "\n";
cout << "==============================================\n";
// 首次运行显示版本信息
static bool firstRun = true;
if (firstRun) {
printVersionInfo();
firstRun = false;
}
cout << "\n支持格式:\n";
cout << " - 一元一次\n";
cout << " - 一元二次 x^2/xx/x*x\n";
cout << " - 一元一次不等式 <,<=,>,>=\n";
cout << " - 一元一次不等式组: 多个不等式用 ; 分隔\n";
cout << " - 二元一次方程组\n";
cout << " - 常数方程 (恒等式/矛盾式)\n";
cout << "==============================================\n";
while (true) {
cout << "\n请选择:\n";
cout << " 1. 解一元方程/不等式 (自动识别)\n";
cout << " 2. 解一元一次不等式组 (用 ; 分隔)\n";
cout << " 3. 解二元一次方程组\n";
cout << " 4. 显示版本更新说明\n";
cout << " 5. 退出\n";
cout << "选择 (1/2/3/4/5): ";
cin >> choice;
if (cin.fail()) { cin.clear(); cin.ignore(10000, '\n'); cout << "输入无效，请输入数字 1-5。\n"; continue; }
cin.ignore(10000, '\n');
switch (choice) {
case 1:
cout << "请输入一元方程或不等式: ";
getline(cin, input);
if (input.empty()) cout << "输入不能为空。\n";
else solveEquation(input);
break;
case 2: {
cout << "请输入不等式组 (多个不等式用 ; 分隔): ";
getline(cin, input);
if (input.empty()) { cout << "输入不能为空。\n"; break; }
inequalities.clear();
stringstream ss(input);
string ineq;
while (getline(ss, ineq, ';')) {
string trimmed = removeSpaces(ineq);
if (!trimmed.empty()) {
inequalities.push_back(trimmed);
}
}
if (inequalities.empty()) {
cout << "没有检测到有效的不等式。\n";
} else if (inequalities.size() < 2) {
cout << "至少需要2个不等式组成不等式组。\n";
} else {
solveInequalitySystem(inequalities);
}
break;
}
case 3: {
string eq1, eq2;
cout << "请输入第一个方程: ";
getline(cin, eq1);
if (eq1.empty()) { cout << "方程不能为空。\n"; break; }
cout << "请输入第二个方程: ";
getline(cin, eq2);
if (eq2.empty()) { cout << "方程不能为空。\n"; break; }
solveSystem(eq1, eq2);
break;
}
case 4:
printVersionInfo();
break;
case 5:
cout << "感谢使用，再见！\n";
return 0;
default:
cout << "无效选择，请输入 1, 2, 3, 4 或 5。\n";
}
}
return 0;
}
#include <bits/stdc++.h>
using namespace std;
// ==================== 版本信息 ====================
const string VERSION = "v2.0";
const string UPDATE_DATE = "2026-07-26";
// ==================== 颜色高亮（必须先定义） ====================
#ifdef _WIN32
#include <windows.h>
void setColor(int color) {
HANDLE hConsole = GetStdHandle(STD_OUTPUT_HANDLE);
SetConsoleTextAttribute(hConsole, color);
}
#define COLOR_RESET 7
#define COLOR_GREEN 10
#define COLOR_RED 12
#define COLOR_YELLOW 14
#define COLOR_CYAN 11
#define COLOR_WHITE 15
#else
#define COLOR_RESET "\033[0m"
#define COLOR_GREEN "\033[1;32m"
#define COLOR_RED "\033[1;31m"
#define COLOR_YELLOW "\033[1;33m"
#define COLOR_CYAN "\033[1;36m"
#define COLOR_WHITE "\033[1;37m"
void setColor(int color) {}
#endif
// 颜色输出函数（必须在 printVersionInfo 之前定义）
void printGreen(const string& s) { setColor(COLOR_GREEN); cout << s; setColor(COLOR_RESET); }
void printRed(const string& s) { setColor(COLOR_RED); cout << s; setColor(COLOR_RESET); }
void printYellow(const string& s) { setColor(COLOR_YELLOW); cout << s; setColor(COLOR_RESET); }
void printCyan(const string& s) { setColor(COLOR_CYAN); cout << s; setColor(COLOR_RESET); }
void printWhite(const string& s) { setColor(COLOR_WHITE); cout << s; setColor(COLOR_RESET); }
// ==================== 版本信息显示 ====================
void printVersionInfo() {
cout << "\n";
printCyan("╔═══════════════════════════════════════════════════════════════╗\n");
printCyan("║");
printWhite(" 方程/不等式计算器 " + VERSION + " 更新说明");
printCyan(" ║\n");
printCyan("╠═══════════════════════════════════════════════════════════════╣\n");
printCyan("║");
printGreen(" 新增功能:");
printCyan(" ║\n");
printCyan("║ 一元一次不等式组求解 (支持2-4个不等式) ║\n");
printCyan("║ 智能识别方程/不等式/方程组类型 ║\n");
printCyan("║ 更完善的错误提示和边界检测 ║\n");
printCyan("║ ║\n");
printCyan("║");
printGreen(" 已有功能:");
printCyan(" ║\n");
printCyan("║ 一元一次方程 一元一次不等式 ║\n");
printCyan("║ 一元二次方程 二元一次方程组 ║\n");
printCyan("║ 常数方程识别 高次项检测 ║\n");
printCyan("║ 自定义变量名 隐式乘法支持 ║\n");
printCyan("║ 分数形式输出 彩色高亮显示 ║\n");
printCyan("║ ║\n");
printCyan("╚═══════════════════════════════════════════════════════════════╝\n");
}
// ==================== 表达式解析器 ====================
class ExpressionParser {
private:
string expr;
size_t pos;
map<char, double> vars;
double parseAddSub();
double parseMulDiv();
double parseFactor();
void skipSpaces() { while (pos < expr.size() && isspace(expr[pos])) pos++; }
public:
ExpressionParser(const string& s) : expr(s), pos(0) {}
void setVar(char name, double value) { vars[name] = value; }
double eval();
};
double ExpressionParser::eval() { pos = 0; return parseAddSub(); }
double ExpressionParser::parseAddSub() {
double result = parseMulDiv();
while (true) {
skipSpaces();
if (pos >= expr.size()) break;
char op = expr[pos];
if (op == '+' || op == '-') { pos++; double val = parseMulDiv(); result += (op == '+') ? val : -val; }
else break;
}
return result;
}
double ExpressionParser::parseMulDiv() {
double result = parseFactor();
while (true) {
skipSpaces();
if (pos >= expr.size()) break;
char op = expr[pos];
if (op == '*' || op == '/') { pos++; double val = parseFactor(); if (op == '*') result *= val; else { if (fabs(val) < 1e-12) throw runtime_error("除以零"); result /= val; } }
else { if (pos < expr.size() && (isalpha(expr[pos]) || expr[pos] == '(')) { double val = parseFactor(); result *= val; } else break; }
}
return result;
}
double ExpressionParser::parseFactor() {
skipSpaces();
if (pos >= expr.size()) throw runtime_error("表达式意外结束");
char ch = expr[pos];
if (ch == '+' || ch == '-') { pos++; double val = parseFactor(); return (ch == '-') ? -val : val; }
if (ch == '(') { pos++; double val = parseAddSub(); skipSpaces(); if (pos >= expr.size() || expr[pos] != ')') throw runtime_error("括号不匹配"); pos++; return val; }
if (isalpha(ch)) { pos++; if (vars.find(ch) != vars.end()) return vars[ch]; throw runtime_error(string("未知变量: ") + ch); }
if (isdigit(ch) || ch == '.') {
string num;
while (pos < expr.size() && (isdigit(expr[pos]) || expr[pos] == '.')) num += expr[pos++];
if (pos < expr.size() && (expr[pos] == 'e' || expr[pos] == 'E')) {
num += expr[pos++];
if (pos < expr.size() && (expr[pos] == '+' || expr[pos] == '-')) num += expr[pos++];
while (pos < expr.size() && isdigit(expr[pos])) num += expr[pos++];
}
try { return stod(num); } catch (...) { throw runtime_error(string("无效数字: ") + num); }
}
throw runtime_error(string("非法字符: ") + ch);
}
string removeSpaces(const string& s) { string r; for (char c : s) if (!isspace(c)) r += c; return r; }
// ==================== 方程类型检测 ====================
bool isInequality(const string& eq) {
string s = removeSpaces(eq);
return s.find('<') != string::npos || s.find('>') != string::npos;
}
struct InequalityInfo {
char sign;
size_t pos;
string signStr;
};
InequalityInfo getInequalitySign(const string& eq) {
string s = removeSpaces(eq);
InequalityInfo info;
info.pos = string::npos;
info.sign = '=';
info.signStr = "";
if (s.find("<=") != string::npos) {
info.pos = s.find("<=");
info.sign = 'l';
info.signStr = "<=";
} else if (s.find(">=") != string::npos) {
info.pos = s.find(">=");
info.sign = 'g';
info.signStr = ">=";
} else if (s.find('<') != string::npos) {
info.pos = s.find('<');
info.sign = '<';
info.signStr = "<";
} else if (s.find('>') != string::npos) {
info.pos = s.find('>');
info.sign = '>';
info.signStr = ">";
}
return info;
}
bool isQuadraticEquation(const string& eq) {
string s = removeSpaces(eq);
for (size_t i = 0; i < s.size(); i++) {
if (s[i] == 'x' || s[i] == 'X') {
if (i + 2 < s.size() && s[i + 1] == '^' && s[i + 2] == '2') return true;
if (i + 2 < s.size() && s[i + 1] == '*' && (s[i + 2] == 'x' || s[i + 2] == 'X')) return true;
if (i + 1 < s.size() && (s[i + 1] == 'x' || s[i + 1] == 'X')) return true;
}
}
return false;
}
bool hasHigherDegree(const string& eq) {
string s = removeSpaces(eq);
for (size_t i = 0; i < s.size(); i++) {
if ((s[i] == 'x' || s[i] == 'X') && i + 2 < s.size() && s[i + 1] == '^') {
if (s[i + 2] >= '3' && s[i + 2] <= '9') return true;
}
}
return false;
}
bool hasVariable(const string& eq) {
string s = removeSpaces(eq);
for (char c : s) {
if (isalpha(c) && c != 'e' && c != 'E') return true;
}
return false;
}
bool isLinearEquation(const string& eq) {
string s = removeSpaces(eq);
size_t pos = s.find('^');
if (pos != string::npos) {
size_t p = pos + 1;
while (p < s.size() && isspace(s[p])) p++;
if (p < s.size() && s[p] == '1') {
if (p + 1 < s.size() && isdigit(s[p + 1])) return false;
return true;
}
return false;
}
for (size_t i = 0; i < s.size(); i++) {
if (isalpha(s[i]) && s[i] != 'e' && s[i] != 'E') {
if (i + 2 < s.size() && s[i + 1] == '*' && isalpha(s[i + 2]) && s[i + 2] != 'e' && s[i + 2] != 'E') return false;
if (i + 1 < s.size() && isalpha(s[i + 1]) && s[i + 1] != 'e' && s[i + 1] != 'E') return false;
}
}
return true;
}
vector<char> extractVariables(const string& eq) {
string s = removeSpaces(eq);
vector<char> vars;
set<char> found;
for (char c : s) {
if (isalpha(c) && c != 'e' && c != 'E') found.insert(c);
}
for (char c : found) vars.push_back(c);
return vars;
}
// ==================== 解析函数 ====================
long long gcdll(long long a, long long b) { a = abs(a); b = abs(b); while (b) { long long t = a % b; a = b; b = t; } return a; }
string doubleToFraction(double val) {
const double EPS = 1e-9;
if (fabs(val - round(val)) < EPS) {
long long n = (long long)round(val);
return to_string(n);
}
long long num = (long long)round(val * 1000000);
long long den = 1000000;
long long g = gcdll(num, den);
num /= g; den /= g;
if (den < 0) { num = -num; den = -den; }
if (den == 1) return to_string(num);
return to_string(num) + "/" + to_string(den);
}
bool parseLinearEquation(const string& eq, double& a, double& b, double& c, string& errorMsg) {
errorMsg = "";
string s = removeSpaces(eq);
if (isInequality(eq)) {
InequalityInfo info = getInequalitySign(s);
if (info.sign == '=') { errorMsg = "无法识别不等号"; return false; }
string left = s.substr(0, info.pos);
string right = s.substr(info.pos + info.signStr.length());
string eqStr = left + "-(" + right + ")=0";
return parseLinearEquation(eqStr, a, b, c, errorMsg);
}
size_t eqPos = s.find('=');
string left, right;
if (eqPos == string::npos) { left = s; right = "0"; }
else { left = s.substr(0, eqPos); right = s.substr(eqPos + 1); }
if (left.empty()) { errorMsg = "方程左边不能为空"; return false; }
vector<char> vars = extractVariables(eq);
if (vars.empty()) {
try {
ExpressionParser p(left);
double f = p.eval();
ExpressionParser rp(right);
double rv = rp.eval();
a = 0; b = 0; c = rv - f;
return true;
} catch (const exception& e) {
errorMsg = string("常数方程解析错误: ") + e.what();
return false;
}
}
char var1 = vars[0];
char var2 = (vars.size() > 1) ? vars[1] : 'y';
try {
ExpressionParser p00(left);
p00.setVar(var1, 0.0);
p00.setVar(var2, 0.0);
double f00_left = p00.eval();
ExpressionParser r00(right);
r00.setVar(var1, 0.0);
r00.setVar(var2, 0.0);
double f00_right = r00.eval();
double F00 = f00_left - f00_right;
ExpressionParser p10(left);
p10.setVar(var1, 1.0);
p10.setVar(var2, 0.0);
double f10_left = p10.eval();
ExpressionParser r10(right);
r10.setVar(var1, 1.0);
r10.setVar(var2, 0.0);
double f10_right = r10.eval();
double F10 = f10_left - f10_right;
ExpressionParser p01(left);
p01.setVar(var1, 0.0);
p01.setVar(var2, 1.0);
double f01_left = p01.eval();
ExpressionParser r01(right);
r01.setVar(var1, 0.0);
r01.setVar(var2, 1.0);
double f01_right = r01.eval();
double F01 = f01_left - f01_right;
double C = F00;
double A = F10 - F00;
double B = F01 - F00;
a = A;
b = B;
c = C;
return true;
} catch (const exception& e) {
errorMsg = string("表达式解析错误: ") + e.what();
return false;
}
}
bool parseQuadraticEquation(const string& eq, double& a, double& b, double& c, string& errorMsg) {
errorMsg = "";
string s = removeSpaces(eq);
size_t eqPos = s.find('=');
string left, right;
if (eqPos == string::npos) { left = s; right = "0"; }
else { left = s.substr(0, eqPos); right = s.substr(eqPos + 1); }
if (left.empty()) { errorMsg = "方程左边不能为空"; return false; }
try {
double x0 = 0, x1 = 1, x2 = 2;
ExpressionParser p0(left);
p0.setVar('x', x0);
double f0_left = p0.eval();
ExpressionParser r0(right);
r0.setVar('x', x0);
double f0_right = r0.eval();
double F0 = f0_left - f0_right;
ExpressionParser p1(left);
p1.setVar('x', x1);
double f1_left = p1.eval();
ExpressionParser r1(right);
r1.setVar('x', x1);
double f1_right = r1.eval();
double F1 = f1_left - f1_right;
ExpressionParser p2(left);
p2.setVar('x', x2);
double f2_left = p2.eval();
ExpressionParser r2(right);
r2.setVar('x', x2);
double f2_right = r2.eval();
double F2 = f2_left - f2_right;
double c0 = F0;
double A = (F2 - 2*F1 + F0) / 2;
double B = F1 - F0 - A;
a = A;
b = B;
c = c0;
return true;
} catch (const exception& e) {
errorMsg = string("方程解析错误: ") + e.what();
return false;
}
}
// ==================== 高亮显示 ====================
void highlightResult(const string& label, const string& value, bool isSuccess = true) {
cout << "\n";
printCyan("╔══════════════════════════════════════════════════════════╗\n");
printCyan("║ ");
printWhite("求解结果");
printCyan(" ║\n");
printCyan("╠══════════════════════════════════════════════════════════╣\n");
printCyan("║ ");
cout << label;
int padding = 56 - label.length() - value.length();
if (padding < 0) padding = 0;
if (isSuccess) {
printGreen(value);
} else {
printRed(value);
}
for (int i = 0; i < padding; i++) cout << " ";
cout << " ║\n";
printCyan("╚══════════════════════════════════════════════════════════╝\n");
setColor(COLOR_RESET);
}
void highlightSimple(const string& msg, bool isSuccess = true) {
cout << "\n";
printCyan("╔══════════════════════════════════════════════════════════╗\n");
printCyan("║ ");
if (isSuccess) {
printGreen(msg);
} else {
printRed(msg);
}
int padding = 56 - msg.length();
if (padding < 0) padding = 0;
for (int i = 0; i < padding; i++) cout << " ";
cout << " ║\n";
printCyan("╚══════════════════════════════════════════════════════════╝\n");
setColor(COLOR_RESET);
}
// ==================== 不等式组求解 ====================
struct InequalityResult {
string var;
double bound;
bool isUpper;
bool isStrict;
bool isValid;
string error;
};
InequalityResult solveSingleInequality(const string& ineq, char var) {
InequalityResult result;
result.isValid = false;
string s = removeSpaces(ineq);
InequalityInfo info = getInequalitySign(s);
if (info.sign == '=') {
result.error = "无法识别不等号";
return result;
}
string left = s.substr(0, info.pos);
string right = s.substr(info.pos + info.signStr.length());
string eq = left + "-(" + right + ")=0";
double a, b, c; string error;
if (!parseLinearEquation(eq, a, b, c, error)) {
result.error = error;
return result;
}
if (fabs(a) < 1e-12) {
bool isTrue;
if (info.sign == '<') isTrue = (c < 0);
else if (info.sign == 'l') isTrue = (c <= 0);
else if (info.sign == '>') isTrue = (c > 0);
else isTrue = (c >= 0);
if (isTrue) {
result.error = "恒成立";
} else {
result.error = "恒不成立";
}
return result;
}
double solution = -c / a;
bool reverseSign = (a < 0);
result.var = var;
result.bound = solution;
result.isValid = true;
if (info.sign == '<') {
result.isUpper = !reverseSign;
result.isStrict = true;
} else if (info.sign == 'l') {
result.isUpper = !reverseSign;
result.isStrict = false;
} else if (info.sign == '>') {
result.isUpper = reverseSign;
result.isStrict = true;
} else {
result.isUpper = reverseSign;
result.isStrict = false;
}
return result;
}
void solveInequalitySystem(const vector<string>& inequalities) {
if (inequalities.empty()) {
printRed("错误: 没有输入不等式\n");
return;
}
vector<char> allVars;
for (const string& ineq : inequalities) {
vector<char> vars = extractVariables(ineq);
for (char v : vars) {
if (find(allVars.begin(), allVars.end(), v) == allVars.end()) {
allVars.push_back(v);
}
}
}
if (allVars.empty()) {
printRed("错误: 没有检测到变量\n");
return;
}
char var = allVars[0];
if (allVars.size() > 1) {
printYellow("警告: 检测到多个变量，仅使用第一个变量 " + string(1, var) + "\n");
}
cout << "\n变量: " << var << "\n";
cout << "不等式组:\n";
for (size_t i = 0; i < inequalities.size(); i++) {
cout << " " << (i+1) << ". " << inequalities[i] << "\n";
}
cout << "\n";
vector<InequalityResult> results;
double lowerBound = -1e100, upperBound = 1e100;
bool hasLower = false, hasUpper = false;
bool lowerStrict = false, upperStrict = false;
bool hasConflict = false;
for (const string& ineq : inequalities) {
InequalityResult r = solveSingleInequality(ineq, var);
if (!r.isValid) {
if (r.error == "恒成立") {
cout << " " << ineq << " 恒成立 ?\n";
continue;
} else if (r.error == "恒不成立") {
cout << " " << ineq << " 恒不成立 ?\n";
hasConflict = true;
break;
} else {
printRed("错误: " + r.error + "\n");
return;
}
}
results.push_back(r);
cout << " " << ineq << " → " << var;
if (r.isUpper) {
cout << (r.isStrict ? " < " : " ≤ ");
if (r.bound < upperBound) {
upperBound = r.bound;
upperStrict = r.isStrict;
hasUpper = true;
}
} else {
cout << (r.isStrict ? " > " : " ≥ ");
if (r.bound > lowerBound) {
lowerBound = r.bound;
lowerStrict = r.isStrict;
hasLower = true;
}
}
cout << doubleToFraction(r.bound) << "\n";
}
if (hasConflict) {
highlightSimple("不等式组无解（存在矛盾不等式）", false);
return;
}
if (hasLower && hasUpper) {
if (lowerBound > upperBound || (fabs(lowerBound - upperBound) < 1e-12 && (lowerStrict || upperStrict))) {
highlightSimple("不等式组无解（上下界矛盾）", false);
return;
}
}
string result;
if (!hasLower && !hasUpper) {
result = string(1, var) + " ∈ R （全体实数）";
} else if (hasLower && hasUpper) {
result = string(1, var);
if (lowerStrict) result += " > ";
else result += " ≥ ";
result += doubleToFraction(lowerBound);
result += " 且 ";
result += string(1, var);
if (upperStrict) result += " < ";
else result += " ≤ ";
result += doubleToFraction(upperBound);
} else if (hasLower) {
result = string(1, var);
if (lowerStrict) result += " > ";
else result += " ≥ ";
result += doubleToFraction(lowerBound);
} else {
result = string(1, var);
if (upperStrict) result += " < ";
else result += " ≤ ";
result += doubleToFraction(upperBound);
}
highlightResult("解集: ", result, true);
}
// ==================== 各类求解函数 ====================
void solveInequality(const string& ineq) {
string s = removeSpaces(ineq);
cout << "输入不等式: " << ineq << "\n";
InequalityInfo info = getInequalitySign(s);
if (info.sign == '=') {
cout << "这不是不等式，请使用方程求解\n";
return;
}
string left = s.substr(0, info.pos);
string right = s.substr(info.pos + info.signStr.length());
string eq = left + "-(" + right + ")=0";
double a, b, c; string error;
if (!parseLinearEquation(eq, a, b, c, error)) {
printRed("错误: " + error + "\n");
return;
}
vector<char> vars = extractVariables(ineq);
char var = (vars.empty()) ? 'x' : vars[0];
if (vars.empty()) {
bool isTrue;
if (info.sign == '<') isTrue = (c < 0);
else if (info.sign == 'l') isTrue = (c <= 0);
else if (info.sign == '>') isTrue = (c > 0);
else isTrue = (c >= 0);
if (isTrue) highlightSimple("不等式恒成立", true);
else highlightSimple("不等式恒不成立", false);
return;
}
if (fabs(a) < 1e-12) {
bool isTrue;
if (info.sign == '<') isTrue = (c < 0);
else if (info.sign == 'l') isTrue = (c <= 0);
else if (info.sign == '>') isTrue = (c > 0);
else isTrue = (c >= 0);
if (isTrue) highlightSimple("不等式恒成立", true);
else highlightSimple("不等式恒不成立", false);
return;
}
double solution = -c / a;
string solStr = doubleToFraction(solution);
string result;
bool reverseSign = (a < 0);
if (info.sign == '<') result = string(1, var) + (reverseSign ? " > " : " < ") + solStr;
else if (info.sign == 'l') result = string(1, var) + (reverseSign ? " ≥ " : " ≤ ") + solStr;
else if (info.sign == '>') result = string(1, var) + (reverseSign ? " < " : " > ") + solStr;
else result = string(1, var) + (reverseSign ? " ≤ " : " ≥ ") + solStr;
cout << "化简为: " << a << var << " + " << c << " " << info.signStr << " 0\n";
cout << "解集: ";
highlightResult("", result, true);
}
void solveQuadratic(const string& eq) {
double a, b, c; string error;
cout << "输入方程: " << eq << "\n";
if (!parseQuadraticEquation(eq, a, b, c, error)) {
printRed("错误: " + error + "\n");
return;
}
if (!hasVariable(eq)) {
if (fabs(c) < 1e-12) {
cout << "化简为: 0 = 0 (常数方程)\n";
highlightSimple("方程恒成立，任意 x 都是解", true);
} else {
cout << "化简为: 0 = " << c << " (常数方程)\n";
highlightSimple("方程恒不成立，无解", false);
}
return;
}
string eqStr = "";
if (fabs(a) > 1e-12) {
if (fabs(a - 1) < 1e-12) eqStr += "x^2";
else if (fabs(a + 1) < 1e-12) eqStr += "-x^2";
else eqStr += doubleToFraction(a) + "x^2";
}
if (fabs(b) > 1e-12) {
if (!eqStr.empty() && b > 0) eqStr += " + ";
else if (!eqStr.empty() && b < 0) eqStr += " - ";
else if (b < 0) eqStr += "-";
if (fabs(fabs(b) - 1) > 1e-12) eqStr += doubleToFraction(fabs(b));
eqStr += "x";
}
if (fabs(c) > 1e-12) {
if (!eqStr.empty() && c > 0) eqStr += " + ";
else if (!eqStr.empty() && c < 0) eqStr += " - ";
else if (c < 0) eqStr += "-";
eqStr += doubleToFraction(fabs(c));
}
if (eqStr.empty()) eqStr = "0";
eqStr += " = 0";
cout << "化简为: " << eqStr << "\n";
const double EPS = 1e-12;
if (fabs(a) < EPS) {
if (fabs(b) < EPS) {
if (fabs(c) < EPS) highlightSimple("方程有无数解 (0 = 0)", true);
else highlightSimple("方程无解 (常数项不为0)", false);
} else {
double x = -c / b;
string result = "x = " + doubleToFraction(x);
highlightResult("解: ", result, true);
cout << " 小数形式: " << setprecision(12) << x << "\n";
}
return;
}
double discriminant = b * b - 4 * a * c;
if (fabs(discriminant) < EPS) {
double x = -b / (2 * a);
string result = "x = " + doubleToFraction(x) + " (重根)";
highlightResult("解: ", result, true);
cout << " 小数形式: " << setprecision(12) << x << "\n";
} else if (discriminant > 0) {
double sqrtD = sqrt(discriminant);
double x1 = (-b + sqrtD) / (2 * a);
double x2 = (-b - sqrtD) / (2 * a);
string result = "x? = " + doubleToFraction(x1) + ", x? = " + doubleToFraction(x2);
highlightResult("解: ", result, true);
cout << " 小数形式: x? = " << setprecision(12) << x1 << ", x? = " << setprecision(12) << x2 << "\n";
} else {
double realPart = -b / (2 * a);
double imagPart = sqrt(-discriminant) / (2 * a);
string realStr = doubleToFraction(realPart);
string imagStr = doubleToFraction(imagPart);
if (realStr == "0") realStr = "0";
if (imagStr == "1") imagStr = "";
else if (imagStr == "-1") imagStr = "-";
string result = "x? = " + realStr + " + " + imagStr + "i, x? = " + realStr + " - " + imagStr + "i";
highlightResult("解: ", result, true);
cout << " 小数形式: x? = " << setprecision(12) << realPart << " + " << imagPart << "i, "
<< "x? = " << realPart << " - " << imagPart << "i\n";
}
}
void solveLinear(const string& eq) {
double a, b, c; string error;
cout << "输入方程: " << eq << "\n";
if (!parseLinearEquation(eq, a, b, c, error)) {
printRed("错误: " + error + "\n");
return;
}
vector<char> vars = extractVariables(eq);
char var = (vars.empty()) ? 'x' : vars[0];
if (vars.empty()) {
if (fabs(c) < 1e-12) {
cout << "化简为: 0 = 0 (常数方程)\n";
highlightSimple("方程恒成立，任意 " + string(1, var) + " 都是解", true);
} else {
cout << "化简为: 0 = " << c << " (常数方程)\n";
highlightSimple("方程恒不成立，无解", false);
}
return;
}
if (fabs(b) > 1e-9 && vars.size() > 1) {
cout << "警告: 此方程包含多个变量 (" << vars[0];
if (vars.size() > 1) cout << ", " << vars[1];
cout << ")，将忽略其他变量，仅解 " << var << "。\n";
}
cout << "化简为: " << a << var << " + " << c << " = 0\n";
cout << "即: " << a << var << " = " << -c << "\n";
const double EPS = 1e-12;
if (fabs(a) < EPS) {
if (fabs(c) < EPS) highlightSimple("方程有无数解 (0 = 0)", true);
else highlightSimple("方程无解 (0 = " + to_string(-c) + ")", false);
} else {
double x = -c / a;
string result = string(1, var) + " = " + doubleToFraction(x);
highlightResult("解: ", result, true);
cout << " 小数形式: " << setprecision(12) << x << "\n";
}
}
void solveSystem(const string& eq1, const string& eq2) {
double a1, b1, c1, a2, b2, c2; string error;
vector<char> vars1 = extractVariables(eq1);
vector<char> vars2 = extractVariables(eq2);
set<char> allVars;
for (char c : vars1) allVars.insert(c);
for (char c : vars2) allVars.insert(c);
vector<char> varList(allVars.begin(), allVars.end());
if (varList.size() == 0) {
printRed("错误: 方程中没有变量\n");
return;
}
char var1 = varList[0];
char var2 = (varList.size() > 1) ? varList[1] : 'y';
cout << "变量: " << var1;
if (varList.size() > 1) cout << ", " << var2;
cout << "\n";
cout << "方程1: " << eq1 << "\n";
if (!parseLinearEquation(eq1, a1, b1, c1, error)) {
printRed("错误 (方程1): " + error + "\n");
return;
}
cout << "方程2: " << eq2 << "\n";
if (!parseLinearEquation(eq2, a2, b2, c2, error)) {
printRed("错误 (方程2): " + error + "\n");
return;
}
cout << "\n解析结果:\n";
cout << " 方程1: " << a1 << var1 << " + " << b1 << var2 << " + " << c1 << " = 0\n";
cout << " 方程2: " << a2 << var1 << " + " << b2 << var2 << " + " << c2 << " = 0\n";
const double EPS = 1e-12;
double D = a1 * b2 - a2 * b1;
double Dx = (-c1) * b2 - (-c2) * b1;
double Dy = a1 * (-c2) - a2 * (-c1);
bool const1 = (fabs(a1) < EPS && fabs(b1) < EPS), const2 = (fabs(a2) < EPS && fabs(b2) < EPS);
if (const1 && const2) {
if (fabs(c1 - c2) < EPS) highlightSimple("方程组有无数解 (两个常数方程相同)", true);
else highlightSimple("方程组无解 (两个常数方程矛盾)", false);
return;
}
if (const1) {
if (fabs(c1) > EPS) {
highlightSimple("方程组无解 (方程1矛盾: 0 = " + to_string(-c1) + ")", false);
return;
}
if (fabs(a2) < EPS && fabs(b2) < EPS) {
if (fabs(c2) < EPS) highlightSimple("方程组有无数解", true);
else highlightSimple("方程组无解", false);
return;
}
if (fabs(a2) < EPS) {
double y = -c2 / b2;
string result = string(1, var1) + " 任意, " + string(1, var2) + " = " + doubleToFraction(y);
highlightResult("解: ", result, true);
cout << " 小数形式: " << setprecision(12) << y << "\n";
} else if (fabs(b2) < EPS) {
double x = -c2 / a2;
string result = string(1, var1) + " = " + doubleToFraction(x) + ", " + string(1, var2) + " 任意";
highlightResult("解: ", result, true);
cout << " 小数形式: " << setprecision(12) << x << "\n";
} else {
string msg = "方程组有无数解 (一个方程约束)\n 关系: " + to_string(a2) + string(1, var1) + " + " + to_string(b2) + string(1, var2) + " + " + to_string(c2) + " = 0";
highlightSimple(msg, true);
}
return;
}
if (const2) {
if (fabs(c2) > EPS) {
highlightSimple("方程组无解 (方程2矛盾: 0 = " + to_string(-c2) + ")", false);
return;
}
if (fabs(a1) < EPS && fabs(b1) < EPS) {
if (fabs(c1) < EPS) highlightSimple("方程组有无数解", true);
else highlightSimple("方程组无解", false);
return;
}
if (fabs(a1) < EPS) {
double y = -c1 / b1;
string result = string(1, var1) + " 任意, " + string(1, var2) + " = " + doubleToFraction(y);
highlightResult("解: ", result, true);
cout << " 小数形式: " << setprecision(12) << y << "\n";
} else if (fabs(b1) < EPS) {
double x = -c1 / a1;
string result = string(1, var1) + " = " + doubleToFraction(x) + ", " + string(1, var2) + " 任意";
highlightResult("解: ", result, true);
cout << " 小数形式: " << setprecision(12) << x << "\n";
} else {
string msg = "方程组有无数解 (一个方程约束)\n 关系: " + to_string(a1) + string(1, var1) + " + " + to_string(b1) + string(1, var2) + " + " + to_string(c1) + " = 0";
highlightSimple(msg, true);
}
return;
}
if (fabs(D) < EPS) {
if (fabs(Dx) < EPS && fabs(Dy) < EPS) {
bool proportional = true;
if (fabs(a1) > EPS && fabs(a2) > EPS) {
double ratio = a1 / a2;
if (fabs(b1 - b2 * ratio) > EPS * 100 || fabs(c1 - c2 * ratio) > EPS * 100) proportional = false;
} else if (fabs(b1) > EPS && fabs(b2) > EPS) {
double ratio = b1 / b2;
if (fabs(a1 - a2 * ratio) > EPS * 100 || fabs(c1 - c2 * ratio) > EPS * 100) proportional = false;
} else proportional = true;
if (proportional) {
string msg = "方程组有无数解 (两个方程成比例)\n 关系: " + to_string(a1) + string(1, var1) + " + " + to_string(b1) + string(1, var2) + " + " + to_string(c1) + " = 0";
highlightSimple(msg, true);
} else {
highlightSimple("方程组有无数解 (方程线性相关)", true);
}
} else {
highlightSimple("方程组无解 (矛盾)", false);
}
} else {
double x = Dx / D, y = Dy / D;
string result = string(1, var1) + " = " + doubleToFraction(x) + ", " +
string(1, var2) + " = " + doubleToFraction(y);
highlightResult("解: ", result, true);
cout << " 小数形式: " << var1 << " = " << setprecision(12) << x << ", " << var2 << " = " << setprecision(12) << y << "\n";
double v1 = a1 * x + b1 * y + c1, v2 = a2 * x + b2 * y + c2;
cout << "验证: " << v1 << " = 0, " << v2 << " = 0\n";
}
}
void solveEquation(const string& eq) {
string s = removeSpaces(eq);
if (isInequality(eq)) {
solveInequality(eq);
return;
}
if (hasHigherDegree(s)) {
printRed("错误: 此方程包含超过2次的高次项，本程序暂不支持\n");
return;
}
if (isQuadraticEquation(eq)) {
vector<char> vars = extractVariables(eq);
if (vars.size() == 1 && (vars[0] == 'x' || vars[0] == 'X')) {
solveQuadratic(eq);
return;
} else {
printRed("错误: 一元二次方程只能包含一个变量 x\n");
return;
}
}
if (isLinearEquation(s)) {
vector<char> vars = extractVariables(eq);
if (vars.size() <= 1) {
solveLinear(eq);
} else {
printRed("错误: 检测到多个变量，请使用二元方程组模式(选项2)\n");
}
return;
}
printRed("错误: 无法识别的方程类型\n");
}
// ==================== 主程序 ====================
int main() {
int choice;
string input;
vector<string> inequalities;
#ifdef _WIN32
system("color 0F");
#endif
cout << "==============================================\n";
printCyan(" 方程/不等式计算器 " + VERSION);
cout << "\n";
printYellow(" " + UPDATE_DATE + " 更新");
cout << "\n";
cout << "==============================================\n";
// 首次运行显示版本信息
static bool firstRun = true;
if (firstRun) {
printVersionInfo();
firstRun = false;
}
cout << "\n支持格式:\n";
cout << " - 一元一次\n";
cout << " - 一元二次 x^2/xx/x*x\n";
cout << " - 一元一次不等式 <,<=,>,>=\n";
cout << " - 一元一次不等式组: 多个不等式用 ; 分隔\n";
cout << " - 二元一次方程组\n";
cout << " - 常数方程 (恒等式/矛盾式)\n";
cout << "==============================================\n";
while (true) {
cout << "\n请选择:\n";
cout << " 1. 解一元方程/不等式 (自动识别)\n";
cout << " 2. 解一元一次不等式组 (用 ; 分隔)\n";
cout << " 3. 解二元一次方程组\n";
cout << " 4. 显示版本更新说明\n";
cout << " 5. 退出\n";
cout << "选择 (1/2/3/4/5): ";
cin >> choice;
if (cin.fail()) { cin.clear(); cin.ignore(10000, '\n'); cout << "输入无效，请输入数字 1-5。\n"; continue; }
cin.ignore(10000, '\n');
switch (choice) {
case 1:
cout << "请输入一元方程或不等式: ";
getline(cin, input);
if (input.empty()) cout << "输入不能为空。\n";
else solveEquation(input);
break;
case 2: {
cout << "请输入不等式组 (多个不等式用 ; 分隔): ";
getline(cin, input);
if (input.empty()) { cout << "输入不能为空。\n"; break; }
inequalities.clear();
stringstream ss(input);
string ineq;
while (getline(ss, ineq, ';')) {
string trimmed = removeSpaces(ineq);
if (!trimmed.empty()) {
inequalities.push_back(trimmed);
}
}
if (inequalities.empty()) {
cout << "没有检测到有效的不等式。\n";
} else if (inequalities.size() < 2) {
cout << "至少需要2个不等式组成不等式组。\n";
} else {
solveInequalitySystem(inequalities);
}
break;
}
case 3: {
string eq1, eq2;
cout << "请输入第一个方程: ";
getline(cin, eq1);
if (eq1.empty()) { cout << "方程不能为空。\n"; break; }
cout << "请输入第二个方程: ";
getline(cin, eq2);
if (eq2.empty()) { cout << "方程不能为空。\n"; break; }
solveSystem(eq1, eq2);
break;
}
case 4:
printVersionInfo();
break;
case 5:
cout << "感谢使用，再见！\n";
return 0;
default:
cout << "无效选择，请输入 1, 2, 3, 4 或 5。\n";
}
}
return 0;
}
js25125
LV 6
@
2026-10-11 13:16:30