?
Ihr könnt ja noch einmal schauen... Es können jetzt auch Koeffizienten =/= +-1 gelöst werden* (hoffe ich), und ich bin erst einmal damit zufrieden:
*: Also auch Matrizen, die nicht nur aus 1 oder -1 bestehen...
#include <string>
#include <vector>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <variant>
#include <cmath>
struct Value
{
double value = 0.0;
bool is_unknown = false;
};
using Row = std::vector<Value>;
using Matrix = std::vector<std::vector<Value>>;
struct System
{
Matrix coefficients;
Row constant_terms;
};
double round_to(double value, double precision = 0.01)
{
return std::round(value / precision) * precision;
}
std::ostream &operator<<(std::ostream &out, const Value &v)
{
if (!v.is_unknown)
{
out << std::setw(6) << std::setfill(' ') << round_to(v.value);
}
else
{
out << " --";
}
return out;
}
std::ostream &operator<<(std::ostream &out, const Matrix &matrix)
{
out << "Matrix: (" << matrix.size() << " x " << matrix[0].size() << ")\n";
for (auto &row : matrix)
{
for (auto &value : row)
{
out << value;
}
out << '\n';
}
return out << '\n';
}
std::ostream &operator<<(std::ostream &out, const Row &row)
{
out << "Matrix: (1 x " << row.size() << ")\n";
for (size_t i = 0; i < row.size(); i++)
{
out << " " << (char)('a' + i);
}
out << '\n';
for (auto &value : row)
{
out << value;
}
out << '\n';
return out << '\n';
}
void printSystem(const System &system)
{
std::cout << system.coefficients;
std::cout << system.constant_terms;
}
System solveAndPrint(const System &input)
{
System result = input;
bool changed = true;
while (changed)
{
changed = false;
printSystem(result);
for (size_t i = 0; i < result.coefficients.size(); i++)
{
size_t magic_n = 0;
size_t magic_i = 0;
for (size_t j = 0; j < result.coefficients[i].size(); j++)
{
if (result.coefficients[i][j].value != 0 && result.constant_terms[j].is_unknown)
{
magic_n++;
magic_i = j;
}
}
if (magic_n == 1)
{
double sum = 0;
for (size_t j = 0; j < result.coefficients[i].size(); j++)
{
if (j != magic_i && result.coefficients[i][j].value != 0)
{
sum -= result.coefficients[i][j].value * result.constant_terms[j].value;
}
}
result.constant_terms[magic_i].value = sum / result.coefficients[i][magic_i].value;
result.constant_terms[magic_i].is_unknown = false;
changed = true;
break;
}
}
}
return result;
}
int main(int argc, char const *argv[])
{
std::vector<std::string> args({"2 6 -8",
"1 0 -1",
"0",
"2 - -"});
System input;
for (int i = 1;; i++)
{
std::cout << "Koeffizienten " << i << ". Zeile oder einfach 0, um die Eingabe abzuschließen:\n";
std::string l;
// getline(std::cin, l);
l = args[i - 1];
std::cout << l << '\n';
if (l == "0")
{
break;
}
std::stringstream ss;
ss << l;
std::string segment;
Row r;
while (getline(ss, segment, ' '))
{
r.push_back(Value());
r.back().value = stod(segment);
}
input.coefficients.push_back(r);
}
{
std::cout << "Bekannte, oder nur -, wenn unbekannt:\n";
std::string l;
// getline(std::cin, l);
l = args[args.size() - 1];
std::cout << l << '\n';
std::stringstream ss;
ss << l;
std::string segment;
while (getline(ss, segment, ' '))
{
input.constant_terms.push_back(Value());
if (segment == "-")
{
input.constant_terms.back().is_unknown = true;
}
else
{
input.constant_terms.back().value = stod(segment);
}
}
}
System result = solveAndPrint(input);
return 0;
}
Ich hab nun noch keine Fehlerbehandlung umgesetzt... Und Kommentare fehlen auch, wo etwas nicht selbsterklärend wäre.
