以下の2つの未知数を持つ2つの方程式のシステムを解きます。
a1、b1、c1、a2、b2、c2はユーザー自身が入力します。
私は最初に問題の数学的な解決策を見つけようとしてきましたが、遠くまで行けないようです。
私がこれまでに試したことは:
これは正しいですか、それともこれを行う簡単な方法はありますか?
現在のコード:
#include <iostream>
using namespace std;
int main()
{
int a1, b1, c1, a2, b2, c2;
cout << "Enter the values for the first equation." << endl;
cout << "Enter the value for a1" << endl;
cin >> a1;
cout << "Enter the value for b1" << endl;
cin >> b1;
cout << "Enter the value for c1" << endl;
cin >> c1;
cout << "Enter the values for the second equation." << endl;
cout << "Enter the value for a2" << endl;
cin >> a2;
cout << "Enter the value for b2" << endl;
cin >> b2;
cout << "Enter the value for c2" << endl;
cin >> c2;
cout << "Your system of equations is the following:" << endl;
cout << a1 << "x+" << b1 << "y=" << c1 << endl;
cout << a2 << "x+" << b2 << "y=" << c2 << endl;
if ((a1 * b2) - (b1 * a2) == 0){
cout << "The system has no solution." << endl;
}
else{
res_x = ((c1*b2) - (b1*c2))/((a1*b2)-(b1*a2));
res_y = ((a1*c2) - (c1*a2)) / ((a1*b2) - (b1*a2));
cout << "x=" << res_x << " y=" << res_y << endl;
}
return 0;
}
クラメルの公式 を使用して線形システムを解きます。
int main(int argc, char** argv) {
/* we solve the linear system
* ax+by=e
* cx+dy=f
*/
if(argc != 7) {
cerr<<"Cramer equations system: error,"
" we need a,b,c,d,e,f parameters.\n";
return -1;
}
double a,b,e;
double c,d,f;
sscanf(argv[1],"%lf",&a);
sscanf(argv[2],"%lf",&b);
sscanf(argv[3],"%lf",&e);
sscanf(argv[4],"%lf",&c);
sscanf(argv[5],"%lf",&d);
sscanf(argv[6],"%lf",&f);
double determinant = a*d - b*c;
if(determinant != 0) {
double x = (e*d - b*f)/determinant;
double y = (a*f - e*c)/determinant;
printf("Cramer equations system: result, x = %f, y = %f\n", x, y);
} else {
printf("Cramer equations system: determinant is zero\n"
"there are either no solutions or many solutions exist.\n");
}
return 0;
}
./cramer_equation_system 1 2 5 1 -1 -1
クレイマー方程式システム:結果、x = 1.000000、y = 2.000000
4pie0の答え に触発されたJavascriptバージョン
// throws error if intersection can't be found
function intersect_2_lines (
a,b,e,
c,d,f
)
{
/* we solve the linear system
* ax+by=e
* cx+dy=f
*/
var determinant = a*d - b*c;
if(determinant != 0) {
var x = (e*d - b*f)/determinant;
var y = (a*f - e*c)/determinant;
console.log(`Cramer equations system: result, x = ${x}, y = ${y}\n`);
} else {
throw new Error("Cramer equations system: determinant is zero\n" +
"there are either no solutions or many solutions exist.\n");
}
return [x,y];
}