#include"iostream"
#include"cmath"
using namespace std;
int n, **matrix;
#define N 100
double l(int m, double x, double a[N])
{
int i, s = a[m - 1];
for (i = m - 1; i >= 0; i--)
{
s = s * x + a[i];
}
return s;
}
int gcd(int x, int y)
{
int r;
do
{
r = x % y;
x = y;
y = r;
} while (y != 0);
return x;
}
int det(int **m, int size) //求解行列式
{
if (size == 2) return m[0][0] * m[1][1] - m[0][1] * m[1][0];
int temp = 0;
for (int i = 0; i < size; i++) {
int **m0 = new int*[size - 1];
for (int v = 0; v < size - 1; v++)
m0[v] = new int[size - 1];
for (int p = 0; p < size - 1; p++) {
for (int q = 0; q < size - 1; q++)
if (q < i) m0[p][q] = m[p + 1][q];
else m0[p][q] = m[p + 1][q + 1];
}
if (i % 2 == 0) temp += m[0][i] * det(m0, size - 1);
else if (i % 2 == 1) temp -= m[0][i] * det(m0, size - 1);
for (int v = 0; v < size - 1; v++) delete[] m0[v];
delete[] m0;
}
return temp;
}
int fun1(int x) //素数判断
{
int range = (int)sqrt(x);
for (int i = 2; i <= range; i++)
{
if (x%i == 0)return false;
}
return true;
}
int fun2(int x, int y) //最大公约数
{
return x == 0 ? y : fun2(y%x, x);
}
void fun3(int a, int b, int c)
{
if ((a*a == b * b + c * c || b * b == a * a + c * c || c * c == a * a + b * b) && a>0 && b>0 && c>0)
{
cout << "这三个数是勾股数" << endl<<endl<<endl;
}
else
{
cout << "这三个数不是勾股数" << endl<<endl<<endl;
}
}
int fun4()
{
int sum = 0;
cout << "请输入行列式阶数" << endl;
cin >> n; // Matrix n * n ( n >= 2)
cout << "请输入行列式元素" << endl;
matrix = new int*[n];
for (int i = 0; i < n; i++) matrix[i] = new int[n];
for (int i = 0; i < n*n; i++) cin >> matrix[i / n][i%n];
//cout << det(matrix, n) << endl;
sum = det(matrix, n);
for (int i = 0; i < n; i++) delete[] matrix[i];
delete[] matrix;
return sum;
}
void fun5()
{
double a, b, c, d, x1, x2;
cout << "输入方程的三个系数a,b,c:";
cin >> a >> b >> c;
if (a == 0)
{
if (b == 0)
{
if (c == 0)
{
cout << "解集是复数集" << endl;
}
else
{
cout << "无解" << endl;
}
}
else
{
cout << "方程的解为:" << -c / b << endl;
}
}
else
{
d = b * b - 4 * a*c;
if (d >= 0)
{
if (b>0)
{
x1 = (-b - sqrt(d)) / (2 * a);
}
else
{
x1 = (-b + sqrt(d)) / (2 * a);
}
if (x1 == 0)
{
x2 = 0;
}
else
{
x2 = c / (a*x1);
}
cout << "方程的解为:" << x1 << "和" << x2 << endl;
}
else
{
cout << "x1=" << -b / (2 * a) <<" + "<<sqrt(-d) / (2 * a) << "i" << endl << "x2=" << -b / (2 * a) << " - "<<sqrt(-d) / (2 * a) << "i" << endl;
}
}
}
bool isrp(int a, int b)
{
if (a == 1 || b == 1)
return true;
while (1) {
int t = a % b;
if (t == 0) break;
else {
a = b;
b = t;
}
}
if (b > 1) return false;
else return true;
}
void start()
{
cout << "数学算法工具 " << endl;
cout << "1.[在复数域中求解ax^2+bx+c=0的根] "<< endl;
cout << "2.[素数判断] " << endl;
cout << "3.[计算公约数 ]" << endl;
cout << "4.[计算行列式] " << endl;
cout << "5.[多项式的计算] " << endl;
cout << "6.[有理数的四则运算]" << endl;
cout << "7.[计算勾股数] " << endl;
cout << "8.[判断三个数是否互素]" << endl;
cout << "9.[退出系统]" << endl;
}
int main()
{
again:int a = 8;
start();
cin >> a;
switch (a)
{
case 1:
{
fun5();
goto again;
}break;
case 2:
{
int x = 0;
cout << "[请输入要判断的数]" << endl;
cin >> x;
if (!fun1(x))
{
cout << "该数非素数" << endl<<endl<<endl;
goto again;
}
cout << "该数为素数" << endl<<endl<<endl;
goto again;
}break;
case 3:
{
int n, m,z=0;
cout << "[请输入两个数]" << endl;
cin >> n >> m;
z=fun2(n,m);
cout<<"最大公约数为" << z << endl<<endl<<endl;
goto again;
}break;
case 4:
{
int sum = 0;
sum=fun4();
cout << "行列式的结果为" << sum << endl << endl<<endl;
goto again;
}break;
case 5:
{
int i, m;
double x, a[N], p;
cout << "输入次数:";
cin >> m;
cout << "输入系数:";
for (i = 0; i<m; i++)
{
cin >> a[i];
}
cout << "输入数x:";
cin >> x;
p = l(m, x, a);
cout << "多项式的值为:" << p << endl << endl << endl;
goto again;
}break;
case 6:
{
int you = 5;
cout << "1.[有理数加法] " << endl;
cout << "2.[有理数减法] " << endl;
cout << "3.[有理数乘法 ]" << endl;
cout << "4.[有理数除法] " << endl;
cout << "5.[返回上一级菜单]" << endl;
cin >> you;
switch (you)
{
case 1:
{
int a, b, c, d, e, f, p;
cout << "输入四个有理数a,b,c,d,表示两个分数a/b和c/d:";
cin >> a >> b >> c >> d;
f = a * d + b * c;
e = b * d;
if (f == 0)
{
e = 1;
}
else
{
p = gcd(abs(f), e);
e /= p;
f /= p;
}
cout << "两个分数的和为：" << f << "/" << e << endl << endl << endl;
goto again;
}break;
case 2:
{
int a, b, c, d, e, f, p;
cout << "输入四个有理数a,b,c,d,表示两个分数a/b和c/d:";
cin >> a >> b >> c >> d;
f = a * d - b * c;
e = b * d;
if (f == 0)
{
e = 1;
}
else
{
p = gcd(abs(f), e);
e /= p;
f /= p;
}
cout << "两个分数的差为：" << f << "/" << e << endl<<endl<<endl;
goto again;
}break;
case 3:
{
int a, b, c, d, e, f, p;
cout << "输入四个有理数a,b,c,d,表示两个分数a/b和c/d:";
cin >> a >> b >> c >> d;
f = a * c;
e = b * d;
if (f == 0)
{
e = 1;
}
else
{
p = gcd(abs(f), e);
e /= p;
f /= p;
}
cout << "两个分数的积为：" << f << "/" << e << endl << endl << endl;
goto again;
}break;
case 4:
{
int a, b, c, d, e, f, p;
cout << "输入四个有理数a,b,c,d,表示两个分数a/b和c/d:";
cin >> a >> b >> c >> d;
f = a * d;
e = b * c;
if (f == 0)
{
e = 1;
}
else
{
p = gcd(abs(f), e);
e /= p;
f /= p;
}
cout << "两个分数的商为：" << f << "/" << e << endl << endl << endl;
goto again;
}break;
case 5:
{
goto again;
}break;
}
}break;
case 7:
{
int x, y, z;
cout << "输入三个整数：";
cin >> x >> y >> z;
fun3(x, y, z);
goto again;
}break;
case 8:
{
int a, b, c;
cout << "输入三个整数:";
cin >> a>> b>>c;
if (gcd(a, b) == 1 || gcd(b, c) == 1)
{
cout << "这三个数互素" << endl << endl << endl;
}
else
{
cout << "这三个数不互素" << endl << endl << endl;
}
goto again;
}break;
case 9:
{
exit(0);
}break;
}
system("pause");
return 0;
}
大兄弟的作业题，希望会有用，如有错误，欢迎指出，感谢。
