#include <iostream>
using namespace std;


// function to reduce matrix to reduced
// row echelon form.
int PerformOperation(float **a, int n)
{
	int i, j, k = 0, c, flag = 0, m = 0;
	float pro = 0;

	// Performing elementary operations
	for (i = 0; i < n; i++) {
		if (a[i][i] == 0) {
			c = 1;
			while (a[i + c][i] == 0 && (i + c) < n)
				c++;
			if ((i + c) == n) {
				flag = 1;
				break;
			}
			for (j = i, k = 0; k <= n; k++)
				swap(a[j][k], a[j+c][k]);
		}

		for (j = 0; j < n; j++) {

			// Excluding all i == j
			if (i != j) {

				// Converting Matrix to reduced row
				// echelon form(diagonal matrix)
				float pro = a[j][i] / a[i][i];

				for (k = 0; k <= n; k++)
					a[j][k] = a[j][k] - (a[i][k]) * pro;
			}
		}
	}
	return flag;
}

// Function to print the desired result
// if unique solutions exists, otherwise
// prints no solution or infinite solutions
// depending upon the input given.
void PrintResult(float **a, int n, int flag) {
	cout << "Result is : "<< endl;

	if (flag == 2)
	cout << "Infinite Solutions Exists" << endl;
	else if (flag == 3)
	cout << "No Solution Exists" << endl;


	// Printing the solution by dividing constants by
	// their respective diagonal elements
	else {
	    for (int i = 0; i < n; i++) {
            a[i][n]=a[i][n]/ a[i][i];
            a[i][i]=a[i][i]/ a[i][i];

	    	for (int j = 0; j < n+1; j++)
	    	    cout << a[i][j] << " ";
	    	cout << endl;
        }
		//for (int i = 0; i < n; i++)
			//cout << a[i][n] / a[i][i] << " ";
	}
}

// To check whether infinite solutions
// exists or no solution exists
int CheckConsistency(float **a, int n, int flag) {
	int i, j;
	float sum;

	// flag == 2 for infinite solution
	// flag == 3 for No solution
	flag = 3;
	for (i = 0; i < n; i++) {
		sum = 0;
		for (j = 0; j < n; j++)
			sum = sum + a[i][j];
		if (sum == a[i][j])
			flag = 2;
	}
	return flag;
}

// Driver code
int main() {

	float **a;
	int m, n, flag = 0;
    cout << "矩陣大小為m*n"<<"\nm:";
    cin>>m;
    cout<<"n:";
    cin>>n;
    cout <<"矩陣:\n";

    a = new float*[m];
    for(int i = 0; i < m; i++)
        a[i] = new float[n];

    for (int i=0; i<m; i++) {
        for (int j=0; j<n+1; j++) {
            cin >> a[i][j];
        }
    }

	// Performing Matrix transformation
	flag = PerformOperation(a, n);

	if (flag == 1)
		flag = CheckConsistency(a, n, flag);

	// Printing Solutions(if exist)
	PrintResult(a, n, flag);

    for(int i = 0; i < m; i++)
        delete [] a[i];
    delete [] a;

	return 0;
}