import java.util.*; public class Program { public static void solve(ArrayList first_row, ArrayList second_row) { double num = 1.0 / first_row.get(0); //getting the inverse of the number in the first row, first column; for example, if the value in the first row, first column is 3, it's inverse, 1/3 for (int index = 0; index < first_row.size(); index++) //we want to multiply the value of the first row, first column, by it's inverse, so it becomes one, but we also need to perform that on the entire row as that's the elementary row operation we're using here { first_row.set(index, first_row.get(index) * num); } num = -second_row.get(0); //here, we are setting off to prepare the second step of Guass-Jordan elimination, and that is multiplying the second row by the first row which gets multiplied by the negative value of the second row, second column first for (int index = 0; index < first_row.size(); index++) { second_row.set(index, second_row.get(index) + first_row.get(index) * num); } num = 1.0 / second_row.get(1); //now we repeat the first step to get a one in the place of the second row, second column for (int index = 0; index < second_row.size(); index++) { second_row.set(index, second_row.get(index) * num); } num = -first_row.get(1); //finally, to convert the value of the number in the first row, second column to 0, we get it's inverse for (int index = 0; index < first_row.size(); index++) { first_row.set(index, first_row.get(index) + second_row.get(index) * num); //we then multiply all the numbers in the first row by the sum of that number and the product of the corresponding number in the second row } if ((first_row.get(2) == Double.POSITIVE_INFINITY || first_row.get(2) == Double.NEGATIVE_INFINITY) && (second_row.get(2) == Double.POSITIVE_INFINITY || second_row.get(2) == Double.NEGATIVE_INFINITY)) //if the value of the third columns for both rows is equal to Java's infinity, Java is telling us there are no solutions { System.out.println("There are no solutions to this system of equations."); } else if (first_row.get(2).isNaN() && second_row.get(2).isNaN()) //if the value of the third columns for both rows is equal to Java's NaN(Not a Number), Java is telling us there are infinite solutions { System.out.println("There are infinite solutions to this system of equations."); } else { int x = first_row.get(2).intValue(); //getting the rounded value of the value of the number in the first row, third column, which happens to be the value of x int y = second_row.get(2).intValue(); //getting the rounded value of the value of the number in the second row, third column, which happens to be the value of y System.out.println("The rounded number solution to the system of equations is: (" + Integer.toString(x) + ", " + Integer.toString(y) + ")"); System.out.println("The exact number solution to the system of equations is: (" + Double.toString(first_row.get(2)) + ", " + Double.toString(second_row.get(2)) + ")"); } } public static void main(String[] args) { Scanner input = new Scanner(System.in); ArrayList first_row = new ArrayList(); ArrayList second_row = new ArrayList(); String first_equation = input.nextLine(); String second_equation = input.nextLine(); String[] first_split = first_equation.split(" ", 0); String[] second_split = second_equation.split(" ", 0); for (String num : first_split) first_row.add(Double.valueOf(Integer.parseInt(num))); for (String num : second_split) { second_row.add(Double.valueOf(Integer.parseInt(num))); } solve(first_row, second_row); input.close(); } }

Solving System Of Equations[Challenge]