Riešenia testu č. 1

Úloha č. 1

import java.math.*;

public class BigFraction {
    private BigInteger numerator;
    private BigInteger denominator;

    public BigFraction(BigInteger numerator, BigInteger denominator) {
        this.numerator = numerator;
        this.denominator = denominator;
    }

    public BigInteger getNumerator() {
        return numerator;
    }

    public BigInteger getDenominator() {
        return denominator;
    }

    public BigFraction reduce() {
        BigInteger gcd = numerator.gcd(denominator);
        BigInteger newNumerator = numerator.divide(gcd);
        BigInteger newDenominator = denominator.divide(gcd);
        if (denominator.signum() == -1) {
            newNumerator = newNumerator.negate();
            newDenominator = newDenominator.negate();
        }
        return new BigFraction(newNumerator, newDenominator);
    }

}

Úloha č. 2

package trees;

public class And extends BinaryOperatorNode {

    // ...

    @Override
    public Node negate() {
        return new Or(getLeft().negate(), getRight().negate());
    }
}

package trees;

public class Or extends BinaryOperatorNode {

    // ...

    @Override
    public Node negate() {
        return new And(getLeft().negate(), getRight().negate());
    }

}

package trees;

public class Not extends UnaryOperatorNode {

    // ...    

    @Override
    public Node negate() {
        return getChild();
    }

}

package trees;

public class Variable extends Node {
    
    // ...

    @Override
    public Node negate() {
        return new Not(this);
    }

}

Úloha č. 3

public class QuadraticForm {
    private int[][] coefficients;
    private int maximumVariableIndex;

    public QuadraticForm() {
        coefficients = new int[0][0];
        maximumVariableIndex = Integer.MIN_VALUE;
    }

    public QuadraticForm(int coefficient, int i, int j) {
        coefficients = new int[i + 1][j + 1];
        coefficients[i][j] = coefficient;
        if (coefficient != 0) {
            maximumVariableIndex = Math.max(i, j);
        } else {
            maximumVariableIndex = Integer.MIN_VALUE;
        }
    }

    public QuadraticForm(int[][] coefficients) {
        maximumVariableIndex = Integer.MIN_VALUE;
        this.coefficients = new int[coefficients.length][];
        for (int i = 0; i <= coefficients.length - 1; i++) {
            this.coefficients[i] = new int[coefficients[i].length];
            for (int j = 0; j <= coefficients[i].length - 1; j++) {
                this.coefficients[i][j] = coefficients[i][j];
                if (coefficients[i][j] != 0) {
                    maximumVariableIndex = Math.max(maximumVariableIndex, Math.max(i, j));
                }
            }
        }
    }

    public int getCoefficient(int i, int j) {
        if (coefficients.length <= i) {
            return 0;
        }
        if (coefficients[i].length <= j) {
            return 0;
        }
        return coefficients[i][j];
    }

    public int maximumVariableIndex() {
        return maximumVariableIndex;
    }

    public int evaluate(int[] values) {
        int sum = 0;
        for (int i = 0; i <= coefficients.length - 1; i++) {
            int xi = 0;
            if (i <= values.length - 1) {
                xi = values[i];
            }
            for (int j = 0; j <= coefficients[i].length - 1; j++) {
                int xj = 0;
                if (j <= values.length - 1) {
                    xj = values[j];
                }
                sum += coefficients[i][j] * xi * xj;
            }
        }
        return sum;
    }

    public QuadraticForm add(QuadraticForm other) {
        int n = Math.max(Math.max(maximumVariableIndex(), other.maximumVariableIndex()), -1) + 1;
        int[][] newCoefficients = new int[n][n];
        for (int i = 0; i <= n - 1; i++) {
            for (int j = 0; j <= n - 1; j++) {
                newCoefficients[i][j] = getCoefficient(i, j) + other.getCoefficient(i, j);
            }
        }
        return new QuadraticForm(newCoefficients);
    }
}