Условие

Даны два комплексных числа. Найдите их сумму или разность.

Входные данные

В каждой строке задан пример на сложение или вычитание комплексных чисел. Комплексное число задается в формате $a+bi$ или $a — bi$, где $a$ целое, $b$ целое неотрицательное. Действительная и мнимая часть каждого комплексного числа по модулю не превышает $10^{9}$.

Выходные данные

Для каждого входного примера выведите ответ в отдельной строке.

Тесты

№	Входные данные	Выходные данные
1	2+3i + 7-4i	9-1i
2	-1-1i — -1-1i	0+0i
3	56743+876i — 1234-124i	55509+1000i
4	331+10i — 331+10i	0+0i

Код

import java.util.*;
 
public class Main {
    public static void main(String args[]) {
        Scanner sc = new Scanner(System.in);
        while (sc.hasNextLine()) {
            String s[] = sc.nextLine().replace("i", "").split(" ");
            int x1 = 1, x2 = 1;
            if (s[0].charAt(0) == '-') {
                s[0] = s[0].substring(1, s[0].length());
                x1 *= -1;
            }
            if (s[0].indexOf("+") != -1) {
                x1 *= Integer.parseInt(s[0].split("\\+")[0]);
                x2 *= Integer.parseInt(s[0].split("\\+")[1]);
            } else {
                x1 *= Integer.parseInt(s[0].split("-")[0]);
                x2 *= Integer.parseInt(s[0].split("-")[1]) * (-1);
            }
            int y1 = 1, y2 = 1;
            if (s[2].charAt(0) == '-') {
                s[2] = s[2].substring(1, s[2].length());
                y1 *= -1;
            }
            if (s[2].indexOf('+') != -1) {
                y1 *= Integer.parseInt(s[2].split("\\+")[0]);
                y2 *= Integer.parseInt(s[2].split("\\+")[1]);
            } else {
                y1 *= Integer.parseInt(s[2].split("-")[0]);
                y2 *= Integer.parseInt(s[2].split("-")[1]) * (-1);
            }
            if (s[1].equals("+")) {
                x1 = x1 + y1;
                x2 = x2 + y2;
            } else {
                x1 = x1 - y1;
                x2 = x2 - y2;
            }
            String c = (x2 >= 0 ? "+" : "");
            System.out.printf("%d%s%di\n", x1, c, x2);
        }
    }
}

import java.util.*;

public class Main {

public static void main(String args[]) {

Scanner sc = new Scanner(System.in);

while (sc.hasNextLine()) {

String s[] = sc.nextLine().replace("i", "").split(" ");

int x1 = 1, x2 = 1;

if (s[0].charAt(0) == '-') {

s[0] = s[0].substring(1, s[0].length());

x1 *= -1;

}

if (s[0].indexOf("+") != -1) {

x1 *= Integer.parseInt(s[0].split("\\+")[0]);

x2 *= Integer.parseInt(s[0].split("\\+")[1]);

} else {

x1 *= Integer.parseInt(s[0].split("-")[0]);

x2 *= Integer.parseInt(s[0].split("-")[1]) * (-1);

}

int y1 = 1, y2 = 1;

if (s[2].charAt(0) == '-') {

s[2] = s[2].substring(1, s[2].length());

y1 *= -1;

}

if (s[2].indexOf('+') != -1) {

y1 *= Integer.parseInt(s[2].split("\\+")[0]);

y2 *= Integer.parseInt(s[2].split("\\+")[1]);

} else {

y1 *= Integer.parseInt(s[2].split("-")[0]);

y2 *= Integer.parseInt(s[2].split("-")[1]) * (-1);

}

if (s[1].equals("+")) {

x1 = x1 + y1;

x2 = x2 + y2;

} else {

x1 = x1 - y1;

x2 = x2 - y2;

}

String c = (x2 >= 0 ? "+" : "");

System.out.printf("%d%s%di\n", x1, c, x2);

}

Решение

Чтобы решить задачу будем разбивать строки на подстроки методом .split() тогда, для каждой строки у нас будет массив из трёх её подстрок, где первый и третий элементы — комплексные числа, а второй — арифметическая операция производимая над ними. Далее оба комплексных числа так же, с помощью .split(), разобьем на реальную и мнимую части и выполним сложение или вычитание соответственных элементов.

Ссылки

E-olymp

Ideone

Задача.

Напишите класс для хранения комплексных чисел и реализуйте основные операции работы с ними.

Тесты.

Исходные числа	Операция	Результат
z1 = 2 + 3i z2 = -1 + 2i	+	1.0 + 5.0i
	—	3.0 + i
	*	-8.0 + i
	/	0.8 — 1.4i
3 + 4i	√	2.0 + i, -2.0 -i
-1 + 2i	pow	-3.0 — 4.0i

Код программы

/**
 * <h1>Complex Numbers</h1>
 * The ComplexNumber program implements an application that
 * allows to calculate complex numbers
 **/

public class ComplexNumber {

    /**
     * Represents the real part of a complex number
     */
    private double re;

    /**
     * Represents imaginary part of a complex number
     */
    private double im;

    public ComplexNumber(double re, double im) {
        this.re = re;
        this.im = im;
    }

    public double getRe() {
        return re;
    }

    public double getIm() {
        return im;
    }

    /**
     * @return modulus (or absolute value) of the number
     */
    private double getModule() {
        return Math.sqrt(this.re * this.re + this.im * this.im);
    }

    /**
     * Allows to get the sum of two complex numbers given in the parameters.
     *
     * @return the new complex number
     */
    public static ComplexNumber sum(ComplexNumber cn1, ComplexNumber cn2) {
        return new ComplexNumber(cn1.getRe() + cn2.getRe(), cn1.getIm() + cn2.getIm());
    }

    /**
     * Allows to get the product of two complex numbers given in the parameters.
     *
     * @return the new complex number
     */
    public static ComplexNumber multiply(ComplexNumber cn1, ComplexNumber cn2) {
        return new ComplexNumber(cn1.getRe() * cn2.getRe() - cn1.getIm() * cn2.getIm(), cn1.getRe() * cn2.getIm() + cn1.getIm() * cn2.getRe());
    }

    /**
     * Allows to get the difference of two complex numbers given in the parameters.
     *
     * @return the new complex number
     */
    public static ComplexNumber subtract(ComplexNumber cn1, ComplexNumber cn2) {
        return new ComplexNumber(cn1.getRe() - cn2.getRe(), cn1.getIm() - cn2.getIm());
    }

    /**
     * Allows to get the product of two complex numbers given in the parameters.
     *
     * @return the new complex number
     */
    public static ComplexNumber divide(ComplexNumber cn1, ComplexNumber cn2) {
        ComplexNumber temp = new ComplexNumber(cn2.getRe(), (-1) * cn2.getIm());
        temp = ComplexNumber.multiply(cn1, temp);
        double denominator = cn2.getRe() * cn2.getRe() + cn2.getIm() * cn2.getIm();
        return new ComplexNumber(temp.getRe() / denominator, temp.getIm() / denominator);
    }

    /**
     * This function allows to get the argument of complex number to represent it in trigonometric form
     *
     * @return argument of complex number
     */
    private double GetArg() {
        if (this.re > 0) {
            return Math.atan(im / re);
        } else {
            if (re < 0 && im > 0) {
                return Math.PI + Math.atan(im / re);
            } else {
                return -Math.PI + Math.atan(im / re);
            }
        }
    }

    /**
     * Allows to raise complex number to specified power with the help of de Moivre's formula.
     *
     * @param cn    needed complex number (the base)
     * @param power the exponent
     * @return the new complex number
     */
    public static ComplexNumber pow(ComplexNumber cn, int power) {
        double factor = Math.pow(cn.getModule(), power);
        return new ComplexNumber(factor * Math.cos(power * cn.GetArg()), factor * Math.sin(power * cn.GetArg()));
    }

    /**
     * The function of getting square roots of complex number cn
     *
     * @return an array of pair of square roots
     */
    public static ComplexNumber[] sqrt(ComplexNumber cn) {
        double a = cn.getModule() / 2;
        ComplexNumber pos = new ComplexNumber(Math.sqrt(a + cn.getRe() / 2), Math.signum(cn.getIm()) * Math.sqrt(a - cn.getRe() / 2));
        ComplexNumber neg = new ComplexNumber((-1) * pos.getRe(), (-1) * pos.getIm());
        ComplexNumber[] answer = {pos, neg};
        return answer;
    }

    /**
     * Defines and returns the sign required for correct record of a number
     *
     * @return string with appropriate sign
     */
    private String sign() {
        if (im > 0) return " + ";
        else return " - ";
    }

    @Override
    public String toString() {
        String string;
        if (im == 1 || im == -1) {
            if (re == 0) {
                string = sign() + "i";
            } else {
                string = Double.toString(re) + sign() + "i";
            }
        } else {
            string = Double.toString(re) + sign() + Double.toString(Math.abs(im)) + "i";
        }
        return string;
    }

    @Override
    public boolean equals(Object obj) {
        if (this.getClass() != obj.getClass() || obj == null)
            return false;
        return true;
    }

    /**
     * In this function main test on the correctness of this program are done.
     * All operations on complex numbers are shown.
     */
    public static void main(String[] args) {
        ComplexNumber x = new ComplexNumber(2, 3);
        ComplexNumber y = new ComplexNumber(-1, 2);
        System.out.println("z1 = " + x + ",     z2 = " + y);

        ComplexNumber z;
        z = ComplexNumber.sum(x, y);
        System.out.println("+ : " + z);

        z = ComplexNumber.subtract(x, y);
        System.out.println("- : " + z);

        z = ComplexNumber.divide(x, y);
        System.out.println("/ : " + z);

        z = ComplexNumber.multiply(x, y);
        System.out.println(" * :" + z);

        z = ComplexNumber.pow(y, 2);
        System.out.println("Pow 2 of z2 : " + z);

        ComplexNumber b = new ComplexNumber(3, 4);
        ComplexNumber[] ans = ComplexNumber.sqrt(b);
        System.out.println("Sqrt of " + b + " = " + ans[0] + ",  " + ans[1]);

    }
}

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/**

* <h1>Complex Numbers</h1>

* The ComplexNumber program implements an application that

* allows to calculate complex numbers

**/

public class ComplexNumber {

/**

* Represents the real part of a complex number

private double re;

/**

* Represents imaginary part of a complex number

private double im;

public ComplexNumber(double re, double im) {

this.re = re;

this.im = im;

}

public double getRe() {

return re;

}

public double getIm() {

return im;

}

/**

* @return modulus (or absolute value) of the number

private double getModule() {

return Math.sqrt(this.re * this.re + this.im * this.im);

}

/**

* Allows to get the sum of two complex numbers given in the parameters.

* @return the new complex number

public static ComplexNumber sum(ComplexNumber cn1, ComplexNumber cn2) {

return new ComplexNumber(cn1.getRe() + cn2.getRe(), cn1.getIm() + cn2.getIm());

}

/**

* Allows to get the product of two complex numbers given in the parameters.

* @return the new complex number

public static ComplexNumber multiply(ComplexNumber cn1, ComplexNumber cn2) {

return new ComplexNumber(cn1.getRe() * cn2.getRe() - cn1.getIm() * cn2.getIm(), cn1.getRe() * cn2.getIm() + cn1.getIm() * cn2.getRe());

}

/**

* Allows to get the difference of two complex numbers given in the parameters.

* @return the new complex number

public static ComplexNumber subtract(ComplexNumber cn1, ComplexNumber cn2) {

return new ComplexNumber(cn1.getRe() - cn2.getRe(), cn1.getIm() - cn2.getIm());

}

/**

* Allows to get the product of two complex numbers given in the parameters.

* @return the new complex number

public static ComplexNumber divide(ComplexNumber cn1, ComplexNumber cn2) {

ComplexNumber temp = new ComplexNumber(cn2.getRe(), (-1) * cn2.getIm());

temp = ComplexNumber.multiply(cn1, temp);

double denominator = cn2.getRe() * cn2.getRe() + cn2.getIm() * cn2.getIm();

return new ComplexNumber(temp.getRe() / denominator, temp.getIm() / denominator);

}

/**

* This function allows to get the argument of complex number to represent it in trigonometric form

* @return argument of complex number

private double GetArg() {

if (this.re > 0) {

return Math.atan(im / re);

} else {

if (re < 0 && im > 0) {

return Math.PI + Math.atan(im / re);

} else {

return -Math.PI + Math.atan(im / re);

}

/**

* Allows to raise complex number to specified power with the help of de Moivre's formula.

* @param cn needed complex number (the base)

* @param power the exponent

* @return the new complex number

public static ComplexNumber pow(ComplexNumber cn, int power) {

double factor = Math.pow(cn.getModule(), power);

return new ComplexNumber(factor * Math.cos(power * cn.GetArg()), factor * Math.sin(power * cn.GetArg()));

}

/**

* The function of getting square roots of complex number cn

* @return an array of pair of square roots

public static ComplexNumber[] sqrt(ComplexNumber cn) {

double a = cn.getModule() / 2;

ComplexNumber pos = new ComplexNumber(Math.sqrt(a + cn.getRe() / 2), Math.signum(cn.getIm()) * Math.sqrt(a - cn.getRe() / 2));

ComplexNumber neg = new ComplexNumber((-1) * pos.getRe(), (-1) * pos.getIm());

ComplexNumber[] answer = {pos, neg};

return answer;

}

/**

* Defines and returns the sign required for correct record of a number

* @return string with appropriate sign

private String sign() {

if (im > 0) return " + ";

else return " - ";

}

@Override

public String toString() {

String string;

if (im == 1 || im == -1) {

if (re == 0) {

string = sign() + "i";

} else {

string = Double.toString(re) + sign() + "i";

}

} else {

string = Double.toString(re) + sign() + Double.toString(Math.abs(im)) + "i";

}

return string;

}

@Override

public boolean equals(Object obj) {

if (this.getClass() != obj.getClass() || obj == null)

return false;

return true;

}

/**

* In this function main test on the correctness of this program are done.

* All operations on complex numbers are shown.

public static void main(String[] args) {

ComplexNumber x = new ComplexNumber(2, 3);

ComplexNumber y = new ComplexNumber(-1, 2);

System.out.println("z1 = " + x + ", z2 = " + y);

ComplexNumber z;

z = ComplexNumber.sum(x, y);

System.out.println("+ : " + z);

z = ComplexNumber.subtract(x, y);

System.out.println("- : " + z);

z = ComplexNumber.divide(x, y);

System.out.println("/ : " + z);

z = ComplexNumber.multiply(x, y);

System.out.println(" * :" + z);

z = ComplexNumber.pow(y, 2);

System.out.println("Pow 2 of z2 : " + z);

ComplexNumber b = new ComplexNumber(3, 4);

ComplexNumber[] ans = ComplexNumber.sqrt(b);

System.out.println("Sqrt of " + b + " = " + ans[0] + ", " + ans[1]);

}

Ссылка на Ideone.

java@Cat

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Tag Archives: комплексные числа

e-olymp 9531. Комплексные числа: сложение и вычитание

Условие

Входные данные

Выходные данные

Тесты

№

Входные данные

Выходные данные

Код

Решение

Ссылки

Класс комплексных чисел