Complex Number Multiplication

本文提供了一种简单的方法来解决LeetCode上的复数乘法问题。通过分解复数为实部和虚部,并利用基本的数学原理实现了字符串形式的复数相乘。此算法将复数相乘转换为简单的代数运算。

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https://leetcode.com/problems/complex-number-multiplication/description/

题解:这道题只要了解复数是怎么运算就好了

class Solution {
    public String complexNumberMultiply(String a, String b) {
        //a1,a2是a的实部和虚部,b1,b2是b的实部和虚部
        int a1, a2, b1, b2;
        a1 = Integer.valueOf(a.substring(0, a.indexOf("+")));
        a2 = Integer.valueOf(a.substring(a.indexOf("+")+1, a.length()-1));
        b1 = Integer.valueOf(b.substring(0, b.indexOf("+")));
        b2 = Integer.valueOf(b.substring(b.indexOf("+")+1, b.length()-1));
        return (a1*b1-a2*b2)+"+"+(a1*b2+b1*a2)+"i";
    }
}
1. Problem Description: A complex number is a number of the form a +bi, where a and b are real numbers and i is √-1 The numbers a and b are known as the real part and imaginary part of the complex number, respectively. You can perform addition, subtraction, multiplication, and division for complex numbers using the following formula: a+bi+c+di=(a+c)+(b+d)i a+bi-(c+di)=(a-c)+(b-d)i 第2页共2页 (a+bi)*(c+di)=(ac-bd)+(bc+ad)i (a+bi)/c+di)=(ac+bd)/c²+d²)+(bc-ad)i/(c²+d²) You can also obtain the absolute value for a complex number using the following formula: latbil=√a²+b (A complex number can be interpreted as a point on a plane by identifying the (a, b) values as the coordinates of the point. The absolute value of the complex number corresponds to the distance of the point to the origin, as shown in Figure 13.12b.) Design a class named Complex for representing complex numbers and the methods add, subtract, multiply, divide, abs for performing complex-number operations, and override toString method for returning a string representation for a complex number. The toString method returns a + bi as a string. If b is 0, it simply returns a. Provide three constructors Complex(a, b), Complex(a), and Complex(). Complex() creates a Complex object for number 0 and Complex(a) creates a Complex object with 0 for b. Also provide the getRealPart() and getlmaginaryPart() methods for returning the real and imaginary part of the complex number, respectively. Your Complex class should also implement the Cloneable interface. Write a test program that prompts the user to enter two complex numbers and display the result of their addition, subtraction, multiplication, and division. Here is a sample run: <Output> Enter the first complex number: 3.5 5.5 Enter the second complex number:-3.5 1 (3.5 + 5.5i) +(-3.5 + 1.0i)= 0.0 + 6.5 (3.5 + 5.5i)-(-3.5 + 1.0i)= 7.0 + 4.5i (3.5 + 5.5i)*(-3.5 + 1.0i) =-17.75 +-15.75i (3.5 + 5.5i) /(-3.5 + 1.0i)=-0.5094 +-1.7i |3.5 + 5.5il = 6.519202405202649 <End Output>
最新发布
06-09
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