LeetCode Complex Number Multiplication

原题链接在这里：https://leetcode.com/problems/complex-number-multiplication/description/

题目：

Given two strings representing two complex numbers.

You need to return a string representing their multiplication. Note i2 = -1 according to the definition.

Example 1:

Input: "1+1i", "1+1i"
Output: "0+2i"
Explanation: (1 + i) * (1 + i) = 1 + i2 + 2 * i = 2i, and you need convert it to the form of 0+2i.

Example 2:

Input: "1+-1i", "1+-1i"
Output: "0+-2i"
Explanation: (1 - i) * (1 - i) = 1 + i2 - 2 * i = -2i, and you need convert it to the form of 0+-2i.

Note:

1. The input strings will not have extra blank.
2. The input strings will be given in the form of a+bi, where the integer a and b will both belong to the range of [-100, 100]. And the output should be also in this form.

题解：

(aReal + aImag*i)*(bReal + bImag*i) = (aReal*bReal- aImag*bImag) + (aReal*bImag+bReal*aImag)*i.

从原有string里提取出实数和虚数两部分组成答案.

Time Complexity: O(a.length() + b.length()). split用时

Space: O(a.length() + b.length()). 中间的string arr.

AC Java:

class Solution {
    public String complexNumberMultiply(String a, String b) {
        String [] aArr = a.split("\+|i");
        String [] bArr = b.split("\+|i");
        int aReal = Integer.valueOf(aArr[0]);
        int aImag = Integer.valueOf(aArr[1]);
        int bReal = Integer.valueOf(bArr[0]);
        int bImag = Integer.valueOf(bArr[1]);
        return (aReal*bReal-aImag*bImag) + "+" + (aReal*bImag+aImag*bReal) + "i";
    }
}