537

537. Complex Number Multiplication (Medium)

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.

Solution 1.

// OJ: https://leetcode.com/problems/complex-number-multiplication/
// Author: github.com/lzl124631x
// Time: O(N)
// Space: O(N)
class Solution {
private:
    vector<int> parse(string &s) {
        vector<int> ans(2, 0);
        ans[0] = stoi(s);
        int i = s.find_first_of("+");
        ans[1] = stoi(s.substr(i + 1));
        return ans;
    }
public:
    string complexNumberMultiply(string a, string b) {
        auto m = parse(a), n = parse(b);
        int x = m[0] * n[0] - m[1] * n[1], y = m[1] * n[0] + m[0] * n[1];
        return to_string(x) + "+" + to_string(y) + "i";
    }
};