537. Complex Number Multiplication

• Difficulty: Medium

• Topics: Math, String

• Similar Questions:

Problem:

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:

Solutions:

class Solution {
public:
    string complexNumberMultiply(string a, string b) {
        auto complex1 = parse(a);
        auto complex2 = parse(b);

        int real = complex1.first * complex2.first - complex1.second * complex2.second;
        int img = complex1.first * complex2.second + complex2.first * complex1.second;

        return to_string(real) + "+" + to_string(img) + "i";
    }

private:
    pair<int, int> parse(const string& str) {
        int real = 0;
        int img = 0;
        int realSign = 1;
        int imgSign = 1;

        int pos = 0;
        if (str[pos] == '-') {
            realSign = -1;
            ++pos;
        }
        while (str[pos] != '+') {
            real = real * 10 + str[pos] - '0';
            ++pos;
        }

        ++pos;

        if (str[pos] == '-') {
            imgSign = -1;
            ++pos;
        }
        while (str[pos] != 'i') {
            img = 10 * img + str[pos] - '0';
            ++pos;
        }

        return {real * realSign, img * imgSign};
    }

};