Formatted question description: https://leetcode.ca/all/537.html

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/

// 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";
    }
};

Java

  • class Solution {
        public String complexNumberMultiply(String a, String b) {
            int aReal = Integer.parseInt(a.substring(0, a.indexOf('+')));
            int aImag = Integer.parseInt(a.substring(a.indexOf('+') + 1, a.indexOf('i')));
            int bReal = Integer.parseInt(b.substring(0, b.indexOf('+')));
            int bImag = Integer.parseInt(b.substring(b.indexOf('+') + 1, b.indexOf('i')));
            int mulReal = aReal * bReal - aImag * bImag;
            int mulImag = aReal * bImag + bReal * aImag;
            return mulReal + "+" + mulImag + "i";
        }
    }
    
  • // OJ: https://leetcode.com/problems/complex-number-multiplication/
    // 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";
        }
    };
    
  • class Solution(object):
      def complexNumberMultiply(self, a, b):
        """
        :type a: str
        :type b: str
        :rtype: str
        """
        (ar, ac), (br, bc) = map(int, a[:-1].split("+")), map(int, b[:-1].split("+"))
        return "{}+{}i".format(str(ar * br - ac * bc), str(ar * bc + br * ac))
    
    

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