LeetCode 0537. Complex Number Multiplication Solution in Java, C++, Python & More | Explanation + Code

Description

A complex number can be represented as a string on the form "real+imaginaryi" where:

• real is the real part and is an integer in the range [-100, 100].
• imaginary is the imaginary part and is an integer in the range [-100, 100].
• i2 == -1.

Given two complex numbers num1 and num2 as strings, return a string of the complex number that represents their multiplications.

 

Example 1:

Input: num1 = "1+1i", num2 = "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: num1 = "1+-1i", num2 = "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.

 

Constraints:

• num1 and num2 are valid complex numbers.

Solutions

Solution 1: Simulation

We can convert the complex number string into its real part a and imaginary part b, and then use the formula for complex number multiplication (a_1 + b_1i) × (a_2 + b_2i) = (a_1a_2 - b_1b_2) + (a_1b_2 + a_2b_1)i to calculate the result.

The time complexity is O(1), and the space complexity is O(1).

PythonJavaC++GoTypeScript

class Solution: def complexNumberMultiply(self, num1: str, num2: str) -> str: a1, b1 = map(int, num1[:-1].split("+")) a2, b2 = map(int, num2[:-1].split("+")) return f"{a1 * a2 - b1 * b2}+{a1 * b2 + a2 * b1}i"(code-box)

class Solution { public String complexNumberMultiply(String num1, String num2) { int[] x = parse(num1); int[] y = parse(num2); int a1 = x[0], b1 = x[1], a2 = y[0], b2 = y[1]; return (a1 * a2 - b1 * b2) + "+" + (a1 * b2 + a2 * b1) + "i"; } private int[] parse(String s) { var cs = s.substring(0, s.length() - 1).split("\\+"); return new int[] {Integer.parseInt(cs[0]), Integer.parseInt(cs[1])}; } }(code-box)

class Solution { public: string complexNumberMultiply(string num1, string num2) { int a1, b1, a2, b2; sscanf(num1.c_str(), "%d+%di", &a1, &b1); sscanf(num2.c_str(), "%d+%di", &a2, &b2); return to_string(a1 * a2 - b1 * b2) + "+" + to_string(a1 * b2 + a2 * b1) + "i"; } };(code-box)

func complexNumberMultiply(num1 string, num2 string) string { x, _ := strconv.ParseComplex(num1, 64) y, _ := strconv.ParseComplex(num2, 64) return fmt.Sprintf("%d+%di", int(real(x*y)), int(imag(x*y))) }(code-box)

function complexNumberMultiply(num1: string, num2: string): string { const [a1, b1] = num1.slice(0, -1).split('+').map(Number); const [a2, b2] = num2.slice(0, -1).split('+').map(Number); return `${a1 * a2 - b1 * b2}+${a1 * b2 + a2 * b1}i`; }(code-box)