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This approach involves parsing the given strings to separate the real and imaginary components of each complex number. Once separated, apply the distributive property of multiplication for complex numbers: (a+bi)(c+di) = ac + adi + bci + bdi^2. Substitute i^2 with -1 and then combine the real and imaginary parts for the final output string.
Time Complexity: O(1) because the operations are constant-time.
Space Complexity: O(1) since it only uses a fixed amount of space for the variables and a small dynamic allocation for the output string.
1#include <iostream>
2#include <string>
3#include <sstream>
4
5void parseComplex(const std::string& complex, int& real, int& imaginary) {
6 char plus, i;
7 std::istringstream iss(complex);
8 iss >> real >> plus >> imaginary >> i;
9}
10
11std::string complexNumberMultiply(std::string num1, std::string num2) {
12 int real1, imag1, real2, imag2;
13 parseComplex(num1, real1, imag1);
14 parseComplex(num2, real2, imag2);
15
16 int realPart = real1 * real2 - imag1 * imag2;
17 int imagPart = real1 * imag2 + imag1 * real2;
18
19 return std::to_string(realPart) + "+" + std::to_string(imagPart) + "i";
20}
21
22int main() {
23 std::string num1 = "1+1i";
24 std::string num2 = "1+1i";
25 std::cout << complexNumberMultiply(num1, num2) << std::endl;
26 return 0;
27}This C++ solution utilizes std::istringstream to parse the complex numbers. The multiplication operation is performed as per the formula (a+bi)(c+di) = ac + adi + bci + bdi^2. The result is converted back to a string using std::to_string and concatenation.
In this approach, regular expressions are used to parse the complex number strings. This involves defining a regex pattern to capture the real and imaginary components. After extracting these components, multiplication is performed using the same algebraic rules, and the result is formatted for output.
Time Complexity: O(1) since the regex operation is effectively constant time for fixed-size strings.
Space Complexity: O(1) involving fixed-size auxiliary storage for components and result.
1import re
2
3def parse_complex_regex(
Using re.match in Python with a regular expression captures the real and imaginary parts directly. The parsed integers are used for multiplication, with results formatted back into strings in the expected form using Python's f-string syntax.