grid47 Exploring patterns and algorithms
Sep 14, 2024
6 min read
Solution to LeetCode 537: Complex Number Multiplication Problem
Given two complex numbers represented as strings, multiply them and return the result as a string in the format ‘real+imaginaryi’.
Problem
Approach
Steps
Complexity
Input: Each input consists of two strings representing complex numbers. Each complex number is represented in the form 'real+imaginaryi', where both real and imaginary are integers within the range [-100, 100].
Example: Input: num1 = "2+3i", num2 = "4+5i"
Constraints:
• num1 and num2 are valid complex numbers, with real and imaginary parts being integers in the range [-100, 100].
Output: The output should be a string representing the product of the two complex numbers in the format 'real+imaginaryi'.
Example: Output: "-7+22i"
Constraints:
• The output should follow the exact format 'real+imaginaryi', where real and imaginary are integers.
Goal: To multiply two complex numbers and return the result in the appropriate format.
Steps:
• Parse the real and imaginary parts of both complex numbers from the input strings.
• Apply the formula for multiplying complex numbers: (a + bi) * (c + di) = (ac - bd) + (ad + bc)i.
• Construct the result string by formatting the real and imaginary parts into the 'real+imaginaryi' format.
Goal: Ensure that the inputs represent valid complex numbers and the result is formatted correctly.
Steps:
• The real and imaginary parts of the complex numbers are within the range [-100, 100].
• The input strings are well-formed as complex numbers.
Assumptions:
• The input complex numbers are valid and conform to the given format.
• Input: Input: num1 = "2+3i", num2 = "4+5i"
• Explanation: Multiplying (2 + 3i) by (4 + 5i) using the formula (a + bi) * (c + di) = (ac - bd) + (ad + bc)i results in -7 + 22i.
Approach: To solve the problem, we need to parse the input strings, apply the complex number multiplication formula, and then return the result in the correct format.
Observations:
• We need to parse the complex numbers into their real and imaginary components and then perform the multiplication.
• The formula for multiplying complex numbers is straightforward, and we need to format the result properly.
Steps:
• Extract the real and imaginary parts from both input complex numbers.
• Apply the multiplication formula to compute the real and imaginary parts of the product.
• Return the result as a string formatted as 'real+imaginaryi'.
Empty Inputs:
• The problem guarantees valid input, so no need to handle empty input cases.
Large Inputs:
• The solution needs to handle all valid inputs as specified within the constraints.
Special Values:
• Ensure that negative values in the real or imaginary parts are correctly handled in the result.
Constraints:
• The solution must handle all inputs within the range [-100, 100] for both real and imaginary parts.
string complexNumberMultiply(string num1, string num2) {
string r1, img1, r2, img2;
int i =0;
while(num1[i] !='+') {
r1 += num1[i];
i++;
}
img1 = num1.substr(i +1, num1.size() -1);
i =0;
while(num2[i] !='+') {
r2 += num2[i];
i++;
}
img2 = num2.substr(i +1, num2.size() -1);
int re1 = stoi(r1);
int re2 = stoi(r2);
int ig1 = stoi(img1);
int ig2 = stoi(img2);
i = re1 * re2 - ig1 * ig2;
int g = re1 * ig2 + re2 * ig1;
return to_string(i) +"+"+ to_string(g) +"i";
}
