How do you solve Complex Number Multiplication on LeetCode?

Complex Number Multiplication (LeetCode #537) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Understanding complex number multiplication is crucial.

What is the brute force solution for Complex Number Multiplication?

The brute force approach for Complex Number Multiplication is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves parsing the complex numbers, extracting their real and imaginary parts, and then applying the formula for multiplying complex numbers. This method is straightforward but can be inefficient due to the need for string manipulation. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Complex Number Multiplication?

Complex Number Multiplication uses the following concepts: Math, String, Simulation. The recommended patterns to study are: String Manipulation, Mathematical Operations.

What are the interview tips for Complex Number Multiplication?

Clarify the input format before starting. Explain your thought process as you code. Test your solution with edge cases.

What are common mistakes when solving Complex Number Multiplication?

Not correctly parsing the input strings. Forgetting to handle the 'i' character properly.

#537

Complex Number Multiplication

Medium

MathStringSimulationString ManipulationMathematical Operations

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

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Intuition

Time O(n)Space O(1)

The optimal solution builds on the brute force approach but focuses on minimizing unnecessary operations. By directly parsing and calculating the result in one go, we reduce the overhead of string manipulation.

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Algorithm

4 steps

1Step 1: Split the input strings to get the real and imaginary parts.
2Step 2: Convert the parts to integers for calculations.
3Step 3: Use the multiplication formula for complex numbers to compute the real and imaginary parts.
4Step 4: Format the result into the required string format.

solution.py4 lines

1def complexNumberMultiply(num1: str, num2: str) -> str:
2    a, b = map(int, num1[:-1].split('+'))
3    c, d = map(int, num2[:-1].split('+'))
4    return f'{a * c - b * d}+{a * d + b * c}i'

ℹ

Complexity note: The time complexity is O(n) as we are only parsing the strings once and performing a constant number of operations. The space complexity is O(1) since we are using a fixed amount of space for calculations.

1Understanding complex number multiplication is crucial.
2String manipulation can be minimized for efficiency.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.