How do I multiply complex numbers in string format?

To multiply complex numbers in string format, first extract the real and imaginary parts, perform the multiplication using the formula, and then reformat the result into a string.

What is the expected time complexity of this problem?

The time complexity is O(n), where n is the length of the input strings. This accounts for parsing and string manipulation.

What if the input has a negative imaginary part?

Ensure that the negative sign is correctly handled when splitting and formatting the result, particularly when the imaginary part is negative.

How do I handle edge cases like zero real or imaginary parts?

Handle these cases by ensuring that the real or imaginary part is still included in the final output, even if it is zero, such as '0+2i' or '3+0i'.

What pattern does this problem involve?

This problem involves the 'Math plus String' pattern, where you need to combine string manipulation with basic mathematical operations to achieve the correct result.

#537

Medium

auto_awesome数学·string

LeetCode 题解工作台

复数乘法

复数可以用字符串表示，遵循 " 实部 + 虚部 i" 的形式，并满足下述条件：实部是一个整数，取值范围是 [-100, 100] 虚部也是一个整数，取值范围是 [-100, 100] i 2 == -1 给你两个字符串表示的复数 num1 和 num2 ，请你遵循复数表示形式，返回表示它们乘…

数学字符串模拟

题目描述

复数可以用字符串表示，遵循 "实部+虚部i" 的形式，并满足下述条件：

实部 是一个整数，取值范围是 [-100, 100]
虚部 也是一个整数，取值范围是 [-100, 100]
i² == -1

给你两个字符串表示的复数 num1 和 num2 ，请你遵循复数表示形式，返回表示它们乘积的字符串。

示例 1：

输入：num1 = "1+1i", num2 = "1+1i"
输出："0+2i"
解释：(1 + i) * (1 + i) = 1 + i2 + 2 * i = 2i ，你需要将它转换为 0+2i 的形式。

示例 2：

输入：num1 = "1+-1i", num2 = "1+-1i"
输出："0+-2i"
解释：(1 - i) * (1 - i) = 1 + i2 - 2 * i = -2i ，你需要将它转换为 0+-2i 的形式。

提示：

num1 和 num2 都是有效的复数表示。

lightbulb

解题思路

方法一：模拟

我们可以将复数字符串转换成对应的实部 $a$ 和虚部 $b$ ，然后根据复数乘法的公式 $(a_1 + b_1i) \times (a_2 + b_2i) = (a_1a_2 - b_1b_2) + (a_1b_2 + a_2b_1)i$ 计算出结果。

时间复杂度 $O(1)$ ，空间复杂度 $O(1)$ 。

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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"

speed

复杂度分析

指标	值
时间	Depends on the final approach
空间	Depends on the final approach

psychology

面试官常问的追问

外企场景

question_mark
Evaluates the candidate's ability to handle string manipulation effectively.
question_mark
Tests understanding of complex number arithmetic and correct use of the multiplication formula.
question_mark
Examines the candidate's ability to reformat a result based on specific requirements.

warning

常见陷阱

外企场景

error
Forgetting to correctly parse the input strings, especially when the signs are negative.
error
Incorrectly formatting the result when the imaginary part is negative, leading to a malformed output.
error
Misunderstanding the complex number multiplication formula, especially when handling the imaginary component.

swap_horiz

进阶变体

外企场景

arrow_right_alt
Implementing the solution with a different method of extracting the real and imaginary parts, such as using regular expressions.
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Handling edge cases where the real or imaginary parts are zero.
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Optimizing the solution for different input formats or handling inputs with larger sizes.

help

常见问题

外企场景

继续练习

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