The Complex Number Multiplication Function

  • 时间:2020-09-18 17:26:09
  • 分类:网络文摘
  • 阅读:130 次

Given two strings representing two complex numbers. You need to return a string representing their multiplication. Note i2 = -1 according to the definition.

Example 1:
Input: “1+1i”, “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: “1+-1i”, “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.

Note:
The input strings will not have extra blank.
The input strings will be given in the form of a+bi, where the integer a and b will both belong to the range of [-100, 100]. And the output should be also in this form.

The Javascript Function to Compute the Complex Number Multiplication

In Javascript, we can use the split function, which allows us to separate the complex number string into two parts: the real and the imaginary. We can use the slice(0, -1) to remove the last character ‘i’ from the imaginary. Then, we just need to compute the real and imaginary of the result complex number respectively using simple math multiplication law.

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
/**
 * @param {string} a
 * @param {string} b
 * @return {string}
 */
var complexNumberMultiply = function(a, b) {
    const process = (x) => {
        x = x.split('+');
        const a = x[0];
        const b = x[1].slice(0, -1);
        return [a, b];
    }
    const aa = process(a);
    const bb = process(b);
    const xx = aa[0] * bb[0] - aa[1] * bb[1];
    const yy = aa[0] * bb[1] + aa[1] * bb[0];
    return `${xx}+${yy}i`;
};
/**
 * @param {string} a
 * @param {string} b
 * @return {string}
 */
var complexNumberMultiply = function(a, b) {
    const process = (x) => {
        x = x.split('+');
        const a = x[0];
        const b = x[1].slice(0, -1);
        return [a, b];
    }
    const aa = process(a);
    const bb = process(b);
    const xx = aa[0] * bb[0] - aa[1] * bb[1];
    const yy = aa[0] * bb[1] + aa[1] * bb[0];
    return `${xx}+${yy}i`;
};

The time and space complexity is both O(1) constant – assuming spliting a complex number string is trivial.

The Complex Number Multiplication in C++

In C++, we can use the sscanf function to extract values from the string by analyzing the string using format/templates. Then the rest are similar.

1
2
3
4
5
6
7
8
9
10
11
class Solution {
public:
    string complexNumberMultiply(string a, string b) {
        int a1, a2, b1, b2;
        sscanf(a.c_str(), "%d+%di", &a1, &a2);
        sscanf(b.c_str(), "%d+%di", &b1, &b2);
        int xx = a1 * b1 - a2 * b2;
        int yy = a1 * b2 + a2 * b1;
        return std::to_string(xx) + "+" + std::to_string(yy) + "i";
    }
};
class Solution {
public:
    string complexNumberMultiply(string a, string b) {
        int a1, a2, b1, b2;
        sscanf(a.c_str(), "%d+%di", &a1, &a2);
        sscanf(b.c_str(), "%d+%di", &b1, &b2);
        int xx = a1 * b1 - a2 * b2;
        int yy = a1 * b2 + a2 * b1;
        return std::to_string(xx) + "+" + std::to_string(yy) + "i";
    }
};

–EOF (The Ultimate Computing & Technology Blog) —

推荐阅读:
三类食品是引发癌症(恶性肿瘤)的因素  枸杞虽好但两种人吃了反而对健康有害  4个与大豆营养价值有关的真假说法  早餐第一口吃什么样的食物最养胃  萝卜颜色各异 营养价值各不相同  冬季养生美味 各种萝卜汤养胃又暖身  电脑族抗辐射可以经常吃这种水果  生活中常见的保护肠道健康的食物  注意三个饮食原则让你远离癌症威胁  羊奶粉调查:10款羊奶粉中有7款掺牛乳 
评论列表
添加评论