Problem
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.
Solution 1
/**
* @param {string} a
* @param {string} b
* @return {string}
*/
var complexNumberMultiply = function(a, b) {
var a = parse(a);
var b = parse(b);
var x = (a.x * b.x) - (a.y * b.y);
var y = (a.x * b.y) + (a.y * b.x);
return stringify(x, y);
};
var parse = function (str) {
var res = /^(-?\d+)\+(-?\d+)i$/.exec(str);
return { x: Number(res[1]), y: Number(res[2]) };
};
var stringify = function (x, y) {
return `${x}+${y}i`
};
Explain:
nope.
Complexity:
- Time complexity :
- Space complexity :
Solution 2
/**
* @param {string} a
* @param {string} b
* @return {string}
*/
var complexNumberMultiply = function(a, b) {
var a = parse(a);
var b = parse(b);
var x = (a.x * b.x) - (a.y * b.y);
var y = (a.x * b.y) + (a.y * b.x);
return stringify(x, y);
};
var parse = function (str) {
var index = str.indexOf('+');
var x = Number(str.substring(0, index));
var y = Number(str.substring(index + 1, str.length - 1));
return { x: x, y: y };
};
var stringify = function (x, y) {
return `${x}+${y}i`
}
Explain:
nope.
Complexity:
- Time complexity :
- Space complexity :