[Swift]LeetCode537. 复数乘法 | Complex Number Multiplication

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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:

1. The input strings will not have extra blank.
2. 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.

---

给定两个表示复数的字符串。

返回表示它们乘积的字符串。注意，根据定义 i2= -1 。

示例 1:

输入: "1+1i", "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: "1+-1i", "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。 

注意:

1. 输入字符串不包含额外的空格。
2. 输入字符串将以 a+bi 的形式给出，其中整数 a 和 b 的范围均在 [-100, 100] 之间。输出也应当符合这种形式。

---

Runtime: 8 ms

Memory Usage: 19.9 MB

class Solution {
    func complexNumberMultiply(_ a: String, _ b: String) -> String {
        var a = a
        var b = b
        //删除最后一个i
        a.remove(at:a.index(before:a.endIndex))
        b.remove(at:b.index(before:b.endIndex))
        //字符串转数组
        let arrA:[String] = a.components(separatedBy:"+")
        let arrB:[String] = b.components(separatedBy:"+")
        let c1:Complex = Complex(real: Int(arrA[0])!, img: Int(arrA[1])!)
        let c2:Complex = Complex(real: Int(arrB[0])!, img: Int(arrB[1])!)
        return (c1 * c2).toString
    }   
}

/*复数结构*/
struct Complex {
    //实部
    var real: Int   
    //虚部
    var img: Int  
    
    //将复数转换成字符串。
    var toString: String {
       return "(real)+(img)i"    
    }
    
    //重载乘法运算符
    //设z1=a+bi，z2=c+di(a、b、c、d∈R)是任意两个复数，那么它们的积(a+bi)(c+di)=(ac-bd)+(bc+ad)i
    static func *(_ x: Complex,_ y: Complex) -> Complex {
        return Complex(real: (x.real * y.real - x.img * y.img), img: (x.img * y.real + x.real * y.img))
    }
}

---

8ms

final class Solution {
    func complexNumberMultiply(_ a: String, _ b: String) -> String {
        let a = Array(a)
        let b = Array(b)
        let (realA, imagA) = splitComplex(a)
        let (realB, imagB) = splitComplex(b)
        let realC = realA &* realB &- imagA &* imagB
        let imagC = realA &* imagB &+ realB &* imagA
        return "(realC)+(imagC)i"
    }
    
    @inline(__always) private func splitComplex(_ a: [Character]) -> (Int, Int) {
        var i = 0
        var j = 0
        var realA = 0
        var imagA = 0
        while i < a.count {
            if a[i] == "+" {
                realA = Int(String(a[0..<i]))!
                j = i &+ 1
            } else if a[i] == "i" {
                imagA = Int(String(a[j..<i]))!
            }
            i &+= 1
        }
        return (realA, imagA)
    }
}

---

12ms

class Solution {
    func complexNumberMultiply(_ a: String, _ b: String) -> String {
        let firstParts = a.split(separator: "+")
        let secondParts = b.split(separator: "+")

        guard firstParts.count == 2 && secondParts.count == 2 else {
            return ""
        }

        //  for given a = a+bi, and b = c+di
        //  multiplication of a and b can be summurized into ac-bd+(ad+bc)i as i^2 will be -1 as pre-defined
        guard let a = Int(firstParts[0]), let b = Int(firstParts[1].replacingOccurrences(of: "i", with: "")), let c = Int(secondParts[0]), let d = Int(secondParts[1].replacingOccurrences(of: "i", with: "")) else {
            return ""
        }

        return "((a*c)-(b*d))+((a*d)+(b*c))i"
    }
}

---

16ms

class Solution {
    func complexNumberMultiply(_ a: String, _ b: String) -> String {
        let strArray1 = a.split(separator: "+")
        let strArray2 = b.split(separator: "+")
        var resultString = ""
        var constantTerm = 0
        var ithTerm = 0
        let product = -1
        
        for i in 0..<strArray1.count {
            for j in 0..<strArray2.count {
                if i == 0 && j == 0 {
                    guard let a = Int(strArray1[i]), let b = Int(strArray2[j]) else { return String() }
                    constantTerm = a*b
                } else if i == strArray1.count-1 && j == strArray2.count-1 {
                    let str1 = strArray1[i]
                    let str2 = strArray2[j]
                    let endIndex1 = str1.index(str1.startIndex, offsetBy: str1.count-1)
                    let endIndex2 = str2.index(str2.startIndex, offsetBy: str2.count-1)
                    guard let constantStr1 = Int(str1[str1.startIndex..<endIndex1]),
                    let constantStr2 = Int(str2[str2.startIndex..<endIndex2]) else { return String() }
                    let tempConstant = constantStr1 * constantStr2
                    constantTerm -= tempConstant
                } else {
                    let str1 = strArray1[i]
                    let str2 = strArray2[j]
                    var constant1 = 0
                    var constant2 = 0
                    
                    if let constantStr1 = Int(str1[str1.startIndex..<str1.endIndex]) {
                        constant1 = constantStr1
                    } else {
                        let endIndex1 = str1.index(str1.startIndex, offsetBy: str1.count-1)
                        guard let constantStr1 = Int(str1[str1.startIndex..<endIndex1]) else { return String() }
                        constant1 = constantStr1
                    }
                    
                    if let constantStr2 = Int(str2[str2.startIndex..<str2.endIndex]) {
                        constant2 = constantStr2
                    } else {
                        let endIndex1 = str2.index(str2.startIndex, offsetBy: str2.count-1)
                        guard let constantStr2 = Int(str2[str2.startIndex..<endIndex1]) else { return String() }
                        constant2 = constantStr2
                    }
                    let tempConstant = constant1*constant2
                    ithTerm += tempConstant
                }
            }
        }
        return String(constantTerm)+"+"+String(ithTerm)+"i"
    }
}

---

20ms

class Solution {
    func complexNumberMultiply(_ a: String, _ b: String) -> String {
        let avals = a.components(separatedBy: "+")
        let bvals = b.components(separatedBy: "+")
        
        let r = Int(avals[0])!
        let t = Int(avals[1].replacingOccurrences(of: "i", with: ""))!
        
        let s = Int(bvals[0])!
        let d = Int(bvals[1].replacingOccurrences(of: "i", with: ""))!
        
        let v1 = r * s - t * d
        let v2 = r * d + t * s
        
        return "(v1)+(v2)i"
    }
}