swift - 在swift中生成一个简单的代数表达式

Question

我正在寻求创建一个函数来返回 x 数学方程式的解，该方程式可以在头脑中执行(显然这有点主观，但我不确定如何表达它)。

示例问题:(x - 15)/10 = 6

注意:方程中只有1个x

我想使用操作 +、-、*、/、sqrt(仅适用于 X -> sqrt(x))

我知道 let mathExpression = NSExpression(format: question) 将字符串转换为数学方程式，但是在求解 x 时我不确定如何去做。

我之前问过Generating random doable math problems swift对于无法解决 x 问题，但我不确定如何将该答案转换为解决 x 问题

编辑:目标是生成方程式并让用户求解变量。

Answer 1

由于您只需要一个表示方程式的字符串和 x 的值，因此您无需进行任何求解。只需从 x 开始并对其进行变换，直到您得到一个很好的方程式。这是一个示例:(将其复制并粘贴到 Playground 中进行试用)

import UIKit

enum Operation: String {
    case addition = "+"
    case subtraction = "-"
    case multiplication = "*"
    case division = "/"


    static func all() -> [Operation] {
        return [.addition, .subtraction, .multiplication, .division]
    }

    static func random() -> Operation {
        let all = Operation.all()
        let selection = Int(arc4random_uniform(UInt32(all.count)))
        return all[selection]
    }

}


func addNewTerm(formula: String, result: Int) -> (formula: String, result: Int) {
    // choose a random number and operation
    let operation = Operation.random()
    let number = chooseRandomNumberFor(operation: operation, on: result)
    // apply to the left side
    let newFormula = applyTermTo(formula: formula, number: number, operation: operation)
    // apply to the right side
    let newResult = applyTermTo(result: result, number: number, operation: operation)
    return (newFormula, newResult)
}

func applyTermTo(formula: String, number:Int, operation:Operation) -> String {
    return "\(formula) \(operation.rawValue) \(number)"
}

func applyTermTo(result: Int, number:Int, operation:Operation) -> Int {
    switch(operation) {
    case .addition: return result + number
    case .subtraction: return result - number
    case .multiplication: return result * number
    case .division: return result / number
    }
}

func chooseRandomNumberFor(operation: Operation, on number: Int) -> Int {
    switch(operation) {
    case .addition, .subtraction, .multiplication:
        return Int(arc4random_uniform(10) + 1)
    case .division:
        // add code here to find integer factors
        return 1
    }
}


func generateFormula(_ numTerms:Int = 1) -> (String, Int) {
    let x = Int(arc4random_uniform(10))
    var leftSide = "x"
    var result = x

    for i in 1...numTerms {
        (leftSide, result) = addNewTerm(formula: leftSide, result: result)
        if i < numTerms {
            leftSide = "(" + leftSide + ")"
        }
    }

    let formula = "\(leftSide) = \(result)"

    return (formula, x)
}

func printFormula(_ numTerms:Int = 1) {
    let (formula, x) = generateFormula(numTerms)
    print(formula, "                      x = ", x)
}


for i in 1...30 {
    printFormula(Int(arc4random_uniform(3)) + 1)
}

有些东西不见了。 sqrt() 函数必须单独实现。为了使除法有用，您必须添加一个系统来查找因子(因为您可能希望结果是整数)。根据您想要的输出类型，还有很多工作要做，但这应该可以帮助您入门。

这是示例输出:

(x + 10) - 5 = 11                       x =  6
((x + 6) + 6) - 1 = 20                       x =  9
x - 2 = 5                       x =  7
((x + 3) * 5) - 6 = 39                       x =  6
(x / 1) + 6 = 11                       x =  5
(x * 6) * 3 = 54                       x =  3
x * 9 = 54                       x =  6
((x / 1) - 6) + 8 = 11                       x =  9