春节刷题计划（三）| 一题双解，搞定求解方程

尝试用正则分割 ```kotlin // 根据“+”、“-”分割式子 private fun splitByOperator(list: String) = list.split(Regex("(?=[+-])")).filter { it.isNotEmpty() } ``` 或者 ```kotlin // 根据“+”、“-”分割式子 private fun splitByOperator(list: String): Sequence<String> = Regex("""[+-]?(\d*x|\d+)""").findAll(list).map { it.value } ```

```Kotlin fun fractionAddition(expression: String): String { // Split the expression to several pairs of numerator and denominator val numbers = expression .replace("-", "+-") .split("+") .filter { it.isNotEmpty() } .map { it.split("/").take(2).map(String::toInt) } // Calculate the lcm of all denominators val rawDenominator = numbers.map { it[1] }.fold(1) { x, y -> lcm(x, y) } // Calculate the sum of all numerators val rawNumerator = numbers.sumOf { it[0] * rawDenominator / it[1] } // Reformat numerator and denominator through their gcd val gcd = abs(gcd(rawNumerator, rawDenominator)) val denominator = rawDenominator / gcd val numerator = rawNumerator / gcd return "$numerator/$denominator" } fun gcd(x: Int, y: Int): Int = if (y == 0) x else gcd(y, x % y) fun lcm(x: Int, y: Int): Int = x * y / gcd(x, y) ```

fun solveEquation(equation: String): String { // x+5-3+2x=6+x-2 var xCount = 0 // 移到左边的 x 系数之和 var addValue = 0 // 移到右边的数字之和 val equalIndex = equation.indexOf('=') // 等号的位置 var i = 0 while (i < equation.length) { val fromIndex = i if (i == 0) { i++ } for (j in i until equation.length) { val c: Char = equation[j] if (c == '+' || c == '-' || c == '=') { break } i++ } var subString = equation.substring(if (fromIndex == 0) fromIndex else fromIndex - 1, i) subString = if (subString.startsWith("=")) subString.substring(1) else subString println("值为：$subString") if (subString.endsWith("x")) { subString = subString.substring(0, subString.length - 1) val tempCount = if (subString.isEmpty()) 1 // x else { if (subString.length == 1 && (subString.startsWith("+") || subString.startsWith("-"))) { // +x 或 -x if (subString[0] == '+') 1 else -1 } else subString.toInt() // +5x 或 5x 或 53x 或 -2x } xCount = if (i > equalIndex) xCount - tempCount else xCount + tempCount // 左正右负 } else if (subString.isNotEmpty()) { // 过滤掉 = 产生的一个空字符串 val tempValue = subString.toInt() addValue = if (i > equalIndex) addValue + tempValue else addValue - tempValue // 左负右正 } i++ } println("结果：${xCount}x = $addValue") return if (xCount == 0) if (addValue == 0) "Infinite solutions" else "No solution" else "x=" + addValue / xCount }

符号处理复杂了，其它与 @郑峰 略同 // 分数的数据结构 symbol为-1 1 // 注意分子/分母为正整数 data class Fraction(val numerator: Int, val denominator: Int, val symbol: Int) fun fractionAddition(expression: String): String { return expression.replace("-", "+-") // "-"前增加+，方便split处理 .split("+") // 按"+"分隔 .filter { it.isNotBlank() } // 去掉可能为空的部分 .map { // 处理成分数实例 var symbol = if (it.startsWith("-")) -1 else 1 val ss = it.replace("-", "").split("/") Fraction(ss[0].toInt(), ss[1].toInt(), symbol) }.run { // 算出分母的最小公倍数，作为分母 val denominator = map { it.denominator }.reduce { a, b -> lcm(a, b) } // 按最小公倍数计算分子结果 var numerator = map { it.symbol * it.numerator * denominator / it.denominator }.reduce { a, b -> a + b } val symbol = if (numerator < 0) -1 else 1 numerator *= symbol // 转正 val gcd = gcd(numerator, denominator) // 结果可能可约分 Fraction(numerator / gcd, denominator / gcd, symbol) }.run { "${if (symbol < 0) "-" else ""}${numerator}/${denominator}" } } // 最小公倍数 private fun lcm(m: Int, n: Int): Int { return m * n / gcd(m, n) } // 最大公约数 private fun gcd(m: Int, n: Int): Int { return if (m % n == 0) n else gcd(n, m % n) }

class Solution { fun solveEquation(equation: String): String = equation.split("=") .map(this::statistics) .calculate() private fun statistics(expr: String): Pair<Int, Int> = expr.replace("-", "+-") .split("+") .fold(Pair(0, 0)) { ans, s -> if (s.contains("x")) { ans.copy(first = ans.first + s.substring(0, s.length-1).toValue()) } else { ans.copy(second = ans.second + if (s.isEmpty()) { 0 } else {s.toValue()}) } } private fun String.toValue(): Int = when(this) { "" -> 1 "-" -> -1 else -> this.toInt() } private fun List<Pair<Int,Int>>.calculate(): String { val left = this[0] val right = this[1] return if (left.first == right.first) { if (left.second == right.second) "Infinite solutions" else "No solution" } else { val x = left.first - right.first val v = right.second - left.second "x=${v / x}" } } }