/*** Created by feichen on 2018/6/11.* <p>* <p>* 给定一个表示分数加减运算表达式的字符串，你需要返回一个字符串形式的计算结果。 这个结果应该是不可约分的分数，即最简分数。* 如果最终结果是一个整数，例如 2，你需要将它转换成分数形式，其分母为 1。所以在上述例子中, 2 应该被转换为 2/1。* <p>* 示例 1:* <p>* 输入:"-1/2+1/2"* 输出: "0/1"* 示例 2:* <p>* 输入:"-1/2+1/2+1/3"* 输出: "1/3"* 示例 3:* <p>* 输入:"1/3-1/2"* 输出: "-1/6"* 示例 4:* <p>* 输入:"5/3+1/3"* 输出: "2/1"* 说明:* <p>* 输入和输出字符串只包含 '0' 到 '9' 的数字，以及 '/', '+' 和 '-'。* 输入和输出分数格式均为 ±分子/分母。如果输入的第一个分数或者输出的分数是正数，则 '+' 会被省略掉。* 输入只包含合法的最简分数，每个分数的分子与分母的范围是  [1,10]。 如果分母是1，意味着这个分数实际上是一个整数。* 输入的分数个数范围是 [1,10]。* 最终结果的分子与分母保证是 32 位整数范围内的有效整数。*/
public class FractionAddition {static class Fraction {//符号TAG tag = TAG.POSITIVE;//分子int numerator;//分母int denominator;@Overridepublic String toString() {return (tag == TAG.NEGATIVE ? "-" : "") + numerator + "/" + denominator;}}enum TAG {NEGATIVE,POSITIVE}public String fractionAddition(String expression) {List<Fraction> fractions = convert(expression);if (!fractions.isEmpty()) {fractions = calculate(fractions);}return !fractions.isEmpty() ? reduceFraction(fractions.get(0)).toString() : "";}/*** 计算** @param fractions* @return*/public static List<Fraction> calculate(List<Fraction> fractions) {if (fractions.isEmpty() || fractions.size() == 1) {return fractions;}Fraction last = fractions.get(fractions.size() - 1);Fraction last2 = fractions.get(fractions.size() - 2);int denominatorLcm = lcm(last.denominator, last2.denominator);int lastNumerator = last.numerator * (denominatorLcm / last.denominator);int last2Numerator = last2.numerator * (denominatorLcm / last2.denominator);if (last.tag == TAG.NEGATIVE) {lastNumerator = -lastNumerator;}if (last2.tag == TAG.NEGATIVE) {last2Numerator = -last2Numerator;}int numeratorResult = lastNumerator + last2Numerator;Fraction newFraction = new Fraction();newFraction.numerator = Math.abs(numeratorResult);newFraction.denominator = denominatorLcm;newFraction.tag = numeratorResult < 0 ? TAG.NEGATIVE : TAG.POSITIVE;fractions.remove(fractions.size() - 1);fractions.remove(fractions.size() - 1);fractions.add(newFraction);return calculate(fractions);}/*** 约分** @param fraction* @return*/public static Fraction reduceFraction(Fraction fraction) {if (fraction.numerator == 0) {fraction.denominator = 1;return fraction;}int gcd = gcd(fraction.numerator, fraction.denominator);if (gcd != 1) {fraction.numerator = fraction.numerator / gcd;fraction.denominator = fraction.denominator / gcd;}return fraction;}/*** 最大公约数** @param a* @param b* @return*///a b 为正整数public static int gcd(int a, int b) {if (a == b) {return a;}if (a < b) {return gcd(b, a);} else {if (((a & 1) == 0) && ((b & 1) == 0)) { //ab都为偶数return gcd(a >> 1, b >> 1) << 1;} else if (((a & 1) == 0) && ((b & 1) == 1)) { //a为偶数,b为奇数return gcd(a >> 1, b);} else if (((a & 1) == 1) && ((b & 1) == 0)) { //a为奇数,b为偶数return gcd(a, b >> 1);} else { //ab都为奇数return gcd(b, a - b);}}}/*** 最小公倍数** @param a* @param b* @return*/public static int lcm(int a, int b) {return a * b / gcd(a, b);}/*** 转换** @param expression* @return*/public static List<Fraction> convert(String expression) {List<Fraction> fractions = new ArrayList<>();char[] chars = expression.toCharArray();for (int i = 0; i < chars.length; i++) {if (chars[i] == '/') {Fraction fraction = new Fraction();List<Character> numeratorCharList = new ArrayList<>();//分子处理for (int j = i - 1; j >= 0; j--) {if (Character.isDigit(chars[j])) {numeratorCharList.add(0, chars[j]);} else {if (chars[j] == '-') {fraction.tag = TAG.NEGATIVE;}break;}}List<Character> denominatorCharList = new ArrayList<>();for (int j = i + 1; j < chars.length; j++) {if (Character.isDigit(chars[j])) {denominatorCharList.add(chars[j]);} else {break;}}String numeratorStr =numeratorCharList.stream().map(e -> e.toString()).reduce((acc, e) -> acc + e).get();String denominatorStr =denominatorCharList.stream().map(e -> e.toString()).reduce((acc, e) -> acc + e).get();fraction.numerator = Integer.valueOf(numeratorStr);fraction.denominator = Integer.valueOf(denominatorStr);fractions.add(fraction);}}return fractions;}public static void main(String[] args) {FractionAddition fractionAddition = new FractionAddition();System.out.println(fractionAddition.fractionAddition("-5/2+10/3+7/9"));}}