java实现中缀表达式转后缀的方法

本文先给出思路与方法，最后将给出完整代码：

算法综述：

一、中缀表达式转后缀表达式：

1.中缀表达式要转后缀表达式，首先需要两个Stack（栈），其中一个应用于存放字符，另一个用于存放数字。

2.读到数字直接存入数字栈中，读到字符时，要咸鱼栈内前一元素（字符）进行比较，当当前（要存入的字符）优先级大于迁移字符时才存入，否则（>=）要仿佛将栈内元素弹出，并依次存入数字栈中。

提示：‘（' 的优先级默认比所有字符都小。所有字符都可以存在它后面；同时夜笔所有字符都大，可以存在所有字符后面

3.遇到 ‘）'时将栈内所有字符依次弹出，并存入数字栈中，知道遇到 ‘（' 为止

4.当所有字符、数字访问完毕时，栈内很可能还会有剩余的字符，这是将他们一次弹出，并纯如数字栈中

小技巧：

1.存放‘+'，‘-'时，如果只有当前一个数位空或者‘（' 时才进行存入操作，否则均弹出。

2.存放 ‘*'，‘/' 时，只有当前一个数位 ‘*'，‘/' 时才弹出其他情况下，均存入。

附上代码：

 /*
 * 中缀转后缀
 */
 public void toPostfix() {
 // TODO Auto-generated method stub
 int sum = 0 ;//用于记入”（）“总个数
 int j = 0 ;//用于读到”）“时循环出栈
 String outStack = null;
 charnum.push(null);
 for( int i = 0 ; i < calculateLength ; i ++){
 if ( calculate[i].equals("(")) {
 charnum.push(calculate[i]);
 sum ++ ;
 }else if ( calculate[i].equals(")") ) {
 outStack = charnum.pop();//进入前先出一个
 while ( !outStack.equals("(") ){
 num.push(outStack);
 outStack = charnum.pop();
 }//最后一次outStack正好接到”（“不入栈
 sum ++ ;
 }else if (calculate[i].equals("*")) {
 outStack = charnum.pop();
 charnum.push(outStack);
 while( ( outStack == "*" || outStack == "/" ) && !(outStack == null) ){
 num.push(outStack);
 charnum.pop();//由于前第三行又将outStack存入栈中，座椅此处再次弹出
 outStack = charnum.pop();
 charnum.push(outStack);
 
 }
 charnum.push("*");
 }else if (calculate[i].equals("/")) {
 outStack = charnum.pop();
 charnum.push(outStack);
 while( ( outStack == "*" || outStack == "/" ) && !(outStack == null) ){
 num.push(outStack);
 charnum.pop();//由于前第三行又将outStack存入栈中，座椅此处再次弹出
 outStack = charnum.pop();
 charnum.push(outStack);
 }
 charnum.push("/");
 }else if (calculate[i].equals("+")) {
 outStack = charnum.pop();
 charnum.push(outStack);
 while( !(outStack=="(") && !(outStack == null) ){
 num.push(outStack);
 charnum.pop();
 outStack = charnum.pop();
 charnum.push(outStack);
 }
 charnum.push("+");
 }else if (calculate[i].equals("-")) {
 outStack = charnum.pop();
 charnum.push(outStack);
 while( !(outStack=="(") && !(outStack == null) ){
 num.push(outStack);
 charnum.pop();
 outStack = charnum.pop();
 charnum.push(outStack);
 }
 charnum.push("-");
 }else {
 num.push(calculate[i]);
 }
 }
 outStack = charnum.pop();
 while ( outStack != null ) {
 num.push(outStack);
 outStack = charnum.pop();
 }
 calculateLength = calculateLength - sum ;
 Stack<String> zanshi = new Stack<>();
 for(int i = 0 ; i < calculateLength ; i ++ ){
 zanshi.push(num.pop());
 }
 CalculateToZero();
 for(int i = 0 ; i < calculateLength ;i ++ ){
 calculate[i] = zanshi.pop();
 }
 }

二、后缀表达式计算

后缀表达式计算只遵循一个原则：

首先将表达式存在栈中

遇到符号时弹出两个相应的数字，进行计算后再次存入栈内

最后栈内身下的唯一一个数，就是所要求的结果

 /*
 * 后缀表达式求值
 */
 public String postfix() {
 int a = 0 , b = 0;//栈中弹出的两数
 int sum ;//求两数运算
 for (int i = 0; i < calculateLength ; i++ ) {
 if (i == 0) {
 num.push(calculate[i]);
 }else if (calculate[i].equals("+") ) {
 b = Integer.parseInt(num.pop());
 a = Integer.parseInt(num.pop());
 sum = a + b ;
 num.push(String.valueOf(sum));
 
 }else if (calculate[i].equals("-") ) {
 b = Integer.parseInt(num.pop());
 a = Integer.parseInt(num.pop());
 sum = a - b ;
 num.push(String.valueOf(sum));
 
 }else if (calculate[i].equals("*") ) {
 b = Integer.parseInt(num.pop());
 a = Integer.parseInt(num.pop());
 sum = a * b ;
 num.push(String.valueOf(sum));
 
 }else if (calculate[i].equals("/") ) {
 b = Integer.parseInt(num.pop());
 a = Integer.parseInt(num.pop());
 sum = a / b ;
 num.push(String.valueOf(sum));
 
 }else if (calculate[i].equals("%") ) {
 b = Integer.parseInt(num.pop());
 a = Integer.parseInt(num.pop());
 sum = a / b ;
 num.push(String.valueOf(sum));
 
 }else {
 num.push(calculate[i]);
 }
 }
 return num.pop();
 }
}

最后附上完整代码

//注：代码中有很多输出方便读者实时查看运算过程中各内容

// 这些输出导致篇幅较长大家看明白后删去即可

public class Text {
 
 Stack<String> num = new Stack<>(); //后缀用栈 中转后数字栈
 
 Stack<String> charnum = new Stack<>();//中转后字符栈
 
 String []calculate = new String[1000];//存字符串数组
 
 int calculateLength = 0 ;//字符串数组长度
 
 public Text() {
 // TODO Auto-generated constructor stub
 }
 
 //转字符串数组
 public void toStringArray(String input) {
 char charArray[] = input.toCharArray();
 int number = 0;//用于导入多位数
 int j = 0 ;//用于计入当前字符串数组的位数
 System.out.println(charArray.length);
 for(int i = 0 ; i < charArray.length ; i++){
 if(charArray[i] == '('){
 calculate[j++] = "(";
 
 }else if(charArray[i] == ')'){
 calculate[j++] = ")";
 
 }else if (charArray[i] == '+') {
 calculate[j++] = "+";
 
 }else if (charArray[i] == '-') {
 calculate[j++] = "-";
 
 }else if (charArray[i] == '*') {
 calculate[j++] = "*";
 
 }else if (charArray[i] == '/') {
 calculate[j++] = "/";
 
 }else if (charArray[i] == '%') {
 calculate[j++] = "%";
 
 }else if (charArray[i] == '#') {
 calculate[j++] = "#";
 
 }else {
 String str=String.valueOf(charArray[i]);
 number = number * 10 + Integer.parseInt(str);System.out.println("123");
 if( (i + 1) == charArray.length || charArray[i+1] < '0' || charArray[i+1] > '9'){
 
 if ( (i + 1) != charArray.length && charArray[i+1] == ' ') {
 System.out.println("456");i++;
 }
 calculate[j++] = String.valueOf(number);
 System.out.println(number);
 number = 0 ;
 }
 }
 
 System.out.println("---z->" + calculate[i]);
 }
 calculateLength = j-- ;//不--会将‘#'存入
 }
 
 public void outPutCalculate() {
 for(int i = 0 ; i < calculateLength ; i ++ ){
 System.out.println(calculate[i]);
 }
 }
 
 public void CalculateToZero() {
 for(int i = 0 ; i < calculateLength ; i ++ ){
 calculate[i]= calculate[999] ;
 }
 }
 
 //中缀转后缀
 public void toPostfix() {
 // TODO Auto-generated method stub
 System.out.println("789");
 int sum = 0 ;//用于记入”（）“总个数
 int j = 0 ;//用于读到”）“时循环出栈
 String outStack = null;
 charnum.push(null);
 System.out.println(calculateLength);
 for( int i = 0 ; i < calculateLength ; i ++){
 System.out.println(calculate[i]);//-----------------------------
 if ( calculate[i].equals("(")) {
 charnum.push(calculate[i]);
 System.out.println("1-1 charpush " + calculate[i]);//-----------------------------
 sum ++ ;
 }else if ( calculate[i].equals(")") ) {
 System.out.println("2-1 charpush " + calculate[i]);//-----------------------------
 outStack = charnum.pop();//进入前先出一个
 System.out.println("2-1 charpush " + outStack);//-----------------------------
 while ( !outStack.equals("(") ){
 System.out.println("2-2 charpush " + outStack);//-----------------------------
 num.push(outStack);
 outStack = charnum.pop();
 }//最后一次outStack正好接到”（“不入栈
 System.out.println("qiangxing 1 = " + outStack );
// outStack = charnum.pop();
 System.out.println("qiangxing 2 = " + outStack );
 sum ++ ;
 }else if (calculate[i].equals("*")) {
 outStack = charnum.pop();
 charnum.push(outStack);
 System.out.println("3-2 charpush " + outStack);//-----------------------------
 while( ( outStack == "*" || outStack == "/" ) && !(outStack == null) ){
 System.out.println("3-1 charpush " + outStack);//-----------------------------
 num.push(outStack);
 charnum.pop();//由于前第三行又将outStack存入栈中，座椅此处再次弹出
 outStack = charnum.pop();
 charnum.push(outStack);
 
 }
 System.out.println("3-3 charpush " + outStack);//-----------------------------
 charnum.push("*");
 }else if (calculate[i].equals("/")) {
 System.out.println("5-1-0 charpush " + "1-1-1-1-1-1-1-1");//-----------------------------
 outStack = charnum.pop();
 System.out.println("5-1-1 charpush " + "2-2-2-2-2-2-22-2");//-----------------------------
 charnum.push(outStack);
 System.out.println("4-1 charpush " + outStack);//-----------------------------
 while( ( outStack == "*" || outStack == "/" ) && !(outStack == null) ){
 System.out.println("4-2 charpush " + outStack);//-----------------------------
 num.push(outStack);
 charnum.pop();//由于前第三行又将outStack存入栈中，座椅此处再次弹出
 outStack = charnum.pop();
 charnum.push(outStack);
 }
 System.out.println("4-3 charpush " + outStack);//-----------------------------
 System.out.println("5-1-2 charpush " + outStack);//-----------------------------
 charnum.push("/");
 }else if (calculate[i].equals("+")) {
 outStack = charnum.pop();
 charnum.push(outStack);
 System.out.println("5-1 charpush " + outStack);//-----------------------------
 while( !(outStack=="(") && !(outStack == null) ){
 System.out.println("5-2 charpush " + outStack);//-----------------------------
 num.push(outStack);
 charnum.pop();
 outStack = charnum.pop();
 charnum.push(outStack);
 }
 System.out.println("5-3 charpush " + outStack);//-----------------------------
 charnum.push("+");
 }else if (calculate[i].equals("-")) {
 outStack = charnum.pop();
 charnum.push(outStack);
 System.out.println("6-1 charpush " + outStack);//-----------------------------
 while( !(outStack=="(") && !(outStack == null) ){
 System.out.println("6-2 charpush " + outStack);//-----------------------------
 num.push(outStack);
 charnum.pop();
 outStack = charnum.pop();
 charnum.push(outStack);
 }
 System.out.println("6-3 charpush " + outStack);//-----------------------------
 charnum.push("-");
 }else {
 System.out.println("7-7 " + calculate[i]);
 num.push(calculate[i]);
 }
 }
 System.out.println("匹配结束" + outStack);
 outStack = charnum.pop();
 System.out.println("finish 1 == " + outStack);
 while ( outStack != null ) {
 num.push(outStack);
 outStack = charnum.pop();
 System.out.println("finish 2 == " + outStack);
 }
 calculateLength = calculateLength - sum ;
 System.out.println( "0.0.0.0 charpush " );//-----------------------------
 System.out.println("sum = " + sum + " calculate = " + 
 calculateLength + "calculateLength-sum = " + (calculateLength-sum));
 System.out.println("over ~~~~~0 ");
 Stack<String> zanshi = new Stack<>();
// num.pop();
 for(int i = 0 ; i < calculateLength ; i ++ ){
 zanshi.push(num.pop());
// System.out.println(num.pop());
 }
 CalculateToZero();
 System.out.println("over ~~~~~1 ");
 for(int i = 0 ; i < calculateLength ;i ++ ){
 calculate[i] = zanshi.pop();
 }
 System.out.println("over ~~~~~2 ");
 for(int i = 0 ; i < calculateLength ;i ++ ){
 System.out.println(calculate[i]);
 }
 System.out.println("over ~~~~~3 ");
// num.push("#");
 }
 
 //后缀计算
 public String postfix() {
 int a = 0 , b = 0;//栈中弹出的两数
 int sum ;//求两数运算
 for (int i = 0; i < calculateLength ; i++ ) {
// System.out.println("目前符号：" + calculate[i]);
 if (i == 0) {
 num.push(calculate[i]);
 }else if (calculate[i].equals("+") ) {
 b = Integer.parseInt(num.pop());
 a = Integer.parseInt(num.pop());
 sum = a + b ;
 num.push(String.valueOf(sum));
 
 }else if (calculate[i].equals("-") ) {
 b = Integer.parseInt(num.pop());
 a = Integer.parseInt(num.pop());
 sum = a - b ;
 num.push(String.valueOf(sum));
 
 }else if (calculate[i].equals("*") ) {
 b = Integer.parseInt(num.pop());
 a = Integer.parseInt(num.pop());
 sum = a * b ;
 num.push(String.valueOf(sum));
 
 }else if (calculate[i].equals("/") ) {
 b = Integer.parseInt(num.pop());
 a = Integer.parseInt(num.pop());
 sum = a / b ;
 num.push(String.valueOf(sum));
 
 }else if (calculate[i].equals("%") ) {
 b = Integer.parseInt(num.pop());
 a = Integer.parseInt(num.pop());
 sum = a / b ;
 num.push(String.valueOf(sum));
 
 }else {
 num.push(calculate[i]);
 }
 }
 return num.pop();
 }
}

结果如下：

一、前缀转后缀并输出

其中over前为转化后的后缀表达式

over后为计算结果

public class Main {
 public static void main(String[] args) {
 Text text = new Text();
 text.toStringArray("1+2*(3-1+2)-3");
 text.outPutCalculate();
 text.toPostfix();
 System.out.println(text.postfix());
 }
}

二、后缀直接输出

注意后缀表达式时

为了实现多位数运算，连续输入一串数时，输入完一个数加空格

如：要计算："1+2*(3-1+2)-3" 则输入："1 2 3 1-2+*+3-"

例：

public class Main {
 public static void main(String[] args) {
 Text text = new Text();
 text.toStringArray("1 2 3 1-2+*+3-");
 text.outPutCalculate();
 System.out.println(text.postfix());
 }
}

输出结果：

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