Java如何实现中缀表达式转后缀表达式

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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 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 Calculate {
 private Stack num; //后缀用栈 中转后数字栈
 private Stack charnum;//中转后字符栈
 private String []calculate;//存字符串数组
 private int calculateLength;//字符串数组长度
 public Calculate() {
  // TODO Auto-generated constructor stub
  num = new Stack<>(); //后缀用栈 中转后数字栈
  charnum = new Stack<>();//中转后字符栈
  calculate = new String[1000];//存字符串数组
  calculateLength = 0 ;//字符串数组长度
 }
 //转字符串数组
 public void toStringArray(String input) {
  boolean pointFalg = false;
  char charArray[] = input.toCharArray();
  double 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
  int sizeOfArray = charArray.length;
  int pointBelow =1
    ;
  for(int i = 0 ; i < sizeOfArray ; 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 if (charArray[i] == '.') {
    System.out.println("find new . :");
    pointBelow = 1;
//        sizeOfArray -- ;
    pointFalg = true;
   }else {
    String str=String.valueOf(charArray[i]);
    if (pointFalg == false) {
     System.out.println("1:" + number);
     number = number * 10 + Double.parseDouble(str);
    }else {
     System.out.println("2:" + charArray[i]);
     number = number + Double.parseDouble(str) * Math.pow(0.1, pointBelow);
    }
    System.out.println("3:" + number + "i==" + i);
    if( (i + 1) == sizeOfArray ||( charArray[i+1] < '0' || charArray[i+1] > '9' ) && charArray[i+1] != '.'){
     if ( (i + 1) != sizeOfArray && charArray[i+1] == ' ') {
      i++;
     }
     calculate[j++] = String.valueOf(number);
     System.out.println("number:" + number);
     number = 0 ;
     pointFalg = false;
    }
   }
   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 == "%" ) && !(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("%")) {
    outStack = charnum.pop();
    charnum.push(outStack);
    System.out.println("3-2 charpush " + outStack);//-----------------------------
    while( ( outStack == "*" || 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 == "%") && !(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 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() {
  BigDecimal a , b ;//栈中弹出的两数
  BigDecimal 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 = new BigDecimal(num.pop());
    a = new BigDecimal(num.pop());
    sum = a.add(b) ;
    num.push(String.valueOf(sum));
   }else if (calculate[i].equals("-") ) {
    b = new BigDecimal(num.pop());
    a = new BigDecimal(num.pop());
    sum = a.subtract(b) ;
    num.push(String.valueOf(sum));
   }else if (calculate[i].equals("*") ) {
    b = new BigDecimal(num.pop());
    a = new BigDecimal(num.pop());
    sum = a.multiply(b) ;
    num.push(String.valueOf(sum));
   }else if (calculate[i].equals("/") ) {
    b = new BigDecimal(num.pop());
    a = new BigDecimal(num.pop());
    sum = a.divide(b,10,RoundingMode.HALF_UP) ;
    num.push(String.valueOf(sum));
   }else if (calculate[i].equals("%") ) {
    b = new BigDecimal(num.pop());
    a = new BigDecimal(num.pop());
    sum = a.divideAndRemainder(b)[1] ;
    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) {
    Calculate text = new Calculate();
    text.toStringArray("1+2*(3-1+2)-3");
    text.outPutCalculate();
    text.toPostfix();
    System.out.println(text.postfix());
  }
}

Java如何实现中缀表达式转后缀表达式

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) {
    Calculate text = new Calculate();
    text.toStringArray("1 2 3 1-2+*+3-");
    text.outPutCalculate();
    System.out.println(text.postfix());
  }
}

输出结果：

Java如何实现中缀表达式转后缀表达式

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Java如何实现中缀表达式转后缀表达式

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