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:
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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 ; Stackzanshi = 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 { Stacknum = new Stack<>(); //后缀用栈 中转后数字栈 Stack 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 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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文章标题:java实现中缀表达式转后缀的方法
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