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());
}
}
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：
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