利用栈实现算术表达式求值(Java语言描述)

  

算术表达式求值是栈的典型应用，自己写栈，实现Java栈算术表达式求值，涉及栈，编译原理方面的知识。声明：部分代码参考自茫茫大海的专栏。

链栈的实现：

package 算数表达式求值;public class Stack<T> {//节点类public class Node{public T data;public Node next;public Node(){}public Node(T data,Node next){this.data = data;this.next = next;}}//Nodepublic Node top = new Node();public int size;public Node oldNode;//入栈public void push(T element){top = new Node(element,top);size++;}//出栈public T pop(){oldNode = top;top = top.next;//oldNode = null;size--;    return oldNode.data;}//返回栈顶对象的数据域，但不出栈public T peek(){return top.data;}//栈长public int length(){return size;}//判断栈是否为空public boolean isEmpty(){return size == 0;}}

 表达式求值的实现：

package 算数表达式求值;import java.util.Scanner;//import java.util.Stack;public class Expression {//运算符之间的优先级,其顺序是+、-、*、/、（、），其中大于号表示优先级高//，小于号表示优先级低，等号表示优先级相同，感叹号表示没有优先关系public static final char[][] relation = {{'>','>','<','<','<','>','>'},{'>','>','<','<','<','>','>'},{'>','>','>','>','<','>','>'},{'>','>','>','>','<','>','>'},{'<','<','<','<','<','=','!'},{'>','>','>','>','!','>','>'},{'<','<','<','<','<','!','='}};public static void main(String[] args) {Scanner input = new Scanner(System.in);while(true){try{System.out.println("请输入要计算的表达式：");String exp = input.next();System.out.println(calc(exp + "#"));}catch(ArithmeticException e1){System.out.println("表达式中的分母不能为0");e1.printStackTrace();}}}/** *  * @param exp 要计算的表达式 * @return 计算的结果 */private static int calc(String exp) {//操作数栈Stack<Integer> num = new Stack<Integer>();//操作符栈Stack<Character> op = new Stack<Character>();op.push('#');int i = 0;char ch = exp.charAt(i);boolean flag = false;//判断连续的几个字符是否是数字，若是，就处理成一个数字。这样就能处理多位数的运算了。while(ch != '#' || op.peek() != '#') {//peek()查看栈顶对象但不移除。if(ch >= '0' && ch <= '9') {if(flag) {int tmp = num.pop();num.push(tmp * 10 + Integer.parseInt(ch + ""));} else {num.push(Integer.parseInt(ch + ""));}flag = true;i++;} else {flag = false;switch(precede(op.peek(), ch)) {case '<':op.push(ch);i++;break;case '=':op.pop();i++;break;case '>':int num2 = num.pop();int num1 = num.pop();int result = operate(num1, op.pop(), num2);num.push(result);break;case '!':System.out.println("输入的表达式错误！");return -1;}}ch = exp.charAt(i);}return num.peek();}private static char precede(char peek, char ch) {return relation[getIndex(peek)][getIndex(ch)];}/** *  * @param ch 操作符 * @return 操作符的索引，按照+、-、*、/、（、）的顺序 */private static int getIndex(char ch) {int index = -1;switch(ch) {case '+':index = 0;break;case '-':index = 1;break;case '*':index = 2;break;case '/':index = 3;break;case '(':index = 4;break;case ')':index = 5;break;case '#':index = 6;break;}return index;}/** *  * @param num1  第一个运算数 * @param ch 运算符 * @param num2 第二个运算数 * @return 运算结果 */private static int operate(int num1, char ch, int num2) {int result = 0;switch(ch) {case '+':result = num1 + num2;break;case '-':result = num1 - num2;break;case '*':result = num1 * num2;break;case '/':result = num1 / num2;break;}return result;}}

异常处理有待完善，引用请指明出处。