1：主方法

package com.baidu;

import java.text.NumberFormat;
import java.util.ArrayList;
import java.util.Stack;

public class CalculateStack {
static private CalculateStack cl = new CalculateStack();
//申明一个存放数字元素的栈
private Stack<String> num = new Stack<>();
//声明一个存放操作符的栈
private Stack<Character> opStack = new Stack<>();
//申明一个优先权规则关系表
private RuleTable ruleTable = new RuleTable();

//运算简单表达式
//测试通过
//可添加运算规则
private double getCalculateNumber(double num1,Character op,double num2) {

double res = 0;
switch(op.charValue()) {

case '+':{
res = num1 + num2;
}break;

case '-':{
res = num1 - num2;
}break;
case 'x':{

res = num1 * num2;
}break;
case '/':{

res = num1 / num2;
}break;

}
return res;
}

//得到指定的俩个操作符的优先关系
/**
* @return 当返回@时为无效字符输入
* */
private char serchOp(char ch, char top) {

//System.out.println("ch:"+ch+" top:"+top);
for(Rule rule:this.ruleTable.getRuleList()) {
if(top == rule.ch1&&rule.ch2 == ch) {
//System.out.println("从表中找到：关系为top" + rule.equ +"ch");
return rule.equ;
}
}
return '@';
}
/**
* @author shilec
* 主运算算法
* @param ch1 ：保存运算表达式的字符串数组
* @return Accuracy 得到运算的结果保留小数后的位数
* */
public String Calculate(String strSource,int Accuracy) {
boolean ret = true;

Object[] ch1 = this.strToOpStr(strSource);
//遍历表达式数组，逐个读入
for(int i = 0; i < ch1.length; i++) {
//判断是否是操作符
if(ch1[i].toString().isEmpty())
break;
if(!this.isOperator(ch1[i].toString())) {
//不是则如数字字符栈
this.num.push(ch1[i].toString());

}else {
//System.out.println(ch);
//从优先关系表中查找当前字符和操作符栈栈顶元素的运算优先关系
switch(this.serchOp(ch1[i].toString().charAt(0),this.opStack.lastElement())){
//如果ch优先顺序大于top 压入操作符栈
case '<':{

this.opStack.push(new Character(ch1[i].toString().charAt(0)));
//System.out.println(ch1[i].charAt(0)+"压入操作符");
}break;
//如果ch优顺序小于top 取出 俩个操作数以及弹出操作符进行运算
case '>': {
//弹出俩个数字元素
double num2 = Double.valueOf(this.num.pop());

double num1 = Double.valueOf(this.num.pop());

char op = this.opStack.pop();
//System.out.println(ch1[i].charAt(0)+"弹出操作符");
this.num.push(new Double(this.getCalculateNumber(num1, op, num2)).toString());
//但前元素不进行操作，返回重新进行比较
//栈顶元素运算，退栈
i--;
}break;
case '@': {
System.out.println("不合法的表达式");
ret = false;
}break;

case '=': {
//去括号，#号
this.opStack.pop();
//System.out.println(ch1[i].charAt(0)+"弹出操作符");
}break;
}
}
}
//格式化结果
NumberFormat nb = NumberFormat.getNumberInstance();
nb.setMinimumFractionDigits(Accuracy);
double res = Double.valueOf(this.num.pop());

return ret?nb.format(res):null;
}

/**
* 此函数用于在表达式进入运算之前检查表达式的合法性
* */
private boolean CheckeStr(String strSource) {

char[] chSource = strSource.toCharArray();
//先检查括号的数量
for(int i = 1; i < chSource.length; i++) {
if((chSource[i-1] == '('||chSource[i-1] == ')')&&!this.isOperater(chSource[i])) {
return false;
}else if((chSource[i] == '('||chSource[i] == ')')&&!this.isOperater(chSource[i-1])) {
return false;
}
}
return true;
}

//初始化俩个栈
private CalculateStack() {
//操作数栈初始化栈顶为0
this.num.push(new Integer(0).toString());
//操作符栈初始化为#(结尾符)
this.opStack.push(new Character('#'));
}

//判断字串是否为操作符
private boolean isOperator(String str) {

if(str.toCharArray().length == 1) {
for(char ch:RuleTable.op) {
if(ch == str.toCharArray()[0])
return true;
}
}else if(str.isEmpty()){
return false;
}else {
return false;
}
return false;
}

//此方法实现把操作符和操作数解析为字符串数组
private Object[] strToOpStr(String strSource) {
int num = 0;
boolean isOp = true;
String[] retStr = new String[100];

char[] ch = strSource.toCharArray();
for(char ch1:ch) {
//起始为数字
if(this.isOperater(ch1)&&num == 0&&!isOp) {
num++;
retStr[num++] = new String(new Character(ch1).toString());
isOp = true;
}else if(this.isOperater(ch1)&&num == 0&&isOp) {
//以操作符起始
retStr[num++] = new String(new Character(ch1).toString());
isOp = true;
}else if(this.isOperater(ch1)&&num != 0){
//不是起始位置并且是操作符
if(!isOp)//如果前一个不是操作符 增加num
num++;
retStr[num++] = new String(new Character(ch1).toString());
isOp = true;
}else if(!this.isOperater(ch1)&&num != 0){
//当前数字并且不是起始位置
if(retStr[num] == null)
retStr[num] = new String(new Character(ch1).toString());
else {
retStr[num] += ch1;
}

isOp = false;
}else if(!this.isOperater(ch1)&&num == 0) {

if(isOp) {
//System.out.println("opchar:" + ch1+"op:"+isOp+"num:"+num);
retStr[num] = new String(new Character(ch1).toString());
//System.out.println("opchar:" + ch1+"op:"+isOp+"num:"+num+"rerStr:"+retStr[num]);
}else {
retStr[num] += ch1;
//System.out.println("opchar:" + ch1+"op:"+isOp+"num:"+0+"rerStr:"+retStr[0]);
}
isOp = false;
}
}
ArrayList<String> list = new ArrayList<>();
for(int i = 0; i < retStr.length; i++) {
if(retStr[i] != null) {
list.add(retStr[i]);
}
}
list.add(list.size(),"#");
return list.toArray();
}
//判断一个字符是否为操作符
private boolean isOperater(char ch) {

for(char ch1:RuleTable.op) {
if(ch == ch1)
return true;
}
return false;
}
//demo
public static void main(String[] args) {

CalculateStack cl = CalculateStack.getCalculateInstance();
System.out.println(cl.Calculate("(3x4)/1.11-3x45+12-12333", 1));

}
//得到计算核心类的实例
static public CalculateStack getCalculateInstance() {
return cl;
}
}

2：算法

package com.baidu;

import java.util.ArrayList;

public class RuleTable {

//此表可添加
//操作符
static public char[] op = {
'+',
'-',
'x',
'/',
'(',
')',
'#'
};

//优先关系模拟表
//此表可添加
private int[][] re = {
{1,1,-1,-1,-1,1,1},
{1,1,-1,-1,-1,1,1},
{1,1,1,1,-1,1,1},
{1,1,1,1,-1,1,1},
{-1,-1,-1,-1,-1,0,2},
{1,1,1,1,-2,1,1},
{-1,-1,-1,-1,-1,2,0},
};
//申明一个运算优先规则列表
private ArrayList<Rule> ruleList = new ArrayList<>();

//获取运算优先规则列表
public ArrayList<Rule> getRuleList() {
return this.ruleList;
}
//生成运算优先关系表
public RuleTable() {

for(int i = 0; i < op.length; i++) {
for(int j = 0; j < op.length; j++) {
Rule rule = new Rule();
rule.ch1 = op[i];
rule.ch2 = op[j];
if(re[i][j] == 1) {
rule.equ = '>';
}else if(re[i][j] == -1) {
rule.equ = '<';
}else if(re[i][j] == 0) {
rule.equ = '=';
}else {
rule.equ = '@';
}

ruleList.add(rule);
}
}
}
//今设 第一个操作符为a 第二个为 b
//当第一个为 运算符第二个位分割符
//则运算符小于分割符
//如果第一个为分隔符第二个为运算符
//则运算符大于分隔符
}
//优先规则关系表元素
class Rule {
char ch1 = 0;
char ch2 = 0;
char equ = 0;
}