1.匹配 + - * / ( ) 运算符

 static final String SYMBOL = "\\+|-|\\*|/|\\(|\\)";

    static final String LEFT = "(";
    static final String RIGHT = ")";
    static final String ADD = "+";
    static final String MINUS= "-";
    static final String TIMES = "*";
    static final String DIVISION = "/";

2.加減 + -

static final int LEVEL_01 = 1;

3.乘除 * /

static final int LEVEL_02 = 2;

4.括号

static final int LEVEL_HIGH = Integer.MAX_VALUE;

5.初始化

 static Stack<String> stack = new Stack<>();
 static List<String> data = Collections.synchronizedList(new ArrayList<String>());

6.去除所有空白符

public static String replaceAllBlank(String s ){
    // \\s+ 匹配任何空白字符，包括空格、制表符、换页符等等, 等价于[ \f\n\r\t\v]
    return s.replaceAll("\\s+","");
}

7.判断是不是数字 int double long float

public static boolean isNumber(String s){
    Pattern pattern = Pattern.compile("^[-\\+]?[.\\d]*$");
    return pattern.matcher(s).matches();
}

8.判断是不是运算符

public static boolean isSymbol(String s){
    return s.matches(SYMBOL);
}

9.匹配运算等级

public static int calcLevel(String s){
    if("+".equals(s) || "-".equals(s)){
        return LEVEL_01;
    } else if("*".equals(s) || "/".equals(s)){
        return LEVEL_02;
    }
    return LEVEL_HIGH;
}

10.匹配

public static List<String> doMatch (String s) throws Exception{
    if(s == null || "".equals(s.trim())) throw new RuntimeException("data is empty");
    if(!isNumber(s.charAt(0)+"")) throw new RuntimeException("data illeagle,start not with a number");

    s = replaceAllBlank(s);

    String each;
    int start = 0;

    for (int i = 0; i < s.length(); i++) {
        if(isSymbol(s.charAt(i)+"")){
            each = s.charAt(i)+"";
            //栈为空，(操作符，或者 操作符优先级大于栈顶优先级 && 操作符优先级不是( )的优先级 及是 ) 不能直接入栈
            if(stack.isEmpty() || LEFT.equals(each)
                    || ((calcLevel(each) > calcLevel(stack.peek())) && calcLevel(each) < LEVEL_HIGH)){
                stack.push(each);
            }else if( !stack.isEmpty() && calcLevel(each) <= calcLevel(stack.peek())){
                //栈非空，操作符优先级小于等于栈顶优先级时出栈入列，直到栈为空，或者遇到了(，最后操作符入栈
                while (!stack.isEmpty() && calcLevel(each) <= calcLevel(stack.peek()) ){
                    if(calcLevel(stack.peek()) == LEVEL_HIGH){
                        break;
                    }
                    data.add(stack.pop());
                }
                stack.push(each);
            }else if(RIGHT.equals(each)){
                // ) 操作符，依次出栈入列直到空栈或者遇到了第一个)操作符，此时)出栈
                while (!stack.isEmpty() && LEVEL_HIGH >= calcLevel(stack.peek())){
                    if(LEVEL_HIGH == calcLevel(stack.peek())){
                        stack.pop();
                        break;
                    }
                    data.add(stack.pop());
                }
            }
            start = i ;    //前一个运算符的位置
        }else if( i == s.length()-1 || isSymbol(s.charAt(i+1)+"") ){
            each = start == 0 ? s.substring(start,i+1) : s.substring(start+1,i+1);
            if(isNumber(each)) {
                data.add(each);
                continue;
            }
            throw new RuntimeException("data not match number");
        }
    }
    //如果栈里还有元素，此时元素需要依次出栈入列，可以想象栈里剩下栈顶为/，栈底为+，应该依次出栈入列，可以直接翻转整个stack 添加到队列
    Collections.reverse(stack);
    data.addAll(new ArrayList<>(stack));

    System.out.println(data);
    return data;
}

11.算出结果

public static Double doCalc(List<String> list){
    Double d = 0d;
    if(list == null || list.isEmpty()){
        return null;
    }
    if (list.size() == 1){
        System.out.println(list);
        d = Double.valueOf(list.get(0));
        return d;
    }
    ArrayList<String> list1 = new ArrayList<>();
    for (int i = 0; i < list.size(); i++) {
        list1.add(list.get(i));
        if(isSymbol(list.get(i))){
            Double d1 = doTheMath(list.get(i - 2), list.get(i - 1), list.get(i));
            list1.remove(i);
            list1.remove(i-1);
            list1.set(i-2,d1+"");
            list1.addAll(list.subList(i+1,list.size()));
            break;
        }
    }
    doCalc(list1);
    return d;
}

12.运算

public static Double doTheMath(String s1,String s2,String symbol){
    Double result ;
    switch (symbol){
        case ADD : result = Double.valueOf(s1) + Double.valueOf(s2); break;
        case MINUS : result = Double.valueOf(s1) - Double.valueOf(s2); break;
        case TIMES : result = Double.valueOf(s1) * Double.valueOf(s2); break;
        case DIVISION : result = Double.valueOf(s1) / Double.valueOf(s2); break;
        default : result = null;
    }
    return result;

}

13.测试

public static void main(String[] args) {
    //String math = "9+(3-1)*3+10/2";
    String math = "12.8 + (2 - 3.55)*4+10/5.0";
    try {
        doCalc(doMatch(math));
    } catch (Exception e) {
        e.printStackTrace();
    }
}