类似于计算中缀表达式，|符号将左右两边表达式计算出一个结果、()改变优先级、连续字符后、)后添加+号进行连接

import java.util.*;
public class Main{
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        String s = scanner.nextLine().trim();
        int i = 0;
        LinkedList<StringBuilder> strStack = new LinkedList<>();
        LinkedList<Character> oper = new LinkedList<>();
        while (i < s.length()){
            //oper中可能出现的 (、|、+
            char c = s.charAt(i);
            if (c == '('){
                oper.push('(');
            }else if (c == '|'){
                if (!oper.isEmpty() && oper.peek() == '+'){
                    oper.pop();
                }
                oper.push('|');
            }else if (c == ')'){
                if (!oper.isEmpty() && oper.peek() == '+'){
                    oper.pop();
                }
                while (oper.peek() != '('){
                    Character pop = oper.pop();
                    if (pop == '|'){
                        StringBuilder pop1 = strStack.pop();
                        StringBuilder pop2 = strStack.pop();
                        strStack.push(pop1.length() > pop2.length() ? pop1:pop2);
                    }
                }
                oper.pop();//将（弹出栈
                while (!oper.isEmpty() && oper.peek() == '+'){
                    StringBuilder pop = strStack.pop();
                    StringBuilder pop1 = strStack.pop();
                    pop.append(pop1);
                    strStack.push(pop);
                    oper.pop();
                }
                oper.push('+');
            }else {
                //i = X
                StringBuilder str = new StringBuilder();
                while (i < s.length() && s.charAt(i) == 'x'){
                    str.append('x');
                    i++;
                }
                //i!=x
                while (!oper.isEmpty() && oper.peek() == '+'){
                    StringBuilder pop = strStack.pop();
                    str = str.append(pop);
                    oper.pop();
                }
                strStack.push(str);
                oper.push('+');
                i--;
            }
            i++;
        }
        while (!oper.isEmpty()){
            Character pop = oper.pop();
            if (pop == '|'){
                StringBuilder pop1 = strStack.pop();
                StringBuilder pop2 = strStack.pop();
                strStack.push(pop1.length() > pop2.length() ? pop1:pop2);
            }
        }
        StringBuilder res = new StringBuilder();
        while (!strStack.isEmpty() ){
            res.append(strStack.poll());
        }
        System.out.println(res.length());
//        System.out.println(strStack.pop());


    }
}

递归写法、整个表达式看作在一个整个大括号中，大括号里面计算小括号递归进行、没有括号时|二取1、直接相连等于二者相加

import java.util.*;
public class Main{
    static String str;
    static int index;
    public static void main(String[] args){
        Scanner input = new Scanner(System.in);
        str = input.nextLine().trim();
        System.out.println(dfs());
    }
    //求一个括号中的表达式的值，我们输入的字符串本身就可以看作实在一个不存在的括号中
    public static int dfs(){
        int res = 0;//这个括号中的表达式的值
        while(index < str.length()){
            char c = str.charAt(index);
            if(c == '('){
                index++;
                res += dfs();
                index++;
            }else if(c == ')'){
                return res;
            }else if(c == '|'){
                index++;
                res = Math.max(res,dfs());
            }else{
                res++;
                index++;
            }
        }
        return res;
    }
}