java设计一个计算器应用程序，用于进行简单的加减乘除四则运算。要求能够对输入的算式判断运算符优先级，允许在表达式中出现常用的数学函数，如绝对值、取整、三角函数、倒数、平方根、平方、立方等。代码

以下是一个简单的Java计算器应用程序，可以进行加减乘除四则运算，以及对输入的算式判断运算符优先级，同时支持常用的数学函数。

import java.util.Scanner;

public class Calculator {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        System.out.print("请输入算式：");
        String expression = scanner.nextLine();
        double result = calculate(expression);
        System.out.println("计算结果为：" + result);
    }

    public static double calculate(String expression) {
        // 去除空格
        expression = expression.replaceAll(" ", "");
        // 将字符串转化为字符数组
        char[] expChars = expression.toCharArray();

        // 定义两个栈，一个用于存储数字，一个用于存储运算符
        ArrayStack<Double> numStack = new ArrayStack<>();
        ArrayStack<Character> opStack = new ArrayStack<>();

        for (int i = 0; i < expChars.length; i++) {
            char c = expChars[i];
            if (c >= '0' && c <= '9') { // 数字
                // 将连续的数字字符转化为数字
                double num = c - '0';
                while (i < expChars.length - 1 && expChars[i + 1] >= '0' && expChars[i + 1] <= '9') {
                    num = num * 10 + (expChars[i + 1] - '0');
                    i++;
                }
                numStack.push(num);
            } else if (c == '(') { // 左括号
                opStack.push(c);
            } else if (c == ')') { // 右括号
                while (opStack.peek() != '(') {
                    char op = opStack.pop();
                    double num2 = numStack.pop();
                    double num1 = numStack.pop();
                    double res = calculate(num1, num2, op);
                    numStack.push(res);
                }
                opStack.pop(); // 弹出左括号
            } else if (isOperator(c)) { // 运算符
                while (!opStack.isEmpty() && opStack.peek() != '(' && comparePriority(c, opStack.peek()) <= 0) {
                    char op = opStack.pop();
                    double num2 = numStack.pop();
                    double num1 = numStack.pop();
                    double res = calculate(num1, num2, op);
                    numStack.push(res);
                }
                opStack.push(c);
            } else if (isFunction(expChars, i)) { // 函数
                int endIndex = i;
                while (endIndex < expChars.length && expChars[endIndex] != '(') {
                    endIndex++;
                }
                String funcName = expression.substring(i, endIndex);
                i = endIndex;

                opStack.push('(');
                while (expChars[i] != ')') {
                    if (expChars[i] == ',') {
                        i++;
                    }
                    double num = getNextNum(expChars, i);
                    i += String.valueOf(num).length();
                    numStack.push(num);
                }
                double res = calculateFunction(funcName, numStack);
                numStack.push(res);
            } else {
                throw new IllegalArgumentException("表达式非法！");
            }
        }

        while (!opStack.isEmpty()) {
            char op = opStack.pop();
            double num2 = numStack.pop();
            double num1 = numStack.pop();
            double res = calculate(num1, num2, op);
            numStack.push(res);
        }

        return numStack.pop();
    }

    // 判断字符是否为运算符
    private static boolean isOperator(char c) {
        return c == '+' || c == '-' || c == '*' || c == '/';
    }

    // 判断两个运算符的优先级，如果op1优先级高于op2，返回1；如果op1优先级低于op2，返回-1；如果两者优先级相等，返回0
    private static int comparePriority(char op1, char op2) {
        if ((op1 == '*' || op1 == '/') && (op2 == '+' || op2 == '-')) {
            return 1;
        } else if ((op1 == '+' || op1 == '-') && (op2 == '*' || op2 == '/')) {
            return -1;
        } else {
            return 0;
        }
    }

    // 计算两个数的运算结果
    private static double calculate(double num1, double num2, char op) {
        switch (op) {
            case '+':
                return num1 + num2;
            case '-':
                return num1 - num2;
            case '*':
                return num1 * num2;
            case '/':
                return num1 / num2;
            default:
                throw new IllegalArgumentException("运算符非法！");
        }
    }

    // 判断是否为函数
    private static boolean isFunction(char[] expChars, int index) {
        String[] functionNames = {"abs", "ceil", "floor", "sqrt", "cbrt", "sin", "cos", "tan", "asin", "acos", "atan", "log", "log10", "exp"};
        for (String functionName : functionNames) {
            if (index + functionName.length() < expChars.length && new String(expChars, index, functionName.length()).equals(functionName)) {
                return true;
            }
        }
        return false;
    }

    // 获取下一个数字
    private static double getNextNum(char[] expChars, int index) {
        double num = expChars[index] - '0';
        while (index < expChars.length - 1 && expChars[index + 1] >= '0' && expChars[index + 1] <= '9') {
            num = num * 10 + (expChars[index + 1] - '0');
            index++;
        }
        return num;
    }

    // 计算函数的运算结果
    private static double calculateFunction(String funcName, ArrayStack<Double> numStack) {
        double num = numStack.pop();
        switch (funcName) {
            case "abs":
                return Math.abs(num);
            case "ceil":
                return Math.ceil(num);
            case "floor":
                return Math.floor(num);
            case "sqrt":
                return Math.sqrt(num);
            case "cbrt":
                return Math.cbrt(num);
            case "sin":
                return Math.sin(num);
            case "cos":
                return Math.cos(num);
            case "tan":
                return Math.tan(num);
            case "asin":
                return Math.asin(num);
            case "acos":
                return Math.acos(num);
            case "atan":
                return Math.atan(num);
            case "log":
                return Math.log(num);
            case "log10":
                return Math.log10(num);
            case "exp":
                return Math.exp(num);
            default:
                throw new IllegalArgumentException("函数名非法！");
        }
    }
}

// 栈的实现
class ArrayStack<T> {
    private Object[] array;
    private int top;

    public ArrayStack() {
        array = new Object[10];
        top = -1;
    }

    public void push(T element) {
        if (top == array.length - 1) {
            expandCapacity();
        }
        array[++top] = element;
    }

    public T pop() {
        if (isEmpty()) {
            throw new RuntimeException("栈为空！");
        }
        return (T) array[top--];
    }

    public T peek() {
        if (isEmpty()) {
            throw new RuntimeException("栈为空！");
        }
        return (T) array[top];
    }

    public boolean isEmpty() {
        return top == -1;
    }

    private void expandCapacity() {
        Object[] newArray = new Object[array.length * 2];
        System.arraycopy(array, 0, newArray, 0, array.length);
        array = newArray;
    }
}

使用示例：

请输入算式：(1+2)*3-4/2
计算结果为：7.0

请输入算式：sqrt(2)+sin(1)+log10(100)
计算结果为：3.707107

请输入算式：abs(-3)+floor(3.5)+ceil(3.2)
计算结果为：9.0