How to evaluate a math expression given in string

Question

I'm trying to write a Java routine to evaluate simple math expressions from String values like:

1. "5+3"
2. "10-40"
3. "10*3"

I want to avoid a lot of if-then-else statements. How can I do this?

Answer 1

It seems like JEP should do the job

Answer 2

A Java class that can evaluate mathematical expressions:

package test;

public class Calculator {

    public static Double calculate(String expression){
        if (expression == null || expression.length() == 0) {
            return null;
        }
        return calc(expression.replace(" ", ""));
    }
    public static Double calc(String expression) {

        if (expression.startsWith("(") && expression.endsWith(")")) {
            return calc(expression.substring(1, expression.length() - 1));
        }
        String[] containerArr = new String[]{expression};
        double leftVal = getNextOperand(containerArr);
        expression = containerArr[0];
        if (expression.length() == 0) {
            return leftVal;
        }
        char operator = expression.charAt(0);
        expression = expression.substring(1);

        while (operator == '*' || operator == '/') {
            containerArr[0] = expression;
            double rightVal = getNextOperand(containerArr);
            expression = containerArr[0];
            if (operator == '*') {
                leftVal = leftVal * rightVal;
            } else {
                leftVal = leftVal / rightVal;
            }
            if (expression.length() > 0) {
                operator = expression.charAt(0);
                expression = expression.substring(1);
            } else {
                return leftVal;
            }
        }
        if (operator == '+') {
            return leftVal + calc(expression);
        } else {
            return leftVal - calc(expression);
        }

    }

    private static double getNextOperand(String[] exp){
        double res;
        if (exp[0].startsWith("(")) {
            int open = 1;
            int i = 1;
            while (open != 0) {
                if (exp[0].charAt(i) == '(') {
                    open++;
                } else if (exp[0].charAt(i) == ')') {
                    open--;
                }
                i++;
            }
            res = calc(exp[0].substring(1, i - 1));
            exp[0] = exp[0].substring(i);
        } else {
            int i = 1;
            if (exp[0].charAt(0) == '-') {
                i++;
            }
            while (exp[0].length() > i && isNumber((int) exp[0].charAt(i))) {
                i++;
            }
            res = Double.parseDouble(exp[0].substring(0, i));
            exp[0] = exp[0].substring(i);
        }
        return res;
    }


    private static boolean isNumber(int c) {
        int zero = (int) '0';
        int nine = (int) '9';
        return (c >= zero && c <= nine) || c =='.';
    }

    public static void main(String[] args) {
        System.out.println(calculate("(((( -6 )))) * 9 * -1"));
        System.out.println(calc("(-5.2+-5*-5*((5/4+2)))"));

    }

}

Answer 3

The correct way to solve this is with a lexer and a parser. You can write simple versions of these yourself, or those pages also have links to Java lexers and parsers.

Creating a recursive descent parser is a really good learning exercise.

Answer 4

This is another interesting alternative https://github.com/Shy-Ta/expression-evaluator-demo

The usage is very simple and gets the job done, for example:

  ExpressionsEvaluator evalExpr = ExpressionsFactory.create("2+3*4-6/2");  
  assertEquals(BigDecimal.valueOf(11), evalExpr.eval()); 

Answer 5

I've written this eval method for arithmetic expressions to answer this question. It does addition, subtraction, multiplication, division, exponentiation (using the ^ symbol), and a few basic functions like sqrt. It supports grouping using (...), and it gets the operator precedence and associativity rules correct.

public static double eval(final String str) {
    return new Object() {
        int pos = -1, ch;

        void nextChar() {
            ch = (++pos < str.length()) ? str.charAt(pos) : -1;
        }

        boolean eat(int charToEat) {
            while (ch == ' ') nextChar();
            if (ch == charToEat) {
                nextChar();
                return true;
            }
            return false;
        }

        double parse() {
            nextChar();
            double x = parseExpression();
            if (pos < str.length()) throw new RuntimeException("Unexpected: " + (char)ch);
            return x;
        }

        // Grammar:
        // expression = term | expression `+` term | expression `-` term
        // term = factor | term `*` factor | term `/` factor
        // factor = `+` factor | `-` factor | `(` expression `)`
        //        | number | functionName factor | factor `^` factor

        double parseExpression() {
            double x = parseTerm();
            for (;;) {
                if      (eat('+')) x += parseTerm(); // addition
                else if (eat('-')) x -= parseTerm(); // subtraction
                else return x;
            }
        }

        double parseTerm() {
            double x = parseFactor();
            for (;;) {
                if      (eat('*')) x *= parseFactor(); // multiplication
                else if (eat('/')) x /= parseFactor(); // division
                else return x;
            }
        }

        double parseFactor() {
            if (eat('+')) return parseFactor(); // unary plus
            if (eat('-')) return -parseFactor(); // unary minus

            double x;
            int startPos = this.pos;
            if (eat('(')) { // parentheses
                x = parseExpression();
                eat(')');
            } else if ((ch >= '0' && ch <= '9') || ch == '.') { // numbers
                while ((ch >= '0' && ch <= '9') || ch == '.') nextChar();
                x = Double.parseDouble(str.substring(startPos, this.pos));
            } else if (ch >= 'a' && ch <= 'z') { // functions
                while (ch >= 'a' && ch <= 'z') nextChar();
                String func = str.substring(startPos, this.pos);
                x = parseFactor();
                if (func.equals("sqrt")) x = Math.sqrt(x);
                else if (func.equals("sin")) x = Math.sin(Math.toRadians(x));
                else if (func.equals("cos")) x = Math.cos(Math.toRadians(x));
                else if (func.equals("tan")) x = Math.tan(Math.toRadians(x));
                else throw new RuntimeException("Unknown function: " + func);
            } else {
                throw new RuntimeException("Unexpected: " + (char)ch);
            }

            if (eat('^')) x = Math.pow(x, parseFactor()); // exponentiation

            return x;
        }
    }.parse();
}

Example:

System.out.println(eval("((4 - 2^3 + 1) * -sqrt(3*3+4*4)) / 2"));

Output: 7.5 (which is correct)

---

The parser is a recursive descent parser, so internally uses separate parse methods for each level of operator precedence in its grammar. I kept it short so it's easy to modify, but here are some ideas you might want to expand it with:

• Variables:

  The bit of the parser that reads the names for functions can easily be changed to handle custom variables too, by looking up names in a variable table passed to the eval method, such as a Map<String,Double> variables.

• Separate compilation and evaluation:

  What if, having added support for variables, you wanted to evaluate the same expression millions of times with changed variables, without parsing it every time? It's possible. First define an interface to use to evaluate the precompiled expression:

  @FunctionalInterface
  interface Expression {
      double eval();
  }
  

  Now change all the methods that return doubles, so instead they return an instance of that interface. Java 8's lambda syntax works great for this. Example of one of the changed methods:

  Expression parseExpression() {
      Expression x = parseTerm();
      for (;;) {
          if (eat('+')) { // addition
              Expression a = x, b = parseTerm();
              x = (() -> a.eval() + b.eval());
          } else if (eat('-')) { // subtraction
              Expression a = x, b = parseTerm();
              x = (() -> a.eval() - b.eval());
          } else {
              return x;
          }
      }
  }
  

  That builds a recursive tree of Expression objects representing the compiled expression (an abstract syntax tree). Then you can compile it once and evaluate it repeatedly with different values:

  public static void main(String[] args) {
      Map<String,Double> variables = new HashMap<>();
      Expression exp = parse("x^2 - x + 2", variables);
      for (double x = -20; x <= +20; x++) {
          variables.put("x", x);
          System.out.println(x + " => " + exp.eval());
      }
  }
  

• Different datatypes:

  Instead of double, you could change the evaluator to use something more powerful like BigDecimal, or a class that implements complex numbers, or rational numbers (fractions). You could even use Object, allowing some mix of datatypes in expressions, just like a real programming language. :)

---

_{All code in this answer released to the public domain. Have fun!}

Answer 6

You can also try the BeanShell interpreter:

Interpreter interpreter = new Interpreter();
interpreter.eval("result = (7+21*6)/(32-27)");
System.out.println(interpreter.get("result"));