Evaluating a math expression given in string form
I'm trying to write a Java routine to evaluate simple math expressions from String values like:
"5+3" "10-40" "10*3" I want to avoid a lot of if-then-else statements. How can I do this?
使用JDK1.6，您可以使用内置的JavaScript引擎。
import javax.script.ScriptEngineManager;
import javax.script.ScriptEngine;
import javax.script.ScriptException;
public class Test {
public static void main(String[] args) throws ScriptException {
ScriptEngineManager mgr = new ScriptEngineManager();
ScriptEngine engine = mgr.getEngineByName("JavaScript");
String foo = "40+2";
System.out.println(engine.eval(foo));
}
}
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 double s, 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!
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.
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