JavaScript — write a function that can solve a math [removed]without eval)

Question

Ultimately I want to take this:

2x + 3 = 5

and solve for x, by first subtract 3 from both sides so 2x = 2, then divide both si

Answer 1

While your problem doesn't require to construct, binary expression tree is a good way to brainstorm the logic to solve a math query.

So for the query 3 - 6 * 3 / 9 + 5, the representative binary expression tree is:

plus
  |_minus
  | |_3
  | |_divide
  |   |_times
  |   | |_3
  |   | |_6
  |   |_9
  |_5

to solve above tree, you recursively solve from the leaf level up to the root.

Again, you don't need to construct a tree. It just helps us to see the logic of parsing here:

• Get the last minus or plus expression in query and solve left and right child of that expression.
• If no plus/minus, get the last times/division expression and solve left and right child
• If meet a number, return that number value.

Given above logic, here is an implementation:

function solve(str) {
  var expressionIndex = Math.max(str.lastIndexOf("-"), str.lastIndexOf("+"));
  if (expressionIndex === -1) {
    expressionIndex = Math.max(str.lastIndexOf("*"), str.lastIndexOf("/"));
  }
  if (expressionIndex === -1) {
    var num = Number.parseInt(str.trim());
    if (isNaN(num)) {
      throw Exception("not a valid number");
    } else {
      return num;
    }
  } else {
    var leftVal = solve(str.substring(0, expressionIndex).trim());
    var rightVal = solve(str.substring(expressionIndex + 1).trim());
    switch (str[expressionIndex]) {
      case "+":
        return leftVal + rightVal;
      case "-":
        return leftVal - rightVal;
      case "*":
        return leftVal * rightVal;
      case "/":
        return leftVal / rightVal;
    }
  }
}

function parse(str) {
  var expressionIndex = Math.max(str.lastIndexOf("-"), str.lastIndexOf("+"));
  if (expressionIndex === -1) {
    expressionIndex = Math.max(str.lastIndexOf("*"), str.lastIndexOf("/"));
  }
  if (expressionIndex === -1) {
    var num = Number.parseInt(str.trim());
    if (isNaN(num)) {
      throw Exception("not a valid number");
    } else {
      return { type: "number", value: num };
    }
  } else {
    var leftNode = parse(str.substring(0, expressionIndex).trim());
    var rightNode = parse(str.substring(expressionIndex + 1).trim());
    return {
      type: "expression",
      value: str[expressionIndex],
      left: leftNode,
      right: rightNode
    };
  }
}

console.log(solve("3 - 6 * 3 / 9 + 5"));
console.log(parse("3 - 6 * 3 / 9 + 5"));

Above is a solution for very simple query with only +, -, *, / (no parenthesis, e.g.). For solving a equation like your first example requires a lot more of work.

EDIT: add a parse function to return the tree.