Question

My introductory tutorial has suddenly become very advanced. I have no idea how this program works. Can you explain in plain language?

At the end it prints (((1 * 3) + 5) * 3), but I don’t get it at all. I understand that findSequence gets passed 24, that triggers function find. I’m assuming that function find gets passed 1,”1″ with the latter being assigned to history?? but I don`t understand why the second 1 is in quotation marks “1!, nor do I understand the use of quotation marks when it returns find(start etc.

function findSequence(goal) {
  function find(start, history) {
    if (start == goal)
      return history;
    else if (start > goal)
      return null;
    else
      return find(start + 5, "(" + history + " + 5)") ||
             find(start * 3, "(" + history + " * 3)");
  }
  return find(1, "1");
}

print(findSequence(24));

Answer 1

You have an “output” string (((1 * 3) + 5) * 3), a goal 24 and a first character 1. The 1 is the 1 in 1 * 3. This program will assemble a string containing a math expression, adding (), *3 and +5 to try to obtain the goal. The two parameters of the find function are the current total and the expression that will generate the total. Clearly the expression is a string. The find compares the current total to the goal, and if it’s equal then the expression is correct and it returns it, if the current total is > of the goal then he failed and return null. Otherwhise he add some operations to the expression. He tries two “ways”, one multiplying * 3 the current result, the other adding +5 to the current result. It’s recursive on a tree (so each time he will bifurcate in two recursive calls). null || something == something, so the branch that will find a response will return his response, the other branch will return null and the “winning” response will be passed back.

Let’s say the goal is 11.

• find(1, “1”)
  1. compares 1 with 11 and calls: (2.) find(1 + 5, “(” + “1” + ” + 5)”) (so find(6, “(1 + 5)”) and (3.) find(1 * 3, “(” + “1” + ” * 3)”) (so find(3, “(1 * 3)”)
  2. compares 6 with 11 and calls (4.) find (6 + 5, “(” + “(1 + 5)” + ” + 5)”) (so finds(11, “((1 + 5) + 5)”) and (5.) find (6 * 3, “(” + “(1 + 5)” + ” * 3)” (so find(18, “((1 + 5) * 3)”
  3. compares 3 with 11 and calls (6.) find (3 + 5, “(” + “(1 * 3)” + ” + 5)”) (so finds(8, “((1 * 3) + 5)”) and (7.) find (3 * 3, “(” + “(1 * 3)” + ” * 3)” (so find(8, “((1 + 3) * 3)”
  4. compares 11 with 11. The numbers are equal. So he returns “((1 + 5) + 5)” (the history). 5, 6, 7 will at a certain point go “overboard” and surpass the 11, so they’ll return null. null || null == null, “((1 + 5) + 5)” || null == “((1 + 5) + 5)”, so the history will win against the nulls and it will be returned.

To make it even clearer, try these versions:

function findSequence(goal) {
  function find(start, history) {
    if (start == goal)
      return history;
    else if (start > goal)
      return null;
    else {
      var ret = find(start + 5, "(" + history + " + 5)");

      if (ret == null)
         ret = find(start * 3, "(" + history + " * 3)");

      return ret;
    }
  }

  return find(1, "1");
}

print(findSequence(24));

And this, where instead of an expression you’ll get only as tring of + and *

function findSequence(goal) {
  function find(start, history) {
    if (start == goal)
      return history;
    else if (start > goal)
      return null;
    else {
      var ret = find(start + 5, history + "+");

      if (ret == null)
         ret = find(start * 3, history + "*");

      return ret;
     }
  }

  return find(1, "1");
}

print(findSequence(24));

And be aware that, as an example, it’s quite complex because it used closures (locally defined functions).