Daniel - 7 months ago 27

Javascript Question

I want to find the shortest distance between two numbers in looping sequence, e.g. 0 to 6:

`... 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 ...`

In also need to know which "way" is shorter (to the left or to the right).

So, if my two numbers are 0 and 6, the shortest distance is 1 by counting backwards (to the left).

The following function works, but only if

`next`

`crt`

`var MAX_NUMBER = 6; // 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6`

function shorterDirection(crt, next) {

var toRight = next - crt;

var toLeft = MAX_NUMBER - (next - crt - 1);

return toLeft < toRight ? 'left' : 'right';

}

console.log(shorterDirection(0, 6));

I can't figure out how to make it work both ways. For example, if I use

`shorterDirection(4, 3)`

`left`

Answer

You could use this:

```
function shorterDirection(crt, next) {
var toRight = (next + MAX_NUMBER+1 - crt) % (MAX_NUMBER+1);
return toRight > (MAX_NUMBER+1) / 2 ? 'left' : 'right';
}
```

Note that there can be ties. In that case the above will return `left`

, even though `right`

would be just as good.

As you can see there is a lot of `MAX_NUMBER+1`

in there. It would be more suitable if you would have a constant `NUMBER_COUNT`

, which would be one greater than the `MAX_NUMBER`

you have now.

You would start by writing this:

```
var toRight = next - crt;
```

But that goes "wrong" when *next* is less than *crt* -- you get a negative number. To solve that you would add `MAX_NUMBER+1`

:

```
var toRight = next + NUMBER+1 - crt;
```

... but now you get a too large number when *next* is greater than *crt*. That you can solve by subtracting as many `NUMBER+1`

as necessary to get within the range *0...MAX_NUMBER*. That is what the modulo (`%`

) operator does. So you get:

```
var toRight = (next + MAX_NUMBER+1 - crt) % (MAX_NUMBER+1);
```

Once you have that result, you can reason that if it takes more than half of the numbers to go to the right, you better go to the left (which will be less than half of the numbers). This is encoded as:

```
return toRight > (MAX_NUMBER+1) / 2 ? 'left' : 'right';
```