determine if array is arithmetic or geometric progression (from Coderbyte)

Question

Here is my functional code, as far as coderbyte is concerned. But I have a feeling it shouldn't be this complicated. Am I missing a simple trick?

function ArithGeo(arr)
{
    var array_type = -1;
    if (arr.length <= 2) return true;

    var a = arr[1], r = a/arr[0], i;
    for (i = 2; i < arr.length; ++i) {
        if ((a *= r) == arr[i]){
            array_type = "Geometric";
        }
        else{
            array_type = -1;
            break;
        }
    }

    if (array_type == "Geometric")
        return array_type;


    a = arr[1], d = a - arr[0], i;
    for (i = 2; i < arr.length; ++i) {
        if ((a += d) == arr[i]){
            array_type = "Arithmetic";
        }
        else {
            array_type = -1;
            break;
        }
    }
    return array_type;
}

ArithGeo([3,9,15,21,27, 28]);

Answer 1

function ArithGeo(arr) { 

var diff = arr[1] - arr[0];
var ratio = arr[1] / arr[0];

var arith = true;
var geo = true;

for(var i = 0; i < arr.length - 1; i++)
{
    if( arr[i + 1] - arr[i] !== diff )
      arith = false;
    if(arr[i + 1] / ratio !== arr[i])
      geo = false;
}

if(arith === true)
    return "arithmetic";
else if(geo === true)
    return" geometric";
else
    return -1;

}

Here's a simple solution as well. I'm either looking for a geometric pattern, where a given element will be divisible by the previous element, or an arithmetic pattern, where each element increases by a constant amount. Two variables, diff and ratio, contain each pattern to search for throughout the array.

I start by assuming that arith and geo are true, and if I find an example where one is not true, I set its value to false. Note that your code has two for loops, with the exact same conditions. This is a good indication that your code can be condensed into one loop.

With each pass through the loop, I test whether the conditions are present to set either arith or geo to false. Finally, after the loop exits, I will determine if either arith or geo remained true throughout the loop. If not, I return - 1 as the problem from Coderbyte requests.

edit: quick note on my for loop condition. Since I am checking the value of i + 1 with each pass, I make sure that I don't reach out of bounds by setting my exit condition to arr.length - 1. This way, i + 1 can still reach the last element, and will be sure not to overreach.

Answer 2

For arithmetic progression, subtract each element from previous element; their difference should be equal; for geometric, divide each element by the previous element, the ratio should stay the same. As for divide by zero when you meet 0, javascript gives you Inf (and it certainly is not a geometric progression). Because floats are inaccurate, maybe you'd want to store the min and max of these values and then see if they are close enough to each other.

function arithGeo(arr) {
    var minRatio = 1/0,
        maxRatio = -1/0,
        minDiff  = 1/0,
        maxDiff  = -1/0,
        epsilon  = 0.000001,
        i,
        ratio,
        diff;

    if (arr.length <= 2) {
        return;
    }

    for (i = 1; i < arr.length; ++i) {
        diff  = arr[i] - arr[i - 1];
        ratio = arr[i] / arr[i - 1];
        minDiff  = Math.min(diff, minDiff);
        maxDiff  = Math.max(diff, maxDiff);
        minRatio = Math.min(ratio, minRatio);
        maxRatio = Math.max(ratio, maxRatio);
    }

    if (Math.abs(minDiff - maxDiff) < epsilon) {
        return "Arithmetic";
    }

    if (Math.abs(minRatio - maxRatio) < epsilon) {
        return "Geometric";
    }

    return;
}

alert(arithGeo([3,9,15,21,27,28]));
alert(arithGeo([3,9,15,21,27]));
alert(arithGeo([4,2,1,0.5]));