Evenly select N elems from array

It looks like you want to include both the first and last elements in your list.

If you want to pull X items from your list of N items, your step size will be (N-1)/(X-1). Just round however you want as you pull out each one.

Let n+1 be the number of elements you want, already bounded to the length of the array.

Then you want elements at indices 0/n, 1/n, ..., n/n of the way to the end of the array.

Let m+1 be the length of the array. Then your indices are round(m*i/n) (with the division done with floating point).

Your step size is (ArraySize-1)/(N-1).
Just add the step size to a floating point accumulator, and round off the accumulator to get the array index. Repeat until accumulator > array size.

Enjoy! (pseudo-code):

function Algorithm(int N,array A)
    float step=(A.size-1)/(N-1)       //set step size

    array R                           //declare return array

    for (int i=0, i<N, i++)
        R.push(A[round(step*i)])  //push each element of a position which is a
                                      //multiple of step to R

    return R

Probably the easiest mistake to make here would be to cast step as an integer or round it at the beginning. However, in order to make sure that the correct elements are pulled, you must declare step as a floating point number, and round multiples of step as you are iterating through the array.

Tested example here in php:

<?

    function Algorithm($N,$A){

        $step=(sizeof($A)-1)/($N-1);
        for ($i=0;$i<$N;$i++)
            echo $A[round($step*$i)]." ";
        echo "\n";
    }

    //some of your test cases:
    Algorithm(3,array(1,2,3));
    Algorithm(5,array(0,1,2,3,4,5,6,7));
    Algorithm(2,array(0,1,2));
    Algorithm(3,array(0,1,2,3,4,5,6));
?>

Outputs:
1 2 3 
0 2 4 5 7 
0 2 
0 3 6 

(you can see your test cases in action and try new ones here: http://codepad.org/2eZp98eD)