Count sequence and distance of numbers in an array

To find the shortest distance between each number you just need to compare the number that goes with the front, and if it is greater than the distance calculated so far, update it.

The sequences already involve more complexity, but you can find them by seeing if the distance to the front element is 1 and if it adds that element to an array, which in turn is added to another global array of sequences. The term of the current sequence is given when the distance ceases to be 1 .

Example of implementing this logic:

$a = array(1, 2, 4, 6, 8, 9, 10, 15, 16, 17, 20, 21, 23, 24, 26, 27, 28, 29, 31, 39);

$maiorDistancia = 0;
$sequencias = [];
$ultimaSeq = 0;

for ($i = 0; $i < count($a)-1; ++$i){
    $dist = abs($a[$i]-$a[$i+1]); //distancia entre este e o proximo

    if ($dist > $maiorDistancia) $maiorDistancia = $dist; //se maior atualiza

    if (($a[$i+1]-$a[$i]) == 1){ //teste para sequencia
        if (isset($sequencias[$ultimaSeq])){
            $sequencias[$ultimaSeq][] = $a[$i+1]; //se ja existe uma sequencia acrescente
        }
        else { //se é uma nova insere os 2 primeiros elementos
            $sequencias[$ultimaSeq][0] = $a[$i];
            $sequencias[$ultimaSeq][1] = $a[$i+1];
        }
    }
    else {
        $ultimaSeq++;
    }
}

Output:

Maior distancia: 8 
 Sequencias: Array
(
    [0] => Array
        (
            [0] => 1
            [1] => 2
        )

    [3] => Array
        (
            [0] => 8
            [1] => 9
            [2] => 10
        )

    [4] => Array
        (
            [0] => 15
            [1] => 16
            [2] => 17
        )

    [5] => Array
        (
            [0] => 20
            [1] => 21
        )

    [6] => Array
        (
            [0] => 23
            [1] => 24
        )

    [7] => Array
        (
            [0] => 26
            [1] => 27
            [2] => 28
            [3] => 29
        )

)

Ideone with this solution

Notes:

• The solution only takes increasing sequences, so if it is possible to have decreasing sequences it becomes necessary to make some adjustments to the code.
• The distance used was calculated based on the abs function, which is why both distance positive and negative.
• The distance between 39 and 31 is even 8 , something the calculator can check, but if you want to get the 7 because you want to ignore the 39 itself you only need to subtract 1 .

Considering that the array is ordered, and that you only need to know the number of sequences and the GREATER distance between the numbers (I understand this).

Just scroll through the array, looking at two consecutive numbers and storing the values. You can do this (I did it in a more python style, not php handle, but the question is quite independent of language):

i=0
MAIOR_DIST = 0
IN_SEQUENCIA = false
SEQUENCIAS = 0
last = null
for elemento in array:
    if last==null:
        last = elemento
        continue
    if elemento - last > 1: //nao e sequencia
        if IN_SEQUENCIA:
            SEQUENCIAS += 1 //significa que terminou uma sequencia
        IN_SEQUENCIA=false
        if elemento - last > MAIOR_DIST://se for maior que a ultima maior distancia, atualiza
            MAIOR_DIST=elemento-last
    else:
        IN_SEQUENCIA=1

 print SEQUENCIAS, MAIOR_DIST