Convert Array of Numbers into a String of Ranges - powershell

Question

I was asking myself how easily you could convert an Array of Numbers Like = 1,2,3,6,7,8,9,12,13,15 into 1 String that "Minimizes" the numbers, so Like = "1-3,6-9,12-13,15".
I am probably overthinking it because right now I don't know how I could achieve this easily.
My Attempt:
$newArray = ""
$array = 1,2,3,6,7,8,9,12,13,15
$before
Foreach($num in $array){
If(($num-1) -eq $before){
# Here Im probably overthinking it because I don't know how I should continue
}else{
$before = $num
$newArray += $num
}
}

Answer 1

This should working, Code is self explaining, hopefully:
$array = #( 1,2,3,6,7,8,9,12,13,15 )
$result = "$($array[0])"
$last = $array[0]
for( $i = 1; $i -lt $array.Length; $i++ ) {
$current = $array[$i]
if( $current -eq $last + 1 ) {
if( !$result.EndsWith('-') ) {
$result += '-'
}
}
elseif( $result.EndsWith('-') ) {
$result += "$last,$current"
}
else {
$result += ",$current"
}
$last = $current
}
if( $result.EndsWith('-') ) {
$result += "$last"
}
$result = $result.Trim(',')
$result = '"' + $result.Replace(',', '","') +'"'
$result

Answer 2

I have a slightly different approach, but was a little too slow to answer. Here it is:
$newArray = ""
$array = 1,2,3,6,7,8,9,12,13,15
$i = 0
while($i -lt $array.Length)
{
$first = $array[$i]
$last = $array[$i]
# while the next number is the successor increment last
while ($array[$i]+1 -eq $array[$i+1] -and ($i -lt $array.Length))
{
$last = $array[++$i]
}
# if only one in the interval, output that
if ($first -eq $last)
{
$newArray += $first
}
else
{
# else output first and last
$newArray += "$first-$last"
}
# don't add the final comma
if ($i -ne $array.Length-1)
{
$newArray += ","
}
$i++
}
$newArray

Answer 3

Here is another approach to the problem. Firstly, you can group elements by index into a hashtable, using index - element as the key. Secondly, you need to sort the dictionary by key then collect the range strings split by "-" in an array. Finally, you can simply join this array by "," and output the result.
$array = 1, 2, 3, 6, 7, 8, 9, 12, 13, 15
$ranges = #{ }
for ($i = 0; $i -lt $array.Length; $i++) {
$key = $i - $array[$i]
if (-not ($ranges.ContainsKey($key))) {
$ranges[$key] = #()
}
$ranges[$key] += $array[$i]
}
$sequences = #()
$ranges.GetEnumerator() | Sort-Object -Property Key -Descending | ForEach-Object {
$sequence = $_.Value
$start = $sequence[0]
if ($sequence.Length -gt 1) {
$end = $sequence[-1]
$sequences += "$start-$end"
}
else {
$sequences += $start
}
}
Write-Output ($sequences -join ",")
Output:
1-3,6-9,12-13,15