Ruby, 75 65 bytes

->s,h{a=['']*h;x=-k=1;s.map{|c|a[x+=k=h-x<2?-1:x<1?1:k]+=c};a*''}

Try it online!

Takes input as an array of chars, returns string

How it works:

• Create h strings
• For each character in the input string, decide which string to put it in based on its index (the index of the string to be modified goes up until h and then down until 0 and so on)
• Return all the strings joined together

Uiua, 15 bytes

⊕⊂↯△,⊂:⇌+1∩⇡-2.

Try it: Uiua pad

For the input 5, this makes the array:

[0 1 2 3 4 3 2 1]

The array is then repeated to the length of the string, and used to group the string.

Japt, 12 11 10 bytes

Dunno why I deleted this! It was a long time ago.

ñÏgVo ê ÅÔ

Try it (includes all test cases)

ñÏgVo ê ÅÔ     :Implicit input of string U & integer V
ñ              :Sort U by
 Ï             :Passing each 0-based index through the following function
  g            :  Modularly index into
   Vo          :    Range [0,V)
      ê        :    Palindromise
        Å      :    Remove first element
         Ô     :    Reverse

Note: If V=1 then Vo will produce an empty array and the sorting function will return undefined for each character, preserving the original order of the string.

Red, 147 bytes

func[s n][i: v: m: 1 foreach k sort collect[forall s[keep/only reduce[v i s/1]v: v + m
if all[n > 1(i: i + 1)%(n - 1)= 1][m: 0 - m]]][prin last k]]

Try it online!

Red, 153 bytes

func[s n][i: v: m: 1 b: collect[foreach c s[keep/only reduce[v i c]v: v + m
if all[n > 1(i: i + 1)%(n - 1)= 1][m: -1 * m]]]foreach k sort b[prin last k]]

Try it online!

Explanation:

f: func [ s n ] [                      ; s is the string, n is the height
    i: 1                               ; index of the current character in the string
    v: 1                               ; value of the "ladder"
    m: 1                               ; step (1 or -1)
    b: collect [                       ; collect the values in a block b
        foreach c s [                  ; foreach character in the string 
            keep/only reduce [ v i c ] ; keep a block of the evaluated [value index char] 
            i: i + 1                   ; increase the index
            v: v + m                   ; calculate the value 
            if all [ n > 1             ; if height is greater than 1 and
                    i % (n - 1) = 1    ; we are at a pick/bottom of the ladder
                   ]
                [ m: -1 * m ]          ; reverse the step
        ]
    ]
    foreach k sort b [ prin last k ]   ; print the characters in the sorted block of blocks
]

Perl 5 -lF, 58 bytes

$#a=<>-1;map$_.=shift@F,@a,reverse@a[1..@a-2]while@F;say@a

Try it online!

05AB1E (legacy), 11 8 bytes

Σ²Lû¨¾è¼

Inspired by @LuisMendo's MATL answer.
-3 bytes thanks to @Adnan

Try it online. (No test suite, because the legacy version of 05AB1E didn't had a reset for the counter_variable.)

Explanation:

Σ           # Sort the (implicit) input-string by:
 ²L         #  Create a list in the range [1, second input-integer]
            #   i.e. 5 → [1,2,3,4,5]
   û        #  Palindromize it
            #   i.e. [1,2,3,4,5] → [1,2,3,4,5,4,3,2,1]
    ¨       #  Remove the last item
            #   i.e. [1,2,3,4,5,4,3,2,1] → [1,2,3,4,5,4,3,2]
     ¾è     #  Index into it (with wraparound) using the counter_variable (default 0)
            #   i.e. counter_variable = 0 → 1
            #   i.e. counter_variable = 13 → 4
       ¼    #  And after every iteration, increase the counter_variable by 1

NOTE: The counter_variable is used, because in the Python Legacy version of 05AB1E, the Σ didn't had an index N, which it does have in the new Elixir rewrite version of 05AB1E. So why do I still use the Legacy version? Because in the Elixir rewrite it has a bug and doesn't sort for \$n=1\$, which would all result in an empty list [] after the indexing. All other test cases work as intended with Σ²Lû¨Nè: try it online, but the test case with \$n=1\$ times out without result, even with --no-lazy argument flag: try it online.

C, 142 134 bytes

8 bytes saved thanks to Jonathan Frech

Code:

t;i;j;d;f(s,n)char*s;{for(t=strlen(s),i=0;i<n;i++)for(j=0;j+i<t;j=d+i+(n<2))d=j-i+2*~-n,putchar(s[i+j]),i>0&i<n-1&d<t&&putchar(s[d]);}

Explanation:

// C variable and function declaration magic
t;i;j;d;f(s,n)char*s;{
    // Iterate through each "row" of the string
    for(t=strlen(s),i=0;i<n;i++)
        // Iterate through each element on the row
        // Original index iterator here was j+=2*(n-1), which is a full "zig-zag" forward
        // The (n<2) is for the edge case of n==1, which will break the existing logic.
        for(j=0; j+i<t; j=d+i+(n<2))
            // If j+i is the "zig", d is the "zag": Original index was d=j+i+2*(n-i-1)
            // Two's complement swag here courtesy of Jonathan Frech
            d=j-i+2*~-n,
            putchar(s[i+j]),
            // Short circuit logic to write the "zag" character for the middle rows
            i>0 & i<n-1 & d<t && putchar(s[d]);
}

Try it online!

Ruby, 84 bytes

->s,n{r=['']*n;[*0...n,*(2-n)..-1].map{|x|r[x.abs]+=s.slice!(0)||''}while s[0];r*''}

Try it online!

Powershell, 99 95 bytes

param($s,$n)$r=,''*$n
$s|% t*y|%{$r[((1..$n+$n..1)*$s.Length|gu)[$i++*($n-gt1)]-1]+=$_}
-join$r

Test script:

$f = {

param($s,$n)$r=,''*$n
$s|% t*y|%{$r[((1..$n+$n..1)*$s.Length|gu)[$i++*($n-gt1)]-1]+=$_}
-join$r

}

@(
    ,("1234567", 3            ,     "1524637")
    ,("qwertyuiop", 1         ,     "qwertyuiop")
    ,("codegolf", 3           ,     "cgoeofdl")
    ,("elephant", 4           ,     "enlatehp")
    ,("programmingpuzzles", 5 ,     "piermnlsomgzgapzru")
) | % {
    $s,$n,$e = $_
    $r = &$f $s $n
    "$($r-eq$e): $r"
}

Output:

True: 1524637
True: qwertyuiop
True: cgoeofdl
True: enlatehp
True: piermnlsomgzgapzru

Explanation

The script:

• creates an array of rows,
• fills rows with appropriate values,
• and returns the joined rows.

The expression ((1..$n+$n..1)*$s.Length|gu generates a sequence like 1,2,3,3,2,1,1,2,3,3,2,1... and removes adjacent duplicates. gu is alias for Get-Unique.

• For $n=3 the deduplicated sequence is: 1,2,3,2,1,2,3,2,1...
• For $n=1 the deduplicated sequence is: 1

The expression $i++*($n-gt1) returns an index in the deduplicated sequence. =$i++ if $n>1, otherwise =0

R, 68 bytes

function(s,n)intToUtf8(unlist(split(utf8ToInt(s),-(n:(2.9-n)-1)^2)))

Try it online!

• -10 bytes thanks to @Giuseppe
• -17 bytes because I was silly
• -9 bytes and n=1 case fixed thanks to @J.Doe
• -3 bytes thanks to @JayCe

I have two solutions to the problem. The first solution I did first then I thought of another way to do it that I thought would save bytes but it didn't so I included it anyway.

Solution 1

PHP, 152 144 116 bytes

<?php
for($i=0;$i<$n=$argv[2];$i++)
    for($j=$i;$s=$argv[1][$j];$j+=$n<2|(($f=!$f|!$i)?$i<$n-1?$n+~$i:$i:$i)*2)
        echo $s;

• 8 bytes thanks to @JoKing
• 28 bytes thanks to @Shaggy

Try it online!

Solution 2

PHP, 162 bytes

<?php
$s=$argv[0];
$n=$argv[1];
$l=strlen($s);
for($i=0;$i<$l;){
    for($j=0;$j<$n&&$i<$l;)
        $a[$j++].=$s[$i++];
    for($j=$n-2;$j>0&&$i<$l;)
        $a[$j--].=$s[$i++];
}
echo join($a);

Try it online!

K ( Kona ), 23 bytes

A translation of the J answer by Galen

{y@<(#y)#-1_(!x),|!x-1}

J, 54, 29, 27 26 bytes

-1 byte thanks to hoosierEE

([\:#@[$[:}:|@i:@<:@]) ::[

Try it online!

Pyth, 22 21 bytes

|seMhD,V*lz+PUQP_UQzz

Takes input as n followed by s on separate lines. Try it online here, or verify all the test cases at once here.

|seMhD,V*lz+PUQP_UQzz   Implicit: Q=eval(input()), z=remaining input
                        
             UQ         Range [0-Q)
            P           All but last from the above
                         e.g. for Q=3, yields [0,1]
               P_UQ     All but last of reversed range
                         e.g. for Q=3, yields [2,1]
           +            Concatenate the previous two results
                          e.g. for Q=3, yields [0,1,2,1]
        *lz              Repeat len(z) times
      ,V           z    Vectorised pair the above with z, truncating longer to length of shorter
                          e.g. for Q=3, z=WATERMELON, yields:
                          [[0,'W'],[1,'A'],[2,'T'],[1,'E'],[0,'R'],[1,'M'],[2,'E'],[1,'L'],[0,'O'],[1,'N']]
    hD                  Sort the above by the first element
                          Note this is a stable sort, so relative ordering between equal keys is preserved
  eM                    Take the last element of each
 s                      Concatenate into string
                          Note that if n=1, the result of the above will be 0 (sum of empty array)
|                   z   If result of above is falsey, yield z instead

Edit: saved a byte by moving the empty check to the end of processing. Previous version: seMhD,V*lz|+PUQP_UQ]0z

Python 2, 119 108 98 92 91 97 93 91 90 bytes

lambda s,n:''.join(c*(j%(2*n-2or 1)in(i,2*n-i-2))for i in range(n)for j,c in enumerate(s))

Try it online!

_{-1 byte, thanks to Jonathan Frech}

APL (Dyalog Classic), 23 bytes

{⍺[⍋(≢⍺)⍴(¯1↓⊢,1↓⌽)⍳⍵]}

Try it online!

JavaScript (ES6), 75 bytes

Shorter formula suggested by @MattH (-3 bytes)

Takes input as (string)(n).

s=>n=>--n?[...s].map((c,x)=>o[x=x/n&1?n-x%n:x%n]=[o[x]]+c,o=[])&&o.join``:s

Try it online!

JavaScript (ES7), 78 bytes

Saved 4 bytes thanks to @ETHproductions

Takes input as (string)(n).

s=>n=>--n?[...s].map((c,x)=>o[x=n*n-(x%(n*2)-n)**2]=[o[x]]+c,o=[])&&o.join``:s

Try it online!

J, 24 bytes

4 :'x\:(#x)$}:|i:<:y'::[

Try it online!

Explicit dyadic verb. Run it like 'codegolf' f 3.

How it works

4 :'x\:(#x)$}:|i:<:y'::[    x: string, y: height
4 :                         Define a dyadic verb:
               i:<:y        Generate a range of -(y-1) .. y-1
            }:|             Take absolute value and remove last
       (#x)$             1) Repeat to match the string's length
    x\:                     Sort x by the decreasing order of above
                     ::[    If 1) causes `Length Error`, return the input string instead

Normally, explicit function takes additional 5 bytes in the form of n :'...'. But if error handling is added, the difference goes down to 2 bytes due to the parens and space in (tacit)<space>::.

Perl 6, 49 bytes

->\n{*.comb.sort({-abs n-1-$++%(2*n-2||1)}).join}

Try it online!

Takes input as a curried function.

Explanation:

->\n{*.comb.sort({-abs n-1-$++%(2*n-2||1)}).join}
->\n{                                           }  # Take an number
     *.comb        # Turn the string into a list of chars
           .sort({                       })   # And sort them by
                           $++    # The index of the char
                              %(2*n-2||1)  # Moduloed by 2*(n-1) or 1 if n is 0
                       n-1-       # Subtract that from n-1
                   abs            # get the absolute value
                  -               # And negate to reverse the list
                                          .join  # and join the characters

The sequence that it is sorted by looks like this (for n=5):

(-4 -3 -2 -1 0 -1 -2 -3 -4 -3 -2 -1 0 -1 -2 -3 -4 -3 -2 -1)

JavaScript (Node.js), 83 bytes

c=>g=(s,d=c*2-2,r=d,n=o='')=>s&&([...s].map((c,i)=>i%d%r?n+=c:o+=c),o)+g(n,r-1,r-2)

Try it online!

Clean, 105 84 bytes

import StdEnv,Data.List
$s n=[c\\l<-[1..n],c<-s&m<-cycle([1..n]++[n-1,n-2..2])|m==l]

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SNOBOL4 (CSNOBOL4), 191 bytes

	S =INPUT
	N =INPUT
	A =ARRAY(N)
	A<1> =EQ(N,1) S	:S(O)
I	I =I + -1 ^ D
	S LEN(1) . X REM . S	:F(O)
	A<I> =A<I> X
	D =EQ(I,N) 1
	D =EQ(I * D,1)	:(I)
O	Y =Y + 1
	O =O A<Y>	:S(O)
	OUTPUT =O
END

Try it online!

Takes S then N on separate lines.

Explanation:

	S =INPUT			;* read S
	N =INPUT			;* read N
	A =ARRAY(N)			;* create array of size N
	A<1> =EQ(N,1) S	:S(O)		;* if N = 1, set A<1> to S and jump to O
I	I =I + -1 ^ D			;* index into I by I + (-1)^D (D starts as '' == 0)
	S LEN(1) . X REM . S	:F(O)	;* extract the first character as X and set S to the
					;* remaining characters, jumping to O when S is empty
	A<I> =A<I> X			;* set A<I> to A<I> concatenated with X
	D =EQ(I,N) 1			;* if I == N, D=1
	D =EQ(I * D,1)	:(I)		;* if I == D == 1, D = 0. Goto I
O	Y =Y + 1			;* increment the counter
	O =O A<Y>	:S(O)		;* concatenate the array contents until last cell
	OUTPUT =O			;* and print
END

Charcoal, 21 bytes

⭆ＮΦη¬⌊Ｅ²﹪⁺μ⎇νι±ι∨⊗⊖θ¹

Try it online! Link is to verbose version of code. Works by noting that indices \$ m \$ of the characters on line \$ i \$ satisfy the relation \$ m \pm i = 0 \pmod {2n - 2} \$. Explanation:

 Ｎ                      First input as a number
⭆                       Map over implicit range and join
   η                    Second input
  Φ                     Filter over characters
       ²                Literal 2
      Ｅ                 Map over implicit range
          μ             Character index
             ι ι        Outer index
              ±         Negate
            ν           Inner index
           ⎇            Ternary
         ⁺              Plus
                   θ    First input
                  ⊖     Decremented
                 ⊗      Doubled
                    ¹   Literal 1
                ∨       Logical Or
        ﹪               Modulo
     ⌊                  Minimum
    ¬                   Logical Not
                        Implicitly print

MATL, 16 bytes

Zv3L)t?yn:)2$S}i

Try it online! Or verify all test cases.

Explanation

Consider inputs 5, 'programmingpuzzles'.

Zv     % Input, implicit: number n. Symmetric range
       % STACK: [1 2 3 4 5 4 3 2 1]
3L     % Push [1 -1+1j]. When used as an index, this means 1:end-1
       % STACK: [1 2 3 4 5 4 3 2 1], [1 -1+1j]
)      % Index. Removes last element
       % STACK: [1 2 3 4 5 4 3 2]
t      % Duplicate
       % STACK: [1 2 3 4 5 4 3 2], [1 2 3 4 5 4 3 2]
?      %   If non-empty and non-zero
       %   STACK: [1 2 3 4 5 4 3 2]
  y    %   Implict input: string s. Duplicate from below
       %   STACK: 'programmingpuzzles', [1 2 3 4 5 4 3 2], 'programmingpuzzles'
  n    %   Number of elements
       %   STACK: 'programmingpuzzles', [1 2 3 4 5 4 3 2], 18
  :    %   Range
       %   STACK: 'programmingpuzzles', [1 2 3 4 5 4 3 2], [1 2 3 ··· 17 18]
  )    %   Index modularly
       %   STACK: 'programmingpuzzles', [1 2 3 4 5 4 3 2 1 2 3 4 5 4 3 2 1 2]
  2$S  %   Two-input sort: stably sorts first input as given by the second
       %   STACK: 'piermnlsomgzgapzru'
}      % Else. This branch is entered when n=1. The stack contains an empty array
       %   STACK: []
  i    %   Take input
       %   STACK: [], [], 'programmingpuzzles'
       % End, implicit
       % Display stack, implicit. Empty arrays are not displayed

Husk, 6 bytes

δÖK…¢ḣ

Try it online!

Works for n = 1 as well.

Explanation

δÖK…¢ḣ  Implicit inputs, say n=4 and s="WATERMELON"
     ḣ  Range: [1,2,3,4]
    ¢   Cycle: [1,2,3,4,1,2,3,4,1,2,3,4..
   …    Rangify: [1,2,3,4,3,2,1,2,3,4,3,2..
δÖK     Sort s by this list: "WEAMLTROEN"
        Print implicitly.

The higher order function δ works like this under the hood. Suppose you have a higher order function that takes a unary function and a list, and returns a new list. For example, Ö takes a function and sorts a list using it as key. Then δÖ takes a binary function and two lists, zips the lists together, applies Ö to sort the pairs using the binary function as key, and finally projects the pairs to the second coordinate. We use K as the key function, which simply returns its first argument and ignores the second.

Jelly, 8 bytes

6 byter fails for height 1; two bytes used to address it ...maybe a 7 can be found?

ŒḄṖȯ1ṁỤị

A dyadic link accepting a positive integer and a list of characters which yields a list of characters.

Try it online!

How?

ŒḄṖȯ1ṁỤị - Link: positive integer N; list of characters, T
ŒḄ       - bounce (implicit range of) N -> [1,2,3,...,N-1,N,N-1,...,3,2,1]
  Ṗ      - pop off the final entry         [1,2,3,...,N-1,N,N-1,...,3,2]
   ȯ1    - OR one                          if this is [] get 1 instead
     ṁ   - mould like T (trim or repeat to make this list the same length as T)
      Ụ  - grade-up (get indices ordered by value - e.g. [1,2,3,2,1,2] -> [1,5,2,4,6,3])
       ị - index into T

Haskell, 64 bytes

s#n=[c|m<-[0..n],(c,i)<-zip s.cycle$[0..n-1]++[n-2,n-3..1],i==m]

Try it online!

MBASIC, 146 159 155 bytes

1 INPUT S$,N:DIM C$(N):P=1:D=1:FOR I=1 TO LEN(S$):C$(P)=C$(P)+MID$(S$,I,1)
2 IF N>1 THEN P=P+D
3 IF P=N OR P=1 THEN D=-D
4 NEXT:FOR I=1 TO N:PRINT C$(I);:NEXT

Updated to handle n=1

Output:

? programmingpuzzles, 5
piermnlsomgzgapzru

? codegolf, 3
cgoeofdl

? elephant, 4
enlatehp

? 1234567, 3
1524637

? WATERMELON, 4
WEAMLTROEN

? qwertyuiop, 1
qwertyuiop

Japt, 16 bytes

¬üÏu´VÑ aV°ÃÔc q

Test it online!

Explanation

 ¬ üÏ   u´ VÑ  aV° Ã Ô c q
Uq üXY{Yu--V*2 aV++} w c q    Ungolfed
                               Implicit: U = input string, V = size of wave
Uq                             Split U into chars.
   üXY{            }           Group the items in U by the following key function:
       Y                         Take the index of the item.
        u--V*2                   Find its value modulo (V-1) * 2.
               aV++              Take the absolute difference between this and (V-1).
                                 This maps e.g. indices [0,1,2,3,4,5,6,7,...] with V=3 to
                                                        [2,1,0,1,2,1,0,1,...]
                                 The items are then grouped by these values, leading to
                                 [[2,6,...],[1,3,5,7,...],[0,4,...]].
                     w         Reverse the result, giving [[0,4,...],[1,3,5,7,...],[2,6,...]].
                       c       Flatten.
                         q     Join back into a single string.