Run-Length Racers

Question

You will be given two pieces of input: a string in run-length encoded format defining the running track, and a capital letter representing the lane to start from. For example, the string "3a4A6b5B" expands to "aaaAAAAbbbbbbBBBBB". You then use the expanded string to create a track, as such:

 A) aaaAAAA
 B) bbbbbbBBBBB

This is a track with two lanes. Lowercase letters represent air. You can not run on air! Uppercase letters represent road you can run on. Your goal for this challenge is, given a capital letter, output how far a racer starting on that lane could run. Racers are allowed to switch lanes if there is a piece of road directly above or below them. They are also allowed to run backwards! On this particular track the output is 0 for any letter input, because neither of the tracks has runnable road at position 1.

Examples:

Input: "4A5B4c3C", "A"

This code expands to a track that looks like this:

A) AAAA
B) BBBBB
C) ccccCCC

The output for this example is 7, because a runner starting on lane A could move down to lane B, and then lane C, and end up at the 7th position.

Input: "4A2B3D", "D"

Track:

A) AAAA
B) BB
C)
D) DDD

The output is 3, because a runner starting on lane D has no way to get to lane B or A

Input: "4A4a4A3b6B5C", "A"

Track:

A) AAAAaaaaAAAA
B) bbbBBBBBB
C) CCCCC

The output is 12, because the runner on A can switch over to B, and then come back to A at the end. The max distance for "C" is also 12. For "B" it is 0.

Input: "12M4n10N11O", "M"

Track:

M) MMMMMMMMMMMM
N) nnnnNNNNNNNNNN
O) OOOOOOOOOOO

Simple example with multi-digit run-lengths. Output is 14.

Input: "4A5B1b2B4c3C", "A"

Track:

A) AAAA
B) BBBBBbBB
C) ccccCCC

The output is 8, because the runner at A can go down to B, then down to C, then come back to B. (Thank you to FryAmTheEggman for this example.)

Input: "1a2A2a2B1c1C1d3D", "B"

Track:

A)aAAaa
B)BB
C)cC
D)dDDD

Output is 4. Runner has to check both paths two see which goes further. (Thanks to user81655 for this example.)

Input: "2A1b1B2C1D3E","A"

Track:

A) AA
B) bB
C) CC
D) D
E) EEE

Output is 3. You have to run backwards to reach the furthest destination. (Once again, thanks to user81655 for this example.)

Notes:

• If a track does not have a letter at a certain position, that counts as air too. As such, if the input is "Q" and no road has been placed on lane "Q" the output should be 0.
• There are two pieces of input. The first is a run-length encoded string. The second is a capital letter (you can use string or char datatype for this.) For readability, there should be some reasonable separator between these inputs (space, new line, tab, comma, semi-colon).
• The run-length encoded string will always list elements in alphabetical order
• The very longest the entire length of a lane can be is 1000. Therefore, the greatest possible output is 1000.

Track Generator:

In honor of our first answer, here is a track generator. Try to come up with something to stump the current answers! (Note: Just because the generator doesn't show an error message doesn't mean your track code is necessarily valid. See above examples for proper form.)

function reset() {
    var t = document.getElementById("track");
    t.innerHTML = "";
    for(var i = 0;i<26;i++) {
      var c = String.fromCharCode(i+65);
      t.innerHTML += "<div><span>"+c+") </span><span id='"+c+"'></span></div>";
      
    }
  }

function rand() {
  var track = "";
  for(var i = 0;i<26;i++) {
  var blocks = Math.floor(Math.random()*4);
  var start = Math.floor(Math.random()*2);
  for(var j = 0;j<blocks;j++) {
    var letter = String.fromCharCode(65+i+32*((start+j)%2));
    var length = Math.floor(Math.random()*4)+1;
    track += length+letter;
  }
  }
  document.getElementById("code").value = track;
}

  function gen() {
  var s = document.getElementById("code").value;
    var check = s.match(/(\d+[A-Za-z])+/);
    if(check == null || check[0]!=s) {
      alert("Invalid Track");
      return false;
    }
    reset();
  var n = s.match(/\d+/g);
    var o = s.match(/[A-Za-z]/g);
    for(var i = 0;i<n.length;i++) {
      var c = o[i].toUpperCase();
      document.getElementById(c).textContent += o[i].repeat(n[i]);
    }
    return true;
    }

<body onload="reset()">
Track: <input type="text" id="code" size="75%" /><input type="submit" onclick="gen()" /><input type="button" value="Random Track" onclick="rand()" /><code id="track"/>
  </body>

Answer 1

JavaScript (ES6), 298 334 bytes

(t,s)=>[a=[],t.match(/\d+(.)(\d+\1)*/gi).map(l=>a[c=l.match`[A-Z]`+"",n=c.charCodeAt(),c==s?i=n:n]=l[r="replace"](/\d+./g,p=>(p.slice(-1)<"a"?"1":"0").repeat(parseInt(p))),i=o=-1),...a.join``,a[i]?a[i]=a[i][r](/^1/,2):0].map(_=>a.map((l,y)=>a[y]=l[r](/1/g,(c,x)=>((a[y-1]||s)[x]|(a[y+1]||s)[x]|l[x-1]|l[x+1])>1?(x>o?o=x:0,2):c)))&&o+1

Explanation

Basically this solution treats the track as a maze. It finds where all the tiles that are possible for the runner to reach are and returns the greatest value of the X index it found.

The first thing it does is decode the input string into an array of lines. Instead of using letters though, it turns a capital letter into a 1 and a lowercase letter into a 0. The resulting map will look something like this:

11100011
0011100
100111

After this it makes the first tile of the starting track a 2 (only if it is already 1) and loops through every tile checking adjacent tiles for a 2. If a 1 has an adjacent 2 it becomes a 2. The above map will become this if the runner started on the first line:

22200011
0022200
100222

The highest X index for a 2 becomes the result.

I made a very minor oversight when I did the initial version of this and it cost me 36 bytes to hack at it until it worked, so there's probably a lot of improvements that could be made to this. *sigh*

Ungolfed

(t,s)=>
  [

    // Decode run-length encoded string into an array of track lanes
    a=[],                           // a = array of track line strings, 0 = air, 1 = tiles
    t.match(/\d+(.)(\d+\1)*/gi)     // regex magic that separates pairs by their letter
    .map(l=>                        // for each line of pairs
      a[                            // add the tiles to the array
        c=l.match`[A-Z]`+"",        // c = pair character
        n=c.charCodeAt(),           // n = index of line
        c==s?i=n:n                  // if this line is the starting line, set i
      ]=l[r="replace"](/\d+./g,p=>  // match each pair, p = pair
        (p.slice(-1)<"a"
          ?"1":"0").repeat(         // repeat 0 for air or 1 for ground
            parseInt(p)             // cast of match would return NaN because of the
          )                         //     letter at the end but parseInt works fine
      ),
        i=                          // i = index of starting line, initialise as invalid
          o=-1                      // o = output (max value of x)
    ),

  // Find all positions that are possible for the runner to get to
    ...a.join``,                   // add every letter of the track lines to an array
    a[i]?a[i]=a[i][r](/^1/,2):0    // set the starting tile to 2 if it is already 1
  ].map(_=>                        // loop for the amount of tiles, this is usually way
                                   //     more than necessary but allows for hard to reach
                                   //     tiles to be parsed
    a.map((l,y)=>                  // for each line l at index y
      a[y]=l[r](/1/g,(c,x)=>       // for each character c at index x

        // Replace a 1 with 2 if there is a 2 to above, below, left or right of it
        ((a[y-1]||s)[x]|(a[y+1]||s)[x]|l[x-1]|l[x+1])>1?
          (x>o?o=x:0,2):c          // set o to max value of x for a 2 tile
      )
    )
  )
  &&o+1                            // return o + 1

Test

Bonus: Output includes the parsed map!

var solution = (t,s)=>[a=[],t.match(/\d+(.)(\d+\1)*/gi).map(l=>a[c=l.match`[A-Z]`+"",n=c.charCodeAt(),c==s?i=n:n]=l[r="replace"](/\d+./g,p=>(p.slice(-1)<"a"?"1":"0").repeat(parseInt(p))),i=o=-1),...a.join``,a[i]?a[i]=a[i][r](/^1/,2):0].map(_=>a.map((l,y)=>a[y]=l[r](/1/g,(c,x)=>((a[y-1]||s)[x]|(a[y+1]||s)[x]|l[x-1]|l[x+1])>1?(x>o?o=x:0,2):c)))&&o+1
function generateMap() { var start = 0; a.some((l, i) => l ? start = i : 0); var end = 0; a.map((l, i) => l && i <= 90 ? end = i : 0); for(var output = "", i = start; i < end + 1; i++) output += String.fromCharCode(i) + ") " + (a[i] || "") + "\n"; return output; }

Track = <input type="text" id="track" value="2A1b1B2C1D3E" /><br />
Starting Letter = <input type="text" id="start" value="A" /><br />
<button onclick="result.textContent=solution(track.value,start.value)+'\n\n'+generateMap()">Go</button>
<pre id="result"></pre>

Answer 2

Perl, 231 219 203 192 189 bytes

includes +1 for -p

sub f{my($l,$p,$m)=@_;map{$m=$_>$m?$_:$m}f($l,$p+1)+1,f($l-1,$p),f($l+1,$p),f($l,$p-1)-1if$L[$l][$p]&&!$V{$l}{$p}++;$m}s/(\d+)(.)\s*/push@{$L[ord$2&~32]},(0|$2lt'a')x$1;()/ge;$_=0|f(ord,0)

Less golfed:

sub f{                          # this is a recursive function, so we need locals.
    my($l,$p,$m)=@_;            # in: lane, position; local: max path length

    map{
      $m = $_ > $m ? $_ : $m    # update max
    }
    f( $l,   $p+1 )+1,          # same lane, forward
    f( $l-1, $p   ),            # left lane, same pos
    f( $l+1, $p   ),            # right lane, same pos
    f( $l,   $p-1 )-1           # same lane, backtrack
    if
        $L[$l][$p]              # check if there's road here
    && !$V{$l}{$p}++            # and we've not visited this point before.
    ;

    $m                          # return the max
}

s/(\d+)(.)\s*/                  # Parse RLE pattern, strip starting lane separator
  push@{ $L[ord$2&~32] }        # index @L using uppercase ascii-code, access as arrayref
  ,(0|$2lt'a')x$1               # unpack RLE as bitstring
  ;()                           # return empty list for replacement
/gex;                           # (x for ungolfing)
                                # $_ now contains trailing data: the start lane.

$_ =                            # assign output for -p
   0|                           # make sure we print 0 instead of undef/nothing
   f(ord,0)                     # begin calculation at start of current lane

Running

Store the code above in a file (say 231.pl). Input in the form of (\d+\w)+ *\w. Example: inputting track 4A5B4c3C and lane A:

echo 4A5B4c3C A | perl -p 231.pl

TestSuite

(not golfed)

printf "==== Testing %s\n", $file = shift // '231.pl';

sub t{
    my($input,$expect) = @_;
#   $input =~ s/\s//g;
    printf "TEST %-20s -> %-3s: ", $input, $expect;

    $output = `echo $input | perl -p $file`;

    printf "%-3s  %s\n", $output,
    $output == $expect
    ? " PASS"
    : " FAIL: $output != $expect";

}

t("4A5B4c3C A", 7);
t("4A5B4c3C C", 0);
t("4A2B3D D", 3);
t("4A4a4A3b6B5C A", 12);
t("4A4a4A3b6B5C B",  0);
t("4A4a4A3b6B5C C", 12);
t("12M4n10N11O M", 14 );
t("4A5B1b2B4c3C A", 8);
t("1a2A2a2B1c1C1d3D B", 4 );
t("2A1b1B2C1D3E A", 3 );
t("10A9b1B8c2C9D1E11F A", 11);

• update 219 save 12 bytes by reworking array indices.
• update 203 Save 16 bytes by refactoring recursion.
• update 192 save 11 bytes by eliminating the @L=map{[/./g]}@L postprocessing.
• update 189 save 3 bytes by postfixing if using map instead of for.