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Question

Oh no, I am lost on the way to finding the great treasures of Marakov! And all I have are these useless instructions that look like S10R10D30... I have no idea what they mean! Can you help me?

Challenge

Given directions consisting of N E S W U D L R 1 2 3 4 5 6 7 8 9 0, output how far I will be from where I started when I follow those directions (i.e. Euclidean Distance).

N E S W refer to me turning North, East, South, and West;

U D L R refer to me turning Up, Down, Left, and Right (So NR is the same as E, and so is SL; SLL is the same as N). Up means keep going forward; Down means turn around.

After each letter direction will be a number, which is how far I will go in that direction. N10E20 means go North 10 units, then turn East, and go East 20 units.

Input Details

• Input will always start with one of NESW (so blank input need not be accounted for).
• Two letter instructions in a row are allowed. NE should be interpreted, "Turn North, then immediately turn East". It's the same as just E. SLL is "Turn South, then immediately turn Left twice". It's the same as N.
• All numbers will be integers (note how . isn't in the character set)
• Input will only consist of NESWUDLR1234567890 (If it needs something else, like '\0' in C; or if your language's input functions has a trailing newline, or something, that's fine.)

Output

• The norm.
• If using a function, should output a numeric datatype or a string.
• Must be accurate to 3 decimal places.

Test Cases

• N10: 10
• N10E10: 14.1421
• N10S10: 0
• NSEWUDLR10: 10
• N100RR20E300D40L12: 268.7452
• ERR10LL20UN30D100: 70.71067

The unimaginative Python program I used to make these.

Winning

This is codegolf, so lowest bytes after a week wins!

Answer 1

Python 3, 137 bytes

v=n=0
d=1
for i in input()+'U':x="NUERSDW0123456789".find(i);c=x<7;v+=d*n*c;n=[n*10+x-7,0][c];d=[d,d**(x%2)*1j**(~-x/2)][c]
print(abs(v))

Try it online!

-9 bytes thanks to Jonathan Allan

Answer 2

(Go)Ruby, 111 bytes

x=0
c=1,1i,-1,-1i
gs.sc(/(\w)(\d*)/){|o,a|x+=c.ro!('URDL'.ix(o)||'NESW'.ix(o)+c.ix(1)).fs*a.toi}
p Mh::hy *x.rc

Try it online!

Takes input on STDIN, outputs it on STDOUT.

Basically, this approach uses complex numbers to store the current position, as well as a stack (c), containing offsets for each direction. If a direction is in URDL, the stack is rotated by the index of the direction in that string; if the direction is in NESW, it's rotated by the index of the direction in that string, plus the index of 1 in the stack. This transforms a rotation relative to the current position into a rotation relative to the position of 1. In any event, the top of the stack is multiplied by the number of steps in the direction and added to the current position.

Answer 3

JavaScript (ES6), 148 142 140 138 137 134 bytes

s=>s.replace(/\d+|./g,_=>~(i='NESW'.search(_))?d=i:~(i='URDL'.search(_))?d+=i:a[d&3]+=+_,a=[0,0,0,0])&&Math.hypot(a[1]-a[3],a[0]-a[2])

f=

s=>s.replace(/\d+|./g,_=>~(i='NESW'.search(_))?d=i:~(i='URDL'.search(_))?d+=i:a[d&3]+=+_,a=[0,0,0,0])&&Math.hypot(a[1]-a[3],a[0]-a[2])

for(test of [
  'N10',
  'N10E10',
  'N10S10',
  'NSEWUDLR10',
  'N100RR20E300D40L12',
  'ERR10LL20UN30D100',
]) console.log(f(test))

-2 bytes: Use .search() instead of .indexOf() (@Shaggy)

-1 byte: Rearrange program to remove enclosing parentheses (@Shaggy)

-3 bytes: Use .replace() instead of .match().map() (@ThePirateBay)

Answer 4

Perl 5, 149 + 1 (-p) = 150 bytes

while(s/(\D+)(\d+)//){$p=/N/?0:/E/?1:/S/?2:/W/?3:/L/?$p-1:/R/?$p+1:/D/?$p+2:$p for split//,$1;$m[$p%4]+=$2}$_=sqrt(($m[0]-$m[2])**2+($m[1]-$m[3])**2)

Try it online!

Explained:

# Each direction is assigned a number:
#
#     0     North
#     1     East
#     2     South
#     3     West
#
# Variables:
#     $p     present direction
#     @m     total movement in each direction
# Inside loop:
#     $1     a set of direction instructions
#     $2     distance

while(s/(\D+)(\d+)//)    # Remove and preserve the first direction set and distance
   for split//,$1        # Loop through individual letters to set new direction
      $p=/N/?0:          # North
         /E/?1:          # South
         /S/?2:          # East
         /W/?3:          # West
         /L/?$p-1:       # Turn left
         /R/?$p+1:       # Turn right
         /D/?$p+2:       # Turn around
         $p              # Do not change direction
   $m[$p%4]+=$2          # Add the directional movement to previous movements

   $_=sqrt(              # Calculate distance
       ($m[0]-$m[2])**2  # Net North/South movement
      +($m[1]-$m[3])**2  # Net East/West movement
      )