# How many lights are on?

You are little speck on a Cartesian plane. Pondering your existence, you decide to roam around your plane and touch things. You notice that every coordinate pair you visit has a light switch. To entertain yourself, you decide to toggle every switch that you come across.

The Challenge: Create a program that will take an input of random length, using only the characters v,^,<, and >. These characters correspond to movements.

• < moves you one unit to the left
• ^ moves you one unit up
• > moves you one unit to the right
• v moves you one unit down

Using this randomly generated input, calculate how many switches will be left in the ON position, assuming you start at (0,0), all lights begin in the OFF state, and you don't turn on any lights until you make your first move. (Meaning, if you start at (0,0), and move up 1 unit to (0,1), there will now be 1 light on). If you come across a switch that is on the ON position, it will be turned OFF.

Test cases:

v>v<^^<v<<^<^><<>^^>>><v>vv^v>v^><><<^>><<<vvv^vvv>v>>v><vv^^<<>vv^^>v^<>>^^<^^>^^v<^>^<vvv^v^v><^<<v<<>><<>v>>^><^>^^<>>>>vv>^<<^<<><vvv<v^>>vvv>v^>>><<v^>^^^^v>>^>^v>v<vv^<>^<<v>vv>><^^<^><vv^^v<v<v^^^>v<^vv^v<><vv^^^>v^>v>vv<<^><v<^v><<v^^v>>v<vv<><^^^v<^v><><<^^<>^>><^^^>vv^<>>>>^<^<<<<>>>v<<v<v<vv><<vv<vv<^v^^^>>vv<>v>><<<v^>vv><v<<<v<<>^vvv^<v^v>^^v^v><<v^>>>v<v<v^>>>v><>>>^<><<<<>vv>v><v>v><^v<>v>>>vv<<>^>^>v<^><^<^vv^><^^>v<^^v>v^v<^^^^vv<>v<>><v^^><>v<<<>v^<v^^><>^<>^<>><>^^<>^v><>>><v<^^>>v>^^^<v

yields 125 lights on.

>>><^>>>^vv><^^v^<<<>>^<>>^<^>^<<^^v^<v^>>^<<><<>^v<^^^vv>v><^>>^<^<v><^v<^<<^^v><>>^v<^>^v<vvv<<<v^vv>>^vv>^^<>>vv>^<^>vv<>v^<^v<^^<v^^^<<^><><>^v>vvv<^vvv<vv><vv<^^v^^<^^>>><<<>^<>>><^<<<>><>^v><^^vv<>>><^^^<^>>>>v<v^><<>v<v<v^<<^><v^^><>v>^<>^^^vvv<v^>^^^^v>v<v>>>v^^<v<vv>><<>^vv><<vv<<>^^v>>v<^^v>><v<v<<>^^vv>>^v>v>v<>^>^v<>>><>v>v<<v<^<>>>vv>>v>^<>vv^v><><^v^>v<^^>v<^v>>v^>^>>v>v>^>^<^^>vv>>^vv<^><>^><<v^<><<^<^>^^vv^<<^^<^^v<v<>^>v>>>>>>vv<<v>^>vv^>^><^<^^><<vvvv>vvv<><<><v^vv><v^^<>^>><^vv<><>^>vv>>>vv^vv<<^v^^<<v^^>^>vvv<><<v>^>^>v<v>^<^^^^<^>^>><>>^^vv<>v<^>v><v<v^>>v<^v<vv>v^>v<v^<^^^^v<^<^<<v<<<v<v^^>vv^>><<<v>>^^^>^<^>>>v^v><^^vv^>><^^vv<vv<v^><>>^><<<>>^^v^v<<v^<vv^^^>><>>^v^^^>>^>^<<^>v>^^v>><>v>^>vv^^<vvvv<><^v>^><<>>><^<^v^<<vvv^v<<<<<><><<><><<v>v<v>v><^v^^vvv>><>^>^>^v<<vv^^^v^vv><v><><v<v<<>>>v<^<^v<<>^v<<^v<><>v>>^^>^<v^<<^v^^^vv>><v^<v>^v><^<>>>>^^<vv<>^^>^>v^v^^>><>^^<^v^<v<<v<^<<^^vv>v>^<vv<<^^v^vv^>^^<>v>^>^<>vv><v>>><<><<vv^^<vv<>>^v>^<<vv>^><<>^<v>v><<v^<v<><v>^<^<^><^^^^>>>^<>^^><>>v^<vv^<^<<vvvv>>>v^v>>^>v^><<>>v<>>^>><vvvvv<<vvvv<v>^v<vv^<>><<><v^^<^<v>^v<^<<>^v<v^<>v<<>^<<vvv><^><^^^<>>v^<<>vv><^^^>><^>v^v>v<v^>>v>>v>vv<<v<<vvv^^^>^<v^^<^<v<^<>>v^<<v>>v^><v<vvvvv^^^<v^^<><v<<^>>^><^<v^v^^>><v><>v>^<vvvv><<v^^v^>^>v>><>^^v>v^>vv^>v<^<<^vv^>vv^<v>^<v^<>^v>v^>v^<<>^^<^>^^>vv^>>vv>v>vvv><>^v<<<<v^>v^^v<><v<v>^<^><^><<v<>><<>v^^>>><<><>>><<>><v^^>><^>><^<>v^^vvv>v<^<<vv^>vv^><<>v><>^<>v^^v>^>v^<>^><v>^><<^v<v^^<v>><^^>>^<^<^v<v>^>^<^<v><><>>>><>^<^<v>v<v^>v><>v^>v^<<><^<>>v<^vv^^^>^<<<<>^>^<><^vvv>^^<v^v>v>v^v>v>>vv>^><>^vv>^<v<v^<>vv^<v<><>^>>vvv><>>^<<v^<<>^<v^>v<^^^<^<^^<>^>>v>^<v>vv<v^^>><<<<<>>v>^v>^>>>>v>>^^>^<<<^<<<v>>^><<<<^vv<<>^v<^>v^<v<<>v<>^<^<^<^<>>^^^vvv<v>^vv>^><^<v^>^v<v>><><vvv<^^>>v<^v>^>>>><v^<v^^<^^v<vvv<v>^^<<>><^<v^v<^vv>v>vv>^^<>^^^^>>^v><vv<<<v>^v^>>v^>><<<^v^v<<>><<vvvvv<v^vv>vvvv><v^v<^^^><vv^^<>><>><^>^^^^v>v><><v^<>^v<>^^<^^>^^^vvv>>vv^v^<v<vv^v>v>>>^v^^vv^<^v>v^v>>^v>v<v^<^^><vvv>><<>><>><v>v<^<v>>>>v^^v^^>^><<v><^<<>>v<>^^<<>vv^>>vv^^^v>>>^v^><v<<^>v<v><>>>^>>^<<>>^><<vv<^^>^^^v^^<>>>vv><<>v<><<<>v<<>>>v<>v<>^<vv^v<^^<<<v>^v>>^^>^><<^vv<><><>v>^v>^<>v>>^^^<^^>>vv>v<<<v^><<v><^v><>v<^<<^<>^vv>^><^^^^^<<v^^<>v>><^<v^^^vv>^v<>^<v<v>v>^><^<<^<>><^^>vv^<>^<>vv<>>v<vv^>><^^<^>v<><>vv<v<>>v><v^^^>^^^<<vv^><^^v>v>^<^>v^><<vvv>v^><vv<><^<><^>^v<><<v^<<><>^^^^<<^>>^>^v^>v>^<<^>vv^vv^v<>^<<^>v<^^<<v<v<<<^>vv^>><>v>><><v>v><v^><vvv>vv<<vvv>v^<<^v<^<><<^v>v<>>vv<<v^>v>v<<>>^vv^<^^^<^v>>^<vv>^<v>><>v>^^<<v^<>>>>>v^v>><>v^>>^<>>^<^vvv^^^<^v<><vvv^>^>v><<v>>^v>v<v>v^<v>v>^<>vvv>vvv^^<>vv>^^^^^>v<<^v<>>>><<<>>><vv>>^v^^v<v^>>>^>^v<^v>^v<>vv<><vvv^v<<<<v<vv>vv^<^vvv<^v>v^^vv<^>>>^^>>^^><>^>>v<>>>^^<<v<^<<<<<^^<v^^^<<>><<<^>^v^>vv<>>>^^v><<>^^^^<vvv><^^<>>>^><<^>><v>^<>^v^<vvvv^>>^><<>><^<v^>>vv^vv<^>>>><^>^v<^<v<^^<^<^><^<>>^<>v^v<<>v>v<>><<v<^v<<<^v<v<>><v<^<^>>v>v>><v^<v><>>>>>v^v>><^<^<v>><v^v>v<>v<v><<<>^^><>^^<^vv^^<>v><><><^>^^v^vv^<><>>>>v><>>^>^<<^<v<v^>v^^<v>>><<^^vv^^>><<^<vvvvv>><^>^>>^vv<><<>v>v^<<<^v<^^<<^vv>v<vvv><^v>vv^vvvv<^>^v^<<<<^v<<<>^vvv>^v><<>>v<v<^v^<>v>>^^v^vv>>>^v^^>>^<><><<<<^vv>>>>>v>v^>v<>><<<>^vv>^^^^<^^^>^^^^>^^^v^v><^>^>>>v<v<^<^^<<^v<<^<>vvv^^^^v^<<>vv>^^>>><^^v<^<<<v<>v<<><>v<><>^<v<<^>^^>><<v>^^><^^v<^<v^<^^<>^<>^v^>>^^v^v^<>v<>^<<<>^v^v>^<vvvv<>v<<>vv^<<>vv>>>>^<v><>>>v^><<>^v>><<>>^^v><^<>>vv^^^>vv^<^^v><v>>vvv^v<^v>v<<^^<>v^^^v^^>><v^>>v^v^vv<^>v^<^>^>v<v^><vvv^>^<>v<<^><^^<vv>v>>vv>v^>>^vvv>>v^>^^>vvv>>v><<>>^^v>v<v<><<<<^^v<^<>^v>><v^^^<>>vvv>v><<v>^^<^vvvv^v>v>^vv>^vv^^v><<>>^^>>v>>>^v><^>v<^^<>vv>v>v^^^>>^^^><<<<>>^>>^<^v<^<^<>^><v<<v>v<>^>>^<<v^^<v^vvvvv>>v^>>^^^<^^<><<><><>^v>vvv^>^^>v<^^>^<<^v^^^><>><<v<^^^<<<<>><>><<^^v><v^<<^v<v><<>^<v>^>^v>vv>><v^<^<v<v<v><^^^^>>><^<><^v^v<<<^>vv^<v^>^^v^>>><<<<^<>>><v>>>vv^>^^<v^v>>>v^<^<>vv>^v^^><<<v>v>v>><>>>v<^>^<>>^^<v^<<^<v^>><^v^><><v><><v^vvv<<>v>>><<><v>v<>>><^<^^v<v>^<<>^v>^>^>^^<^^><^>>>>><^^>vv>^<^^<><^>^<^^><^<v>v^>><^>^^^>>v^v<^>>^<v^<>^><><v>>^v<v^^^^v<^vv><^v>>^^^<>^<^<^>vv^v<<>vv>^<>v>^>^>vv^v<vv<^^^v<v>v>v^<^^^v><v<<<^^<><^^>>>><<^^v<<^>v<<vv^^^vv^vv^<v><>^v<v>>><vv^v<v^>>>>^<<<vv^>>v>^><<><<^<^><<vv^>v^>><>v^<<<>v^><>><<>>v><>v^<v><>^v>>><><>>>^vvv^v>vv>>>^^v^><<v<>>^^^v^^><<^v<><><v<<v<v<><<<v^<^^^<>v^^v<^^<<^>v<<v><^<<<<>><>^v>^<>^<^^v^vvv>^^<>^>><v^^vv^<>^<><<^^^v<^^^>>^^v>^>^<^>v><<^<>^v<><vv^vv<><<<<<<v<<v<<vv^<<^<^vvvv><v^v^v<>>>vvvvv^<vv^<^<>vv>^<><<v><>v^^<v<>>>vvv^><^<^>v^^<v>^<>>>^^v^<vv<<<<^><v<<<>v<<<v<>>^^^>^><>v>^v^>^<v^^><^v^^<^v^^>^v>>^^^<<><><<<>v>><^><>>>vvvv>v>>v>^^^^v<><vv<^<v^v>>^^vv<^>vvv>^v>>><v<v<v^<^>^^<vvv<vv<v>>^vv>^<<^<^<v>v^<vv^^^v>vv<v><v><v>^<v>>vv<>v>^^>v^^^<>v<>v^v<>^<><v><^>^<v^v><<^v^v^v<<v><<^^<^vv>^<^v><>v>><v^v^>><><><<<v<>v<^vv>v<v<<>^vvvvv^<<<^<vv><<><>v^<^v<<<^>v>v<v^<<^>v<<^<v><<<^>vv>v>^<^^v>>>><>vv>>vv>vvv<>^^<>^v^<>vvv<^^^vv>v><<<<vv^v><v^<^<<<><v<>^><<>^>v<^^<<>v>>v<<>><^^<<<^<^vv^^>v>v<>^^>>^v^vvv>^v^>v>>v>v>v>>vv^<><<<<>v^^>vv<^^v>>v<vv<^>>^<>^^v<><vv^<><v><v<<v^v<^^<^v^v<>v<<><vvv><<<^<^^<<>>^v>>>^v>>>v<>>^><<<><><<<v<vv<^<>v^^v^^>^<<^^^v^>^<<^>^>^>>>>v<v<v<>vv<<vv^<<^<vv>^^<^<<>><^v><><>^<v><v^>^v>^<^>^^><v><<^<v^^<<^><><v>v<>>><<^><v<^vvv^<<<>><<>^v^^><vv>vv<>^>^>vv<>v^<^<>vv><<>^<v<vv<^<^<><^vv<<^>>>v<>><<>>>^^^^<<^v>>v<vv>^^>v<v<vv^><<><>>>v>>^^v<^v^^>>v^<>>v^>><^<^^v<v<><<><>>^<>><^v<^^^^><>^>vv>>^vv<<>v<<<<<<><<<><<>><v><^^^<>>v<^><^vvv<>^>^^v>^<v><^v^vv^<<>v<<<<v>^vv>>v>vv<<^>^<>>vvv^<v<><>><>^^^^vvvvvvv<<>v<^><^^>vv^^<v<<^^<vvv<v<v<<>><<><v^^>><^<>^v^vv<<v<v<>><<>>>>>^vv<><v<>v><v>v>><v<v^vvvvv<><>v>>v<><<<^^<>^<^^<v>v^<vv>^vv^<>^<<^<vv><v<v>>v>^<>v^<<v^<v>^v<>><v>>>>^<<^^^v<^<>><^<><v>>vv^>^<^<^>>v^>^^^^>vvvvv>^v<^><^^<^^>^<^^^^^^^>v>>vv>v^^^v^^^<>v><^>>>v>^>^>^>vv<vv<^^>>^>>>v<>v><<^<<v^>^>>>>^^><^^<v<<<<>>v>v^v^^<>><v<^<<<<v^^^^<v<<<^>v>^^<vv<^^^^^v>^v^<v><>>^^>^v>^>^vv^v>v>v^>v>^>>^^^^>>^>>^><>><v>v>>><<^v^v^>^>^>>vv><<^>v<v<v^<<>>^v<<^v<<^><^>>^<v>^>vv>v>^^^>v^^<^<^^>vv>^^><v>>^v>^v<<^^^<<^v^>^<<^>vv^>>^<^v><<>v><^^^<^^>>vv>^vv>><^<<<^>vv^v>v<^<<<^<^<<><^^>>>v^<^^^>^<><^v>>^<<v<^v>>v^<^<^<^^^<v^><<vvv^<^v^vv^vv<v<<v<^<>^v>^^^<^^v<v<v><<<^<>^^^^v>v^v^v^v<v><v>>^v><vv^^^v>><<v^vvvv<<<^v<<><^>^<v^^v<>vvvv^vv<>^v<><>^^<>>vvv<^>><v^<<>v>v<>^v^>v^>><<>>^^<^v<>>^>^><>>^<v<v^^<^v><v^<v<><><^<<><v^v<<>vv<v<v<^>>><>vv^^<><<v<^^<<^<><^^^>^>>>^<^>>>^>><^^^<^v^^^v^v^v>v>v><vv>><vvv<<v><><^^>^v<v>><v><^><^<<>v^vv^v><^vv>^>>v<vv><^<^^v<^^vv<vv<v<v>v><v<vv<<>^^v^^v<<<^<>v^^^<><>>><^>v^^^v^vv<<<^>>v><^>v^<>>>>^<>^^vvv^^<><^>^^<><>^vvv^^<vv^>vv^^^^v<>vv<^^^v<<>><<vvvvv>v>^^^vv>><v><v<>vvvv<v^><^<>^>^<>v>v>v^vvvv<><^v>>>^^>><vvv<>^>^v^<vvv>v^vv^vv><>><>v^^v^vv<^v>vv>>v<v><^<<^v<>>^vv^<v>v><v>v>^v>^<v>^<<^>vv>v<^<^vv^<^><<<v<<^^vv<vvv><>v>v<vv^<><><^vvv>>vv<^^^v><^v><<^>^^v>^<>><v<>>^^<<<v><>^>^><vvvv<>^<<<><<<^<>>v^vv^>><^vv^^>^<v^<v>><^^>>>^v>^v<>^v<><^><vv>v^^^<^>>^<<^<^><<<^^<v<<^vv<^<>v<^<<^^<v<vv<<><v<v^<>^<>v>>v<^v>v<>^^vvv<>vv^v^<><v^vv^<^v^v><>^><v^<>>^^^<>>vv^<v>^^v><v<^>^^^^^^><>>vvv<<><><v<^>v<>v^v<<<<>v^>>>>^v>^^<v^>v><v^<^^v<<<<v<<<>^v<^>^v>v^^>v^^vvv>vv<>^>v><v<>^<vv><>>><<^>>><<v>v^^<^<<<<v^<>>>v<<<^v^vv<>^v>v<<<<>^^>><v><>v<v><^^>><>^>^>v>>><v>^vvvv<><><^>>^v^><<>^v<><><^><<<>v^^>v>^>v^<v^vv<>><^vv^^>^^><vv<<>v>v^^>><v^>^<^<>>>vv<>^>v>v^<>v<^<<v>>>^<>v^>v>>vv^^<>>v<v<<^<>v>v^<^^^>v^^>v>v>vv<^<v>v^^><<<v<><>^^<>v>v>^^v>v>v^v>>^<v^v>><>^^>^<>>>^vv^><v^<^>v^>^v><^>^^^vv^^v<>vv<>>^><<^v>^v^>>v>^v^<<^^^vv<<vvv>^vv^v<<<v^^<<><vv<>>^^vv>^^^vv>><><v>v<^v^>>>vv^><>><v<^v<>^><v<^^^^>><^<>v>^v<^vv>v>v<^<>v>v>^<vv>v<^>vvv<v^<vv<vv<>v>^><v^v<>>>>>v>><^v<>v>^v><v^v^vv<>^<vvv^>><v^<vvv^^<^vvv^v^<>><v>v^^v<><>v^^^v<<<^><v<<<>><<vv<<><vvv^v>>v^v<v^>>><<v<>^v><>vv<<v>v^vv>v^v<^<vv<><><^v>^<vv>v^^>>^^^><vv<><^>>>^<v^<<^^>^>vv^><v<vvv>^^>>>^><<vv>vv>^<>>^^><^v><<>^<<<v^>^

yields 1408 lights on.

To generate input, you may use the following Python script:

import random
length = random.randint(15, 10000)
walk = ''
chars = ['v', '<', '>', '^']
for i in range(length):
walk += random.choice(chars)
print(walk)

Standard scoring, winner is the smallest number of bytes.

• 4. 4 lights are on. – Beta Decay Aug 15 '16 at 20:36
• No, there are five. – CasperTheFriendlyCode Aug 15 '16 at 20:39
• Oh, people, don't be so harsh on a newcomer. – Leaky Nun Aug 15 '16 at 21:33
• The challenge looks pretty clear (and interesting) to me. Voting to reopen – Luis Mendo Aug 15 '16 at 21:51
• I don't see any harshness, just advice on what needs improving, and now the challenge is ready. Nice first challenge! – trichoplax Aug 15 '16 at 22:08

# MATL, 191817 13 bytes

5 bytes off thanks to @LeakyNun's idea (see his answer) of using the imaginary unit as a base for exponentiation.

Jj11\^Ys8#uos

Try it online! Test cases: 1, 2.

### Explanation

The code traces the path using unit steps in the complex plane. Then it counts how many times each position was visited, and outputs how many positions were visited an odd number of times.

J         % Push the imaginary unit, 1j
j         % Input string
11\       % Modulo 11. This gives 7 6 5 8 for > ^ < v
^         % 1j raised to those numbers, element-wise. This gives -1j for >, -1 for ^,
% 1j for < and 1 for v. So it gives the displacements in a "transposed"
% complex plane
Ys        % Cumulative sum. This transforms displacements into positions
8#u       % Count of occurrences of each unique position
o         % 1 if odd, 0 if even
s         % Sum. Implicitly display
• This looks curious – Leaky Nun Aug 15 '16 at 23:38
• If you mean the spacing, yes, it's ugly. On Matlab it does look better: 0+1i 0-1i -1+0i 1+0i – Luis Mendo Aug 15 '16 at 23:41
• No, that was golfing you 3 bytes – Leaky Nun Aug 15 '16 at 23:45
• @LeakyNun Yes, I just realized :-) 13 bytes now! – Luis Mendo Aug 15 '16 at 23:49
• Why use i instead of j? – Leaky Nun Aug 15 '16 at 23:54

# Python, 68 bytes

25 bytes thanks to Sp3000.

2 bytes thanks to Luis Mendo's idea of taking modulus with 11.

17 bytes thanks to xnor.

d=set()
p=0
for c in input():p+=1j**(ord(c)%11);d^={p}
print(len(d))

Ideone it!

• It's shorter to use a set doing d^={p} and len(d). – xnor Aug 16 '16 at 1:38

# Java 8, 169130 127 bytes

Thanks to Leaky Nun for saving 29 32 bytes.

s->{int l=s.length,d=2*l+1,p=l*d+d,r=0,m[]=new int[d*d];for(char c:s){p+=c<61?-1:c<63?1:c<95?-l:l;m[p]^=2;r+=m[p]-1;}return r;}

Ungolfed (sorta):

public static int f(char[] s) {
int l = s.length, d = 2*l+1, p=l*d+d, r = 0;
int[] m = new int[d*d];
for(char c : s) {
p += c<61 ? -1 : c<63 ? 1 : c<95 ? -l : l;
m[p] ^= 2;
r += m[p] - 1;
}
return r;
}
• for(char c:s){p+=c<61?-1:c<63?1:c<95?-l:l;m[p]^=2;r+=m[p]-1;} can be for(int c:s)r+=(m[p+=c<61?-1:c<63?1:c<95?-l:l]^=2)-1; to save 8 bytes: Try it online. – Kevin Cruijssen Jun 14 '19 at 8:42

# Jelly, 13 bytes

A port of Luis Mendo's answer in MATL

O%11*@ı+\œ^/L

Try it online!

O%11*@ı+\œ^/L
O             convert to codepoint
%11          modulo 11
*@ı       power of i (imaginary unit)
+\     cumulative sum
œ^/  reduce by multiset symmetric difference
L length

Credits of the œ^/ trick to Dennis

# Perl, 49 bytes

Includes +1 for -p Run with the control string on STDIN

./lights.pl <<< "<<>"

lights.pl:

#!/usr/bin/perl -p
$\-=1-($a{$x+=/</-/>/,$y+=/\^/-/v/}^=2)for/./g}{

If input is restricted to 10000 bytes this reduces to 44+1:

$\+=$#{$x+=/</-/>/.e5+/\^/-/v/}*=-1for/./g}{ # TSQL, 238235203 191 bytes Creating a table in memory using recursive SQL. Selecting and calculating from that table(one line code). Golfed: DECLARE @ varchar(max)= 'v>v<'; WITH C as(SELECT 0 a,b=1UNION ALL SELECT a+POWER(CHARINDEX(SUBSTRING(@,b,1),'> <v')-2,15),b+1FROM C WHERE b<=LEN(@))SELECT top 1sum(sum(1-1/b)%2)over()FROM c GROUP BY a OPTION(MAXRECURSION 0) Ungolfed: DECLARE @ varchar(max)= '>>>><^v^v'; WITH C as ( SELECT 0 a,b=1 UNION ALL SELECT a+POWER(CHARINDEX(SUBSTRING(@,b,1),'> <v')-2,15),b+1 FROM C WHERE b<=LEN(@) ) SELECT top 1sum(sum(1-1/b)%2)over() FROM c GROUP BY a OPTION(MAXRECURSION 0) Fiddle # Mathematica, 64 bytes A port of Luis Mendo's MATL answer. Count[{_,_?OddQ}]@Tally@Accumulate[I^Mod[ToCharacterCode@#,11]]& # SQF, 160 bytes Using the function-as-a-file format: x=0;y=0;a=[];{switch(_x){case"v":{y=y-1};case"^":{y=y+1};case"<":{x=x-1};case">":{x=x+1};};if([x,y]in a)then{a=a-[[x,y]]}else{a=a+[[x,y]]}}forEach _this;count a Call as: "STRING" call NAME_OF_COMPILED_FUNCTION Ungolfed: //position tracker variables x = 0; y = 0; //a keeps track of which coords are switched on a = []; { //switch based on the magic variable _x //which is the current element of the forEach //and adjust coord tracker variables switch(_x) { case "v": { y = y - 1 }; case "^": { y = y + 1 }; case "<": { x = x - 1 }; case ">": { x = x + 1 }; }; //check if the coord is already turned on if ([x, y] in a) then { //remove it from a using array exclusion a = a - [[x, y]] } else { //append it to a a = a + [[x, y]] } //do this for each character in _this (the argument) } forEach _this; //return the length of a count a • easily followed, but how is the performance? – zinking Aug 16 '16 at 9:35 • @zinking That depends on how you execute it. Really fast with a static compile at engine load time, much slower with compile "CODE". – Οurous Aug 16 '16 at 21:35 ## Python: 207189 181 Bytes a = input() l=[] for i in range(0,len(a)): if a[i]=='v':y-=1 if a[i]=='^':y+=1 if a[i]=='<':x-=1 if a[i]=='>':x+=1 if [x,y] in l:l.remove([x,y]) else:l.append([x,y]) print(l) Input is a string. Thanks to @LuisMendo for pointing out that I can actually only indent by 1 space. Darn my Python teachers for telling me to always do it increments of four. Fixing it so that input was obtained rather than assumed stored actually saved me 8 bytes. • I don't know Python, but I think 1-space indenting is enough, and it will save you a few bytes – Luis Mendo Aug 15 '16 at 22:34 • But not in code golf :-) – Luis Mendo Aug 15 '16 at 22:37 • You can't assume that the input is pre-stored. Just use input() and store it somewhere – Leaky Nun Aug 15 '16 at 23:02 • If you ever need more than one level of nested indentation, there's a great tip about mixing spaces and tabs – trichoplax Aug 15 '16 at 23:10 • Um... Maybe removing the whitespace around the first = and l+=[[x,y]] is also shorter then l.append([x,y]). – Mega Man Aug 18 '16 at 18:22 # Ruby, 64 + 6 = 70 bytes +6 bytes for -rset flag. A straight port of Leaky Nun's Python answer. ->s{d=Set.new q=0 s.each_char{|c|d^=[q+=1i**(c.ord%11)]} d.size} See it on repl.it: https://repl.it/Cnjy • I believe the -rset flag only counts as 4 bytes. – Cyoce Aug 18 '16 at 20:17 • With the newest meta changes the -rset flag now counts as 0 bytes. – Value Ink Jun 15 '19 at 0:44 • @ValueInk Oof. I don’t like that at all. Thanks for the heads-up, though. – Jordan Jun 15 '19 at 0:48 • I think they made some pretty good points as to why they want to do this (like how -e being "free" in Ruby means -n is 1 byte instead of 3 but people who don't know about that could report different bytecounts) but to each their own. BTW, Set[] saves 2 bytes over Set.new. – Value Ink Jun 15 '19 at 2:27 • Another thought I had while thinking up a non-rset answer: bytes.map saves 4 bytes over each_char because you can take out the ord call. – Value Ink Jun 18 '19 at 22:25 # R, 172156 137101 96 bytes n=function(a)sum(table(cumsum(sapply(strsplit(a,"")[[1]],switch,v=-1,"^"=1,">"=1i,"<"=-1i)))%%2) Using @LeakyNun's complex plane idea. ungolfed n=function(a){ b=strsplit(a,"")[[1]] #Splits String up p=sapply(b,switch,v=-1,"^"=1,">"=1i,"<"=-1i) #Replaces characters with directions q=cumsum(p) #Finds each location visitied t=table(q)%%2 #Determines if spots were visited an odd # of times sum(t) #counts odd visited spots } ## Javascript (ES6), 9793 85 bytes i=>[...i].reduce((c,d)=>c-1+(v[p+=v['^<>v'.search(d)]]^=2),0,p=1E6,v=[-1E3,-1,1,1E3]) EDIT: -8 bytes, thanks to Neil Test: var test0 = 'v>v<^^<v<<^<^><<>^^>>><v>vv^v>v^><><<^>><<<vvv^vvv>v>>v><vv^^<<>vv^^>v^<>>^^<^^>^^v<^>^<vvv^v^v><^<<v<<>><<>v>>^><^>^^<>>>>vv>^<<^<<><vvv<v^>>vvv>v^>>><<v^>^^^^v>>^>^v>v<vv^<>^<<v>vv>><^^<^><vv^^v<v<v^^^>v<^vv^v<><vv^^^>v^>v>vv<<^><v<^v><<v^^v>>v<vv<><^^^v<^v><><<^^<>^>><^^^>vv^<>>>>^<^<<<<>>>v<<v<v<vv><<vv<vv<^v^^^>>vv<>v>><<<v^>vv><v<<<v<<>^vvv^<v^v>^^v^v><<v^>>>v<v<v^>>>v><>>>^<><<<<>vv>v><v>v><^v<>v>>>vv<<>^>^>v<^><^<^vv^><^^>v<^^v>v^v<^^^^vv<>v<>><v^^><>v<<<>v^<v^^><>^<>^<>><>^^<>^v><>>><v<^^>>v>^^^<v'; var test1 = '>>><^>>>^vv><^^v^<<<>>^<>>^<^>^<<^^v^<v^>>^<<><<>^v<^^^vv>v><^>>^<^<v><^v<^<<^^v><>>^v<^>^v<vvv<<<v^vv>>^vv>^^<>>vv>^<^>vv<>v^<^v<^^<v^^^<<^><><>^v>vvv<^vvv<vv><vv<^^v^^<^^>>><<<>^<>>><^<<<>><>^v><^^vv<>>><^^^<^>>>>v<v^><<>v<v<v^<<^><v^^><>v>^<>^^^vvv<v^>^^^^v>v<v>>>v^^<v<vv>><<>^vv><<vv<<>^^v>>v<^^v>><v<v<<>^^vv>>^v>v>v<>^>^v<>>><>v>v<<v<^<>>>vv>>v>^<>vv^v><><^v^>v<^^>v<^v>>v^>^>>v>v>^>^<^^>vv>>^vv<^><>^><<v^<><<^<^>^^vv^<<^^<^^v<v<>^>v>>>>>>vv<<v>^>vv^>^><^<^^><<vvvv>vvv<><<><v^vv><v^^<>^>><^vv<><>^>vv>>>vv^vv<<^v^^<<v^^>^>vvv<><<v>^>^>v<v>^<^^^^<^>^>><>>^^vv<>v<^>v><v<v^>>v<^v<vv>v^>v<v^<^^^^v<^<^<<v<<<v<v^^>vv^>><<<v>>^^^>^<^>>>v^v><^^vv^>><^^vv<vv<v^><>>^><<<>>^^v^v<<v^<vv^^^>><>>^v^^^>>^>^<<^>v>^^v>><>v>^>vv^^<vvvv<><^v>^><<>>><^<^v^<<vvv^v<<<<<><><<><><<v>v<v>v><^v^^vvv>><>^>^>^v<<vv^^^v^vv><v><><v<v<<>>>v<^<^v<<>^v<<^v<><>v>>^^>^<v^<<^v^^^vv>><v^<v>^v><^<>>>>^^<vv<>^^>^>v^v^^>><>^^<^v^<v<<v<^<<^^vv>v>^<vv<<^^v^vv^>^^<>v>^>^<>vv><v>>><<><<vv^^<vv<>>^v>^<<vv>^><<>^<v>v><<v^<v<><v>^<^<^><^^^^>>>^<>^^><>>v^<vv^<^<<vvvv>>>v^v>>^>v^><<>>v<>>^>><vvvvv<<vvvv<v>^v<vv^<>><<><v^^<^<v>^v<^<<>^v<v^<>v<<>^<<vvv><^><^^^<>>v^<<>vv><^^^>><^>v^v>v<v^>>v>>v>vv<<v<<vvv^^^>^<v^^<^<v<^<>>v^<<v>>v^><v<vvvvv^^^<v^^<><v<<^>>^><^<v^v^^>><v><>v>^<vvvv><<v^^v^>^>v>><>^^v>v^>vv^>v<^<<^vv^>vv^<v>^<v^<>^v>v^>v^<<>^^<^>^^>vv^>>vv>v>vvv><>^v<<<<v^>v^^v<><v<v>^<^><^><<v<>><<>v^^>>><<><>>><<>><v^^>><^>><^<>v^^vvv>v<^<<vv^>vv^><<>v><>^<>v^^v>^>v^<>^><v>^><<^v<v^^<v>><^^>>^<^<^v<v>^>^<^<v><><>>>><>^<^<v>v<v^>v><>v^>v^<<><^<>>v<^vv^^^>^<<<<>^>^<><^vvv>^^<v^v>v>v^v>v>>vv>^><>^vv>^<v<v^<>vv^<v<><>^>>vvv><>>^<<v^<<>^<v^>v<^^^<^<^^<>^>>v>^<v>vv<v^^>><<<<<>>v>^v>^>>>>v>>^^>^<<<^<<<v>>^><<<<^vv<<>^v<^>v^<v<<>v<>^<^<^<^<>>^^^vvv<v>^vv>^><^<v^>^v<v>><><vvv<^^>>v<^v>^>>>><v^<v^^<^^v<vvv<v>^^<<>><^<v^v<^vv>v>vv>^^<>^^^^>>^v><vv<<<v>^v^>>v^>><<<^v^v<<>><<vvvvv<v^vv>vvvv><v^v<^^^><vv^^<>><>><^>^^^^v>v><><v^<>^v<>^^<^^>^^^vvv>>vv^v^<v<vv^v>v>>>^v^^vv^<^v>v^v>>^v>v<v^<^^><vvv>><<>><>><v>v<^<v>>>>v^^v^^>^><<v><^<<>>v<>^^<<>vv^>>vv^^^v>>>^v^><v<<^>v<v><>>>^>>^<<>>^><<vv<^^>^^^v^^<>>>vv><<>v<><<<>v<<>>>v<>v<>^<vv^v<^^<<<v>^v>>^^>^><<^vv<><><>v>^v>^<>v>>^^^<^^>>vv>v<<<v^><<v><^v><>v<^<<^<>^vv>^><^^^^^<<v^^<>v>><^<v^^^vv>^v<>^<v<v>v>^><^<<^<>><^^>vv^<>^<>vv<>>v<vv^>><^^<^>v<><>vv<v<>>v><v^^^>^^^<<vv^><^^v>v>^<^>v^><<vvv>v^><vv<><^<><^>^v<><<v^<<><>^^^^<<^>>^>^v^>v>^<<^>vv^vv^v<>^<<^>v<^^<<v<v<<<^>vv^>><>v>><><v>v><v^><vvv>vv<<vvv>v^<<^v<^<><<^v>v<>>vv<<v^>v>v<<>>^vv^<^^^<^v>>^<vv>^<v>><>v>^^<<v^<>>>>>v^v>><>v^>>^<>>^<^vvv^^^<^v<><vvv^>^>v><<v>>^v>v<v>v^<v>v>^<>vvv>vvv^^<>vv>^^^^^>v<<^v<>>>><<<>>><vv>>^v^^v<v^>>>^>^v<^v>^v<>vv<><vvv^v<<<<v<vv>vv^<^vvv<^v>v^^vv<^>>>^^>>^^><>^>>v<>>>^^<<v<^<<<<<^^<v^^^<<>><<<^>^v^>vv<>>>^^v><<>^^^^<vvv><^^<>>>^><<^>><v>^<>^v^<vvvv^>>^><<>><^<v^>>vv^vv<^>>>><^>^v<^<v<^^<^<^><^<>>^<>v^v<<>v>v<>><<v<^v<<<^v<v<>><v<^<^>>v>v>><v^<v><>>>>>v^v>><^<^<v>><v^v>v<>v<v><<<>^^><>^^<^vv^^<>v><><><^>^^v^vv^<><>>>>v><>>^>^<<^<v<v^>v^^<v>>><<^^vv^^>><<^<vvvvv>><^>^>>^vv<><<>v>v^<<<^v<^^<<^vv>v<vvv><^v>vv^vvvv<^>^v^<<<<^v<<<>^vvv>^v><<>>v<v<^v^<>v>>^^v^vv>>>^v^^>>^<><><<<<^vv>>>>>v>v^>v<>><<<>^vv>^^^^<^^^>^^^^>^^^v^v><^>^>>>v<v<^<^^<<^v<<^<>vvv^^^^v^<<>vv>^^>>><^^v<^<<<v<>v<<><>v<><>^<v<<^>^^>><<v>^^><^^v<^<v^<^^<>^<>^v^>>^^v^v^<>v<>^<<<>^v^v>^<vvvv<>v<<>vv^<<>vv>>>>^<v><>>>v^><<>^v>><<>>^^v><^<>>vv^^^>vv^<^^v><v>>vvv^v<^v>v<<^^<>v^^^v^^>><v^>>v^v^vv<^>v^<^>^>v<v^><vvv^>^<>v<<^><^^<vv>v>>vv>v^>>^vvv>>v^>^^>vvv>>v><<>>^^v>v<v<><<<<^^v<^<>^v>><v^^^<>>vvv>v><<v>^^<^vvvv^v>v>^vv>^vv^^v><<>>^^>>v>>>^v><^>v<^^<>vv>v>v^^^>>^^^><<<<>>^>>^<^v<^<^<>^><v<<v>v<>^>>^<<v^^<v^vvvvv>>v^>>^^^<^^<><<><><>^v>vvv^>^^>v<^^>^<<^v^^^><>><<v<^^^<<<<>><>><<^^v><v^<<^v<v><<>^<v>^>^v>vv>><v^<^<v<v<v><^^^^>>><^<><^v^v<<<^>vv^<v^>^^v^>>><<<<^<>>><v>>>vv^>^^<v^v>>>v^<^<>vv>^v^^><<<v>v>v>><>>>v<^>^<>>^^<v^<<^<v^>><^v^><><v><><v^vvv<<>v>>><<><v>v<>>><^<^^v<v>^<<>^v>^>^>^^<^^><^>>>>><^^>vv>^<^^<><^>^<^^><^<v>v^>><^>^^^>>v^v<^>>^<v^<>^><><v>>^v<v^^^^v<^vv><^v>>^^^<>^<^<^>vv^v<<>vv>^<>v>^>^>vv^v<vv<^^^v<v>v>v^<^^^v><v<<<^^<><^^>>>><<^^v<<^>v<<vv^^^vv^vv^<v><>^v<v>>><vv^v<v^>>>>^<<<vv^>>v>^><<><<^<^><<vv^>v^>><>v^<<<>v^><>><<>>v><>v^<v><>^v>>><><>>>^vvv^v>vv>>>^^v^><<v<>>^^^v^^><<^v<><><v<<v<v<><<<v^<^^^<>v^^v<^^<<^>v<<v><^<<<<>><>^v>^<>^<^^v^vvv>^^<>^>><v^^vv^<>^<><<^^^v<^^^>>^^v>^>^<^>v><<^<>^v<><vv^vv<><<<<<<v<<v<<vv^<<^<^vvvv><v^v^v<>>>vvvvv^<vv^<^<>vv>^<><<v><>v^^<v<>>>vvv^><^<^>v^^<v>^<>>>^^v^<vv<<<<^><v<<<>v<<<v<>>^^^>^><>v>^v^>^<v^^><^v^^<^v^^>^v>>^^^<<><><<<>v>><^><>>>vvvv>v>>v>^^^^v<><vv<^<v^v>>^^vv<^>vvv>^v>>><v<v<v^<^>^^<vvv<vv<v>>^vv>^<<^<^<v>v^<vv^^^v>vv<v><v><v>^<v>>vv<>v>^^>v^^^<>v<>v^v<>^<><v><^>^<v^v><<^v^v^v<<v><<^^<^vv>^<^v><>v>><v^v^>><><><<<v<>v<^vv>v<v<<>^vvvvv^<<<^<vv><<><>v^<^v<<<^>v>v<v^<<^>v<<^<v><<<^>vv>v>^<^^v>>>><>vv>>vv>vvv<>^^<>^v^<>vvv<^^^vv>v><<<<vv^v><v^<^<<<><v<>^><<>^>v<^^<<>v>>v<<>><^^<<<^<^vv^^>v>v<>^^>>^v^vvv>^v^>v>>v>v>v>>vv^<><<<<>v^^>vv<^^v>>v<vv<^>>^<>^^v<><vv^<><v><v<<v^v<^^<^v^v<>v<<><vvv><<<^<^^<<>>^v>>>^v>>>v<>>^><<<><><<<v<vv<^<>v^^v^^>^<<^^^v^>^<<^>^>^>>>>v<v<v<>vv<<vv^<<^<vv>^^<^<<>><^v><><>^<v><v^>^v>^<^>^^><v><<^<v^^<<^><><v>v<>>><<^><v<^vvv^<<<>><<>^v^^><vv>vv<>^>^>vv<>v^<^<>vv><<>^<v<vv<^<^<><^vv<<^>>>v<>><<>>>^^^^<<^v>>v<vv>^^>v<v<vv^><<><>>>v>>^^v<^v^^>>v^<>>v^>><^<^^v<v<><<><>>^<>><^v<^^^^><>^>vv>>^vv<<>v<<<<<<><<<><<>><v><^^^<>>v<^><^vvv<>^>^^v>^<v><^v^vv^<<>v<<<<v>^vv>>v>vv<<^>^<>>vvv^<v<><>><>^^^^vvvvvvv<<>v<^><^^>vv^^<v<<^^<vvv<v<v<<>><<><v^^>><^<>^v^vv<<v<v<>><<>>>>>^vv<><v<>v><v>v>><v<v^vvvvv<><>v>>v<><<<^^<>^<^^<v>v^<vv>^vv^<>^<<^<vv><v<v>>v>^<>v^<<v^<v>^v<>><v>>>>^<<^^^v<^<>><^<><v>>vv^>^<^<^>>v^>^^^^>vvvvv>^v<^><^^<^^>^<^^^^^^^>v>>vv>v^^^v^^^<>v><^>>>v>^>^>^>vv<vv<^^>>^>>>v<>v><<^<<v^>^>>>>^^><^^<v<<<<>>v>v^v^^<>><v<^<<<<v^^^^<v<<<^>v>^^<vv<^^^^^v>^v^<v><>>^^>^v>^>^vv^v>v>v^>v>^>>^^^^>>^>>^><>><v>v>>><<^v^v^>^>^>>vv><<^>v<v<v^<<>>^v<<^v<<^><^>>^<v>^>vv>v>^^^>v^^<^<^^>vv>^^><v>>^v>^v<<^^^<<^v^>^<<^>vv^>>^<^v><<>v><^^^<^^>>vv>^vv>><^<<<^>vv^v>v<^<<<^<^<<><^^>>>v^<^^^>^<><^v>>^<<v<^v>>v^<^<^<^^^<v^><<vvv^<^v^vv^vv<v<<v<^<>^v>^^^<^^v<v<v><<<^<>^^^^v>v^v^v^v<v><v>>^v><vv^^^v>><<v^vvvv<<<^v<<><^>^<v^^v<>vvvv^vv<>^v<><>^^<>>vvv<^>><v^<<>v>v<>^v^>v^>><<>>^^<^v<>>^>^><>>^<v<v^^<^v><v^<v<><><^<<><v^v<<>vv<v<v<^>>><>vv^^<><<v<^^<<^<><^^^>^>>>^<^>>>^>><^^^<^v^^^v^v^v>v>v><vv>><vvv<<v><><^^>^v<v>><v><^><^<<>v^vv^v><^vv>^>>v<vv><^<^^v<^^vv<vv<v<v>v><v<vv<<>^^v^^v<<<^<>v^^^<><>>><^>v^^^v^vv<<<^>>v><^>v^<>>>>^<>^^vvv^^<><^>^^<><>^vvv^^<vv^>vv^^^^v<>vv<^^^v<<>><<vvvvv>v>^^^vv>><v><v<>vvvv<v^><^<>^>^<>v>v>v^vvvv<><^v>>>^^>><vvv<>^>^v^<vvv>v^vv^vv><>><>v^^v^vv<^v>vv>>v<v><^<<^v<>>^vv^<v>v><v>v>^v>^<v>^<<^>vv>v<^<^vv^<^><<<v<<^^vv<vvv><>v>v<vv^<><><^vvv>>vv<^^^v><^v><<^>^^v>^<>><v<>>^^<<<v><>^>^><vvvv<>^<<<><<<^<>>v^vv^>><^vv^^>^<v^<v>><^^>>>^v>^v<>^v<><^><vv>v^^^<^>>^<<^<^><<<^^<v<<^vv<^<>v<^<<^^<v<vv<<><v<v^<>^<>v>>v<^v>v<>^^vvv<>vv^v^<><v^vv^<^v^v><>^><v^<>>^^^<>>vv^<v>^^v><v<^>^^^^^^><>>vvv<<><><v<^>v<>v^v<<<<>v^>>>>^v>^^<v^>v><v^<^^v<<<<v<<<>^v<^>^v>v^^>v^^vvv>vv<>^>v><v<>^<vv><>>><<^>>><<v>v^^<^<<<<v^<>>>v<<<^v^vv<>^v>v<<<<>^^>><v><>v<v><^^>><>^>^>v>>><v>^vvvv<><><^>>^v^><<>^v<><><^><<<>v^^>v>^>v^<v^vv<>><^vv^^>^^><vv<<>v>v^^>><v^>^<^<>>>vv<>^>v>v^<>v<^<<v>>>^<>v^>v>>vv^^<>>v<v<<^<>v>v^<^^^>v^^>v>v>vv<^<v>v^^><<<v<><>^^<>v>v>^^v>v>v^v>>^<v^v>><>^^>^<>>>^vv^><v^<^>v^>^v><^>^^^vv^^v<>vv<>>^><<^v>^v^>>v>^v^<<^^^vv<<vvv>^vv^v<<<v^^<<><vv<>>^^vv>^^^vv>><><v>v<^v^>>>vv^><>><v<^v<>^><v<^^^^>><^<>v>^v<^vv>v>v<^<>v>v>^<vv>v<^>vvv<v^<vv<vv<>v>^><v^v<>>>>>v>><^v<>v>^v><v^v^vv<>^<vvv^>><v^<vvv^^<^vvv^v^<>><v>v^^v<><>v^^^v<<<^><v<<<>><<vv<<><vvv^v>>v^v<v^>>><<v<>^v><>vv<<v>v^vv>v^v<^<vv<><><^v>^<vv>v^^>>^^^><vv<><^>>>^<v^<<^^>^>vv^><v<vvv>^^>>>^><<vv>vv>^<>>^^><^v><<>^<<<v^>^'; S=i=>[...i].reduce((c,d)=>c-1+(v[p+=v['^<>v'.search(d)]]^=2),0,p=1E6,v=[-1E3,-1,1,1E3]) console.log(S(test0)) console.log(S(test1)) • Use [...i] instead of i.split(''). Also, I think you can write (p=1E6,v=[-1,1,-1E3,1E3],0) as 0,p=1E6,v=[-1,1,-1E3,1E3]. – Neil Aug 16 '16 at 18:35 • If you can arrange for the ^ to be first, search saves a byte over indexOf. (You need the ^ to be first because search treats ^ as a regexp metacharacter.) – Neil Aug 16 '16 at 18:38 • You don't have to count the S= part. – user2428118 Aug 17 '16 at 12:50 • @Arnauld No, the argument name(s) itself is/are part of the function and should remain. However, assigning the function to a variable ("S=") is optional (as you can just call the function like («function code here»)(«argument»)). – user2428118 Aug 17 '16 at 13:56 # PowerShell, 136 bytes$a=@();switch -w($args|% t*y){'^'{$y++}'>'{$x++}'v'{$y--}'<'{$x--}*{if("$x,$y"-in$a){$a=$a|?{$_-ne"$x,$y"}}else{$a+="$x,$y"}}};$a.length Try it online! I think there's more to optimize here, but this is the lowest I got for now. Easier to read:$a=@();switch -w($args|% t*y){ '^'{$y++}
'>'{$x++} 'v'{$y--}
'<'{$x--} *{if("$x,$y"-in$a){$a=$a|?{$_-ne"$x,$y"}}else{$a+="$x,$y"}}
};$a.length Explanation: The input is changed to a character array and each piece is matched to one of the first 4 switch cases to increment the x or y coord. Everything matches the 5th case where we decide if a light is turned on or off. Length at the end determines total number of switches turned on. Note: The comma in the coordinates is necessary so we don't get collisions like (10,10) and (101,0) • Strip some apostrophes and pull$x,$y into a variable for 127bytes – Veskah Jun 14 '19 at 3:40 • -ne works with array 115 bytes – mazzy Jun 14 '19 at 6:37 • Length -> Count for 114 – Veskah Jun 26 '19 at 18:42 # PowerShell, 96 95 bytes$(switch -w($args|% t*y){^{$y++}'>'{$x++}v{$y--}'<'{$x--}*{"$x,$y"}})|group|% c*|%{$r+=$_%2}$r

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Unrolled:

$plane=$(switch -w($args|% toCharArray){ ^ {$y++}
'>'{$x++} v {$y--}
'<'{$x--} * {"$x,$y"} })$plane|group|% count|{$result+=$_%2}

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# Actually, 24 23 bytes

This is a port of Luis Mendo's MATL answer. Golfing suggestions welcome. Try it online!

Edit: One byte thanks to Leaky Nun.

O⌠4P@%ïⁿ⌡Mσ;╗╔⌠╜c2@%⌡MΣ

Ungolfing:

O        ord(c) of the input string (implicit input)
⌠...⌡M   Start a function, and map over the list of ord(). Call the variable i.
4P@%     i mod 11 (the 4-th prime).
ïⁿ       1i to the power of (i%11).

σ        Push a list of cumulative sums of the new list of complex numbers.
This is a list of the coordinate visited.
;╗       Duplicate coord_list, and push to register 0.
╔        uniquify(coord_list)

⌠...⌡M   Map over the uniquified list. Call the variable j.
╜c       Push coord_list.count(j)
2@%      Push count mod 2

Σ        Return the sum of this last list.
• Other than writing :11 as 4P, I am unable to come up with any golf advice – Leaky Nun Aug 30 '16 at 4:12

# C, 203190 189 bytes

#define S(s)1-(*s%11<7)*2<<*s%11%2*16
char*t,*u;P,p,r,L,e;
f(char*s){for(P=L=0,t=s;*t;++t){P+=S(t);e=r=1;for(p=0,u=s;u<t;u++)e*=(p+=S(u))!=P;for(p=P;*++u;r^=p==P)p+=S(u);L+=e*r;}return L;}

O(n^2) with O(1) memory algorithm.

It loops over every position, checks if this position occurs earlier, and if not checks if this position occurs an even/odd amount of time afterwards, adding it to the total.

## Perl, 102 98 91 90 (89 + -n) bytes

perl -nE '$i=ord()%5,$x+=(-1..1)[$i],$y+=((0)x3,1,-1)[$i],$p{$x,$y}^=1 for/./g;say~~grep$_,values%p' Readable:$_ = <>; # -n
for (/./g) {
$i = ord() % 5;$x += (-1 .. 1)[$i];$y += ((0) x 3, 1, -1)[$i];$p{$x,$y} ^= 1;
}

say 0 + grep $_, values %p; • thanks Dada for -4 and -7 • it's the first time I see "readable" and "perl" in the same post I think! – Dada Aug 16 '16 at 16:23 • More seriously, great answer. You can still win a few byte if you use for/./g instead of while, which allows you to use ord() instead of ord($&). – Dada Aug 16 '16 at 16:25

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# Explanation

^>:\L\T                ~ lambda expression, import list and tuple module
[length],^v>xy:       ~  the answer is the number of lattice points
~  which were visited an odd number of times
!tTxy                ~   current lattice point
!V ?[elem]tv         ~   if the lattice point is already present,
[without]vLtE    ~    remove it, else
Ltv              ~    add it
?#?E> V              ~   no further moves
!c#!f>               ~   move character
?=c$62. @V#!r>+x1y ~ move right ?=c$60. @V#!r>-x1y  ~    move left
?=c\$94. @V#!r>x-y1 ~     move up
@V#!r>x+y1        ~      move down
.LT00E>00.            ~ initialize at point (0, 0)

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Unfortunately, krrp only has one rather slow implementation, making the long test cases difficult to verify.
krrp String conversion.

# APL (Dyalog Unicode), 21 20 bytesSBCS

+/≠/×⊢⌸+\0j1*'^<v'⍳⎕

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uses ⎕io←1

input

'^<v'⍳ find the index of each input char among '^<v', i.e. ^ becomes 1, < 2, v 3, and anything else 4

0j1* i to the power (the imaginary constant)

+\ partials sums

⊢⌸ matrix in which each row is the list of occurrences (indices) of a unique partial sum; padded with 0s to make it rectangular

× signum - all indices become 1s, the padding remains 0s

≠/ sum mod 2 for each row

+/ sum

# Ruby, 67 bytes

Inspired by orlp's C solution. Assembles a list of all visited positions, and then for each unique one (using setwise intersection (d&d) since it saves a byte over d.uniq), count the ones with an odd number of occurrences (technically, map it to the occurances%2, and sum them together, since that does the same thing)

->s,q=0{d=s.bytes.map{|c|q+=1i**(c%11)}
(d&d).sum{|c|d.count(c)%2}}

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