Euclidean Vectors

Question

Given the ASCII art of two vectors, find the resultant vector's magnitude and degree.

---

Input

This can be received via STDIN, read from a local file, or provided through a function call. Here is an example of a two vector input:

^------>
|
|
|
x

This represents a change of 4 units north and 7 units east. Every input's starting point will be represented by an x (decimal 120).

• All vectors are horizontal or vertical lines.

• Each vector has one of these four endpoints: ^v<>, and is made up of either a dash (-, decimal 45) or a vertical bar (|, decimal 124).

• Empty points on the plane are filled with spaces (, decimal 32).

• The input may be a single x.

• Adjacent vectors are always perpendicular to each other.

• All vectors are tip-to-tail.

---

Output

This will be the displacement of the resulting point (distance from the starting point) and the degree to which it has moved, relative to the starting point.

For the above input, the output should be 8.06 units and 60.3 degrees. Each should have exactly 3 significant figures. Here are a few examples of numbers with 3 significant digits:

• 1.00
• 60.1
• 453
• 7.08
• 4.50
• 349

All unit measurements will be <= 999.

---

These numbers should be output in the below format. This is using the numbers from above.

8.06 units @ 60.3 degrees

This may be followed by a single trailing space or newline.

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If the input is a single x, with no displacement and hence no angle of displacement, the output should be either an empty line (a single newline character) or in the following format:

0 units @ - degrees

If you're trying to qualify for the bonus, the direction should be - as well.

---

In the case that bonuses 2, 3, or both are completed, the output should follow the below model and abide by the same restrictions as the above.

8.06 units @ 60.3 degrees NE

---

Degrees should be measured according to the standard plane.

       90
  135  |  45
      \|/
180 ---x---- 0
      /|\
  225  |  315
      270

0 degrees is east, 1 - 89 degrees is northeast, 90 is north, etc.

---

Bonuses

The following are worth a total of -50%.

1. Take a -10% bonus for each additional vector that can be handled. This bonus can be applied to up to 3 times. Vectors will never overlap or cross.

2. Take a -10% bonus if your output includes the cardinal direction of the angle (north, south, east, west).

3. Take a -10% bonus if your output includes the intermediate directions of the angle (northeast, northwest, southeast, southwest).

---

Examples

In:

x---->
     |
     v

Out:

5.39 units @ 338 degrees

Optionally SE

---

In:

<--------------^
               |
               |
               x

Out:

15.3 units @ 169 degrees

Optionally NW

---

In:

x
|
|<-----^
|      |
v------>

Out:

2.24 units @ 297 degrees

Optionally SE

---

Examples (multiple vectors)

In:

x--->
    |
    |
    v----------->

Out:

16.3 units @ 349 degrees

Optionally SE

---

In:

<-------^
|       |
|       |
v       |
        |
        |
        x

Out:

8.54 units @ 159 degrees

Optionally NW

---

In:

^-->
|  |
|  v
|
<--------x

Out:

6.32 units @ 162 degrees

Optionally NW

Answer 1

Python 2, 238.5 (594 562 482 477-50%) bytes

from math import*
def F(x):s='%.3g'%x;return[[s+'.',s]['.'in s].ljust(4,'0'),s][x>99]
I=input()
V=I.split('\n');N=len(V)
l=max(len(x)for x in V)
q=[' '*(l+2)];V=q+[' '+x.ljust(l+1)for x in V]+q
for k in range(N*l):
 i,j=k/l,k%l;c=V[i+1][j+1]
 if c in'<>^v'and['|'not in zip(*V)[j+1][i:i+3],'-'not in V[i+1][j:j+3]][c>'?']:a,b=i,j
 if c=='x':A,B=i,j
Y=A-a;X=b-B;a=atan2(Y,X)/pi*180%360
print[F(hypot(X,Y))+' units @ '+F(a)+' degrees '+' NS'[cmp(Y,0)]+' EW'[cmp(X,0)],''][I=='x']

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Explanation

Finds the start and end positions by looking at each character in the input.

Start is x

End is found by looking at each arrow (<>^v), and their neighbors. If neighbors are continuing vectors, ignore. Else, this is the end.

Look at the neighbors perpendicular to the arrow direction.

If they contain a perpendicular line, then it is a continuing vector.

Examples (_ indicates space):

_#_   
->_   Neighbors marked by #
_#_ 

___   
->_   (end)
___   

_|_   
->_   (not end)
___ 

___   
->|   (end)
___ 

---   
->_   (end)
___ 

Because the end point is found, there can be any number of vectors (30% bonus).

Answer 2

JavaScript (ES6), 305 bytes - 50% bonus = 152.5 score

v=>(l=v.search`
`+1,s=v.search`x`,u=0,d="-",v.replace(/[<>v^]/g,(p,i)=>{c=o=>v[i+o]!=q;with(Math)if(p<"?"?c(l,q="|")&c(-l):c(1,q="-")&c(-1))d=(atan2(x=i%l-s%l,y=(i/l|0)-(s/l|0))*180/PI+270)%360,u=sqrt(x*x+y*y)}),u[p="toPrecision"](3)+` units @ ${d[p](3)} degrees`)

Explanation

Input must be padded with spaces. Uses all bonuses.

v=>(
  l=v.search`
`+1,                                                     // l = line length
  s=v.search`x`,                                         // s = index of start point
  u=0,                                                   // u = units
  d=                                                     // d = degrees
  w="-",                                                 // w = cardinal direction
  v.replace(/[<>v^]/g,(p,i)=>{                           // for each endpoint
    c=o=>v[i+o]!=q;                                      // compares cell at offset to char
    with(Math)                                           // save having to write "Math."
      if(p<"?"?c(l,q="|")&c(-l):c(1,q="-")&c(-1))        // check for line branching off
        d=(atan2(
          x=i%l-s%l,                                     // x = relative x
          y=(i/l|0)-(s/l|0)                              // y = relative y
        )*180/PI+270)%360,                               // convert to degrees
        u=sqrt(x*x+y*y),
        w="N S"[sign(y)+1]+"W E"[sign(x)+1]              // get cardinal direction
  }),
  u[p="toPrecision"](3)+` units @ ${d[p](3)} degrees `+w // format output
)

Test

var solution = v=>(l=v.search`
`+1,s=v.search`x`,u=0,d=w="-",v.replace(/[<>v^]/g,(p,i)=>{c=o=>v[i+o]!=q;with(Math)if(p<"?"?c(l,q="|")&c(-l):c(1,q="-")&c(-1))d=(atan2(x=i%l-s%l,y=(i/l|0)-(s/l|0))*180/PI+270)%360,u=sqrt(x*x+y*y),w="N S"[sign(y)+1]+"W E"[sign(x)+1]}),u[p="toPrecision"](3)+` units @ ${d[p](3)} degrees `+w)

<textarea id="input" rows="6" cols="60">x       
|       
|<-----^
|      |
v------></textarea><br />
<button onclick="result.textContent=solution(input.value)">Go</button>
<pre id="result"></pre>