Falling ASCII balls

Question

Input

You are given a 2D map with balls and ground in it. It looks like this:

  1         5          2
                 3
     4


__________________________

Each number is a ball, and the _ is ground level. The underscore _ character is not allowed in any other line than ground level line. There are only spaces, newlines and digits 0-9 allowed above ground level. You cannot assume that last line is the ground level - empty lines below ground level are allowed. You can also add spaces, to fill empty lines, if that does help you.

Balls can have numbers from 0 to 9, can be placed above each other, but not under ground. The ball's numbers will be unique.

Assume that each character is one meter.

Get map from pastebin!
Test case 1 - should output something like this
Test case 2 - should produce same results as first map

Challenge

Your challenge is to read a map like that from a file or from stdin — you are allowed to use cat balls.txt | ./yourexecutable — and output velocity of each ball when it hits the ground.

Here's the formula for velocity:

Assume that h is the line number difference between the ground's line number, and the ball's line number, and that g equals 10m/s^2.

Output

You should output each balls number and velocity in m/s at ground level. For example N - Vm/s, where N is ball number and V is its velocity. You can also output an array if you want.

Happy coding! :)

Answer 1

MATL, 31 30 27 25 bytes

95\16\5B#fG&X>1)b- 20*X^h

Input is a 2D char array with ; as row separator:

['  1         5          2  ';'                 3        ';'     4                    ';'                          ';'                          ';'__________________________']

Try it online! Or include an initial t in the code to display the map for greater clarity.

Here are the other test cases: first, second.

Explanation

95\      % Take input implicitly. Modulo 95: convert to numbers and map '_' into 0
16\      % Modulo 16: map space into 0 and digit chars into corresponding numbers
5B#f     % Find row indices and values of nonzero entries
G        % Push input again
&X>      % Index of maximum of each column. This finds character '_'
1)       % Get first value (they are all equal)
b        % Bubble row indices of numbers up in the stack
-        % Subtract to get distance from each number to the ground
20*X^    % Multiply by 20, take sqrt. This gives the velocity values
h        % Horizontally concat numbers and velocities. Display implicitly

Answer 2

C, 125 122 121 bytes

b[99]={};main(l,c){for(;(c=getchar())<95u;)b[c]=(l+=c==10);for(c=47;++c<58;)b[c]&&printf("%c,%f\n",c,sqrt((l-b[c])*20));}

Compile & run with gcc -w golf.c -lm && cat balls.txt | ./a.out.

Answer 3

C -194(-5) 150 137 bytes

With a little bit more time and thinking, I golfed off 44 bytes
Thanks to orlp for helping me to save 13 bytes

I'll start with my C code:

b[256]={},n,i=47;main(l,c){for(;~(c=getchar());n=c==95?l:n)b[c]=(l+=c==10);for(;++i<58;)b[i]&&printf("%d %f\n",i-48,sqrt((n-b[i])*20));}

And human readable version:

//Throws many warnings, but lack of libraries is tolerated

/*
    c - current character
    l - line number (starts at 1)
    n - ground level
    i - iterator
    b - balls array
*/

b[256] = {}, n, i = 47; //That actually works, as long as you are using ASCII

main( l, c )
{
    for ( ;~( c = getchar( ) ); n = c == 95 ? l : n ) //Read stdin and search for ground
        b[c] = ( l += c == 10 ); //Increment lines counter on newlines, and save line numbers

    for ( ; ++i < 58; ) //Iterate through balls
        b[i] && printf( "%d %f\n", i - 48, sqrt( ( n - b[i] ) * 20 ) ); //Print out data    
}

Compile and run like that: gcc -o balls ballsgolf.c -lm && cat 1.txt | ./balls

Output

1 10.000000
2 10.000000
3 8.944272
4 7.745967
5 10.000000

Answer 4

Pyth, 27 26 25 24 bytes

smf-hT" _".e,b@*20-xd\_k2dC
smf@hT`M;.e,b@*20-xd\_k2dC
smf@T`M;.e,b@*20-xd\_k2dC
sm@#`M;.e,b@*20-xd\_k2dC

Try it online!

Answer 5

Matlab, 100 96 89 90 bytes

s=input('');X=find(s==95);for i=0:9
[x y]=find(s==48+i);if(x)[i sqrt(20*(X(1)-x))]
end
end

Many bytes saved thanks to Luis Mendo

Input format:

['  1         9          2  ';'                 3        ';'     4                    ';'                          ';'                          ';'__________________________']

Explanation:

X=find(s==95)         -- finds '_', we'll need X(1) to determine max height
for i=0:9             -- loops through balls' numbers
[x y]=find(s==48+i)   -- finds the ball
if(x)                 -- if it is present
[i sqrt(20*(X(1)-x))] -- output its number and velocity

Answer 6

Python 3, 84 bytes

Version 6, 84 bytes: (Thanks to Leaky Nun!)

lambda a:[(c,(~-(len(a)-i)*20)**.5)for i,s in enumerate(a)for c in s if c.isdigit()]

Version 5, 91 bytes:

lambda a:[c+":"+str((~-(len(a)-i)*20)**.5)for i,s in enumerate(a)for c in s if c.isdigit()]

Version 4, 92 bytes:

lambda i:[c+":"+str((~-(len(i)-n)*20)**.5)for n in range(len(i))for c in i[n]if c.isdigit()]

Version 3, 99 bytes:

def r(i):x=len(i);print([c+":"+str((~-(x-n)*20)**.5)for n in range(x)for c in i[n] if c.isdigit()])

Version 2, 102 bytes:

def r(i):
 n=len(i)
 for l in i:
  for c in l:
   if c.isdigit():print(c+":"+str((~-n*20)**.5))
  n-=1

The above versions take an array of strings as input.

Version 1, 140 bytes:

with open(input(),"r")as i:
 n=sum(1for l in i);i.seek(0)
 for l in i:
  for c in l:
   if c.isdigit():print(c+":"+str((~-n*20)**.5))
  n-=1

This takes the directory of the file as input from the user.

Answer 7

Python 3, 84 bytes

lambda x:[[i,(20*x[x.find(i):x.find('_')].count('\n'))**.5]for i in x if i.isdigit()]

An anonymous function that accepts input by argument as a multi-line string with all empty lines filled with spaces, and returns an array where each element is of the form [ball number, speed].

How it works

lambda x                      Function with input x
...for i in x if i.isdigit()  Loop through all characters i in x for which i is a digit,
                              and hence one of the balls
x[x.find(i):x.find('_')]      Slice x to give the substring between the ball and the ground
....count('\n')               Count the number of newlines in the substring to give the
                              height of the ball
(20*...)**.5                  Calculate the speed of the ball as it hits the ground
[i,...]                       Package the ball number and speed into a list
:[...]                        Return all ball-speed pairs as a list with elements [ball
                              number, speed]

Try it on Ideone

Answer 8

JavaScript (ES6) 93

Edit 2 bytes saved thx @Jacajack

A function with a multiline string as input parameter. Output is not sorted (as this in not requested)

a=>[...a].reverse().map(c=>c>'Z'?b=i:c<' '?++i:c>' '&&console.log(c,Math.sqrt((i-b)*20)),i=0)

Test

F=
a=>[...a].reverse().map(c=>c>'Z'?b=i:c<' '?++i:c>' '&&console.log(c,Math.sqrt((i-b)*20)),i=0)

function test()
{
  F(I.value);
}

test()

#I { height: 12em; width: 30em}

<textarea id=I>
    
 
  1         5          2
                 3
     4


__________________________




</textarea>
<button onclick="test()"></button>