Eating fish, growing in size

Question

You are fish in a pond that needs to survive by eating other fish. You can only eat fish that are the same size or smaller than yourself. You must create a program that takes a shoal of fish as sorted input. From this you must work out how many fish you can eat and ultimately the size you will grow to.

Size chart

+--------------+--------------+--------------+--------------+
|              | Amount extra | Total size 1 | Increase to  |
| Current size |  needed for  |     fish     |    size      |
|              |  next size   |              |              |
+--------------+--------------+--------------+--------------+
|      1       |      4       |      4       |      2       |
+--------------+--------------+--------------+--------------+
|      2       |      8       |      12      |      3       |
+--------------+--------------+--------------+--------------+
|      3       |      12      |      24      |      4       |
+--------------+--------------+--------------+--------------+
|      4       |      16      |      40      |      5       |
+--------------+--------------+--------------+--------------+
|      5       |      20      |      60      |      6       |
+--------------+--------------+--------------+--------------+
|      6       |      24      |      84      |      7       |
+--------------+--------------+--------------+--------------+

Rules

1. Your size starts at 1
2. The shoal input will contain fish integers between 0-9
3. 0 = algae and wont help you feed.
4. The fish integer represents the size of the fish (1-9).
5. You can only eat fish the same size or less than yourself.
6. You can eat the fish in any order you choose to maximize your size.
7. You can only eat each fish once.
8. The bigger fish you eat, the faster you grow. A size 2 fish equals two size 1 fish, size 3 fish equals three size 1 fish, and so on.
9. Your size increments by one each time you reach the amounts below.

Returns an integer of the maximum size you could be

Examples

"11112222" => 3  
4 fish size 1 increases to 2, 4 size 2 makes you 3

"111111111111" => 3
4 fish size 1 increases to 2, 8 size 1 makes you 3

The shortest code (counting in bytes) to do so in any language in which numbers wins.

Answer 1

JavaScript (ES6), 44 bytes

Takes input as an array of integers.

a=>a.map(x=>s+=(t+=s>=x&&x)>s*-~s*2,t=s=1)|s

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How?

The threshold \$T_s\$ to reach the size \$s+1\$ is given by:

$$T_s=2s(s+1)$$

We keep track of our current size in \$s\$ and of what we've eaten so far in \$t\$ (we start with \$t=1\$, so this is actually off by \$1\$).

For each fish \$x\$ in the shoal, assuming it's sorted from smallest to biggest:

• we add \$x\$ to \$t\$ (i.e. we eat the fish) whenever we have \$s\ge x\$
• we increment \$s\$ (i.e. we grow in size) if \$t > T_s\$

Answer 2

Wolfram Language (Mathematica), 40 39 bytes

(f:=Floor@s;s=1;s<#||(s+=#/4/f)&/@#;f)&

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Explanation

f:=Floor@s;s=1;

Store floor(s) in f, symbolically. Start with s=1 (size).

... /@#

Iterate through each element in input...

s<#||(s+=#/4/f)

If the element is not greater than s, then increment s by <element> / (4 * floor(s)). The Or (||) short-circuits otherwise.

f

Return floor(s).

Answer 3

Python 2, 60 bytes

f=lambda l,n=1,c=1:c>n*~-n*2and f(l,n+1,c+l.count(n)*n)or~-n

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Answer 4

Jelly, 17 bytes

J×4ÄfSR$ịx`>JTḢȯ1

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An interesting method which could well get beaten by some kind of loop or recursion.

How?

J×4ÄfSR$ịx`>JTḢȯ1 - Link: list A (ascending digits) e.g. [1,1,1,1,1,1,1,2,2,3]
J                 - range of length                      [1,2,3,4,5,6,7,8,9,10]
 ×4               - multiply all by 4                    [4,8,12,16,20,24,28,32,36,40]
   Ä              - cumulative sums                      [4,12,24,40,60,84,112,144,180,220]
       $          - last two links as a monad (of A):
     S            -   sum                                14
      R           -   range                              [1,2,3,4,5,6,7,8,9,10,11,12,13,14]
   f              - filter keep                          [4,12]
          `       - use left argument as right with:
         x        -   repeat elements                    [1,1,1,1,1,1,1,2,2,2,2,3,3,3]
        ị         - index into                           [      1,              3    ]
                  -                                    = [1,3]
            J     - range of length (of A)               [1,2,3,4,5,6,7,8,9,10]
           >      - greater than?                        [0,1,3,4,5,6,7,8,9,10]
                  -                1 not greater than 1---^ ^---3 is greater than 2
                  -   (note keeps values of longer - i.e. the 3,4,... here)
             T    - truthy indices                       [  2,3,4,5,6,7,8,9,10]
              Ḣ   - head                                 2
                1 - literal one                          1
               ȯ  - logical OR                           2
                  -   (edge-case handling when the head of an empty list yields 0)
                  -   (note that when the shoal is fully consumed the final size will
                  -    still be less than the length of that shoal, so TḢ will still give
                  -    this size due to >J keeping values of the longer argument.)

Answer 5

Haskell, 46 bytes

(!0)
a!b|sum[y|y<-a,y<=b]/2<b*b+b=b|q<-b+1=a!q

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Answer 6

Lua, 214 bytes

l,f=1,{}for j=1,9 do s,f[j]=(...):gsub(j,0)end::z::a,n=0,l*4 for i=1,l do a=a+i*f[i]end if a>=n then e=l while n>0 do if 0<f[e]and e<=n then n=n-e f[e]=-1+f[e]else e=e-1 end end l=l+1 else print(l)return end goto z

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Not even near shortest one here but it was fun to figure it out :D