Repeat average‎

Question

Background

It was a normal presentation that I were in as a audience, until the presenter gave a math problem about repeat taking 2 number out of a list a replacing them with average, claiming that there will be something special about it, and our math teacher, sitting at the end of classroom, exciting rushed to me, and tasked me to code that out.

Task

2 input length and generation

1. Generate a range, start from 0, with length of length

2. Randomly choose 2 number (or item) X and Y and replace both X and Y with the average of X and Y

3. Repeat step 2 for generation times

4. Output minimum, maximum, average, and the processed list.

Example

I'll let this semi-golfed python code explain itself :)

import random
a,b=map(int,input().split())
l=[*range(a)]
s=lambda:random.randint(0,a-1)
for i in range(b):
    x,y=s(),s();l[x],l[y]=[(l[x]+l[y])/2]*2
print(min(l),max(l),sum(l)/a,l)

Rules

• Standard rules applies
• Input can be in any convenience form.
• As long as you output is clean, understandable, readable, it is allowed.
• The two random value X,Y should be uniform statistically independent random by itself(X and Y are not affecting each other no matter what)

what you should do?

• Start golfing right now!

Answer 1

Jelly, 25 bytes

ḶJX,XƊṬ×ịÆm¥oʋƊ⁹¡µṂ;Ṁ;Æm,

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Outputs [[min, max, mean], list]. Takes length as the first argument, and generation as the second

How it works

ḶJX,XƊṬ×ịÆm¥oʋƊ⁹¡µṂ;Ṁ;Æm, - Main link. Takes L on the left, G on the right
Ḷ                         - [0, 1, ..., L-1]
              Ɗ           - Previous 3 links as a monad f(R):
 J                        -   Indices of R
     Ɗ                    -   To the indices of R:
  X                       -     Randomly choose one
    X                     -     Randomly choose one again
   ,                      -     Pair; [i, j]
             ʋ            -   Last 4 links as a dyad g([i, j], R):
      Ṭ                   -     Boolean array with 1s at i and j
           ¥              -     Last 2 links as a dyad h([i, j], R):
        ị                 -       Get R[i] and R[j]
         Æm               -       Take the mean
       ×                  -     Replace the 1s with the mean
            o             -     Or; replace the elements at i and j in R with the mean
               ⁹¡         - Apply f(R) G times
                 µ        - Use this list L' as the new argument
                  Ṃ       - Minimum
                    Ṁ     - Maximum
                      Æm  - Mean
                   ; ;    - [Min, Max, Mean]
                        , - Pair with L'

Answer 2

APL+WIN, 60 bytes

Prompts for length and generation. Index origin = 0

v←⍳l←⎕⋄⍎∊⎕⍴⊂'v[i]←(+/v[i←(?l),?l])÷2⋄'⋄(⌊/v),(⌈/v),(+/v÷l),v

Try it online!Thanks to Dyalog Classic

The results in TIO are output in the order listed in the question. The second example in TIO shows that by generation=1000 all elements of the output have converged to the mean in that particular case.

Answer 3

Vyxal, 25 bytes

ʁ?(₅‹₍℅℅~İṁ£(n¥Ȧ)):₌₍GgṁW

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25 bytes of fun. Takes length then generations and outputs [list, [Max, Min], average]. Can be 24 bytes with the W flag

Explained

ʁ?(₅‹₍℅℅~İṁ£(n¥Ȧ)):₌₍GgṁW
ʁ                          # The range [0, length) - this will be the list we modify
 ?(                        # (generation) times:
   ₅‹                      #   push the top of the stack, and its length + 1
     ₍℅℅                   #   choose two random items from the range [0, length) and place them into a list
        ~İ                 #   without popping anything, get the item at each randomly chosen index from the top list - this leaves [list, indexes, items] on the stack
          ṁ£               #   place the average of those two items into the register
            (...)          #   for each index i in the indexes list:
             n¥Ȧ           #      list[i] = register (the mean)
                 )         # close the main for loop
                  :        # now the top of the stack is the list with all the replaced items. We duplicate it so we can extract the juicy info from it
                   ₌₍Ggṁ   # Push a list of [max, min] and push the mean of that list
                        W  # Wrap everything into a single list and implicitly print

Answer 4

JavaScript (ES6), 145 bytes

Expects (length)(generation). Returns [min, max, avg, list].

with(Math)f=(n,a=[k=n],R=random)=>g=m=>k?g(m,a[--k]=k):m?g(m-1,a[i=R()*n|0]=a[j=R()*n|0]=(a[i]+a[j])/2):[min(...a),max(...a),eval(a.join`+`)/n,a]

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Answer 5

Python, 134 bytes

from random import*
R=randrange
def f(l,g):*a,=range(l);exec("a[x]=a[y]=a[x:=R(l)]/2+a[y:=R(l)]/2;"*g);return min(a),max(a),sum(a)/l,a

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-13 bytes thanks to pxeger using randrange and :=

Answer 6

Charcoal, 39 bytes

ＦＮ⊞υιＦＥＮＥ²‽ＬυＵＭυ⎇№ιλ⊘ΣＥι§υμκＩ⟦⌊υ⌈υ⊘⊖Ｌυυ

Try it online! Link is to verbose version of code. Explanation:

ＦＮ⊞υι

Generate a range of length length.

ＦＥＮＥ²‽Ｌυ

Generate generation pairs of random integers also in that range, and loop over those pairs.

ＵＭυ⎇№ιλ⊘ΣＥι§υμκ

Update the array at those two indices with the average of the two values that are there.

Ｉ⟦⌊υ⌈υ⊘⊖Ｌυυ

Output the minimum, maximum, average and values.

Answer 7

Python3, 133 131 128 bytes

from random import*
def f(l,g):
 *r,=range(l)
 while g:shuffle(r);*r,x,y=r;r+=[(x+y)/2]*2;g-=1
 return min(r),max(r),sum(r)/l,r

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Answer 8

J, 44 bytes

(<./;>./;];+/%#)@(2&((?#)(2%~1#.{)`[`]}])i.)

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Outputs Min / Max / List / Avg

Answer 9

Factor, 87 bytes

[ iota >array [ randomize 2 cut* mean dup 2array append ] repeat dup minmax pick mean ]

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Answer 10

BQN (CBQN), 56 bytes

{A←+´÷≠,(⌈´∾⌊´∾A∾⋈){∾˜∘A⌾((2•rand.Range≠𝕩)⊸⊏)𝕩}⍟𝕨↕𝕩}

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fixed after ovs' comment.

-1 from ovs.

Answer 11

Julia, 81 bytes

l\g=(L=[0.:~-l;];1:g.|>_->(r=rand(1:l,2);L[r].=sum(L[r])/2);(extrema(L),~-l/2,L))

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expects length\generation and returns ((min, max), mean, list)

Answer 12

TI-Basic, 85 bytes

Prompt L,G
seq(I,I,0,L-1→A
For(I,1,G
rand(dim(ʟA→B
SortA(ʟB,ʟA
mean({ʟA(1),ʟA(2→ʟA(1
Ans→ʟA(2
End
Disp min(ʟA),max(ʟA),mean(ʟA),ʟA

^{seq(I,I, can be replaced with randIntNoRep( for -3 bytes if the calculator supports it.}

Output is displayed.