Desafio

Dada uma lista não vazia de números reais, calcule sua mediana.

Definições

A mediana é calculada da seguinte forma: primeiro classifique a lista,

• se o número de entradas for ímpar , a mediana é o valor no centro da lista classificada,
• caso contrário, a mediana é a média aritmética dos dois valores mais próximos do centro da lista classificada.

Exemplos

[1,2,3,4,5,6,7,8,9] -> 5
[1,4,3,2] -> 2.5
[1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,-5,100000,1.3,1.4] -> 1.5
[1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,-5,100000,1.3,1.4] -> 1.5

Python 2 , 48 bytes

Uma função sem nome que retorna o resultado. -1 byte graças ao xnor.

lambda l:l.sort()or(l[len(l)/2]+l[~len(l)/2])/2.

O primeiro passo é obviamente classificar a matriz usando l.sort(). No entanto, só podemos ter uma instrução em um lambda, portanto, utilizamos o fato de que a função de classificação retorna Noneadicionando um or- como Noneé falso no Python, isso indica para avaliar e retornar a próxima parte da instrução.

Agora que temos a lista classificada, precisamos encontrar os valores intermediários ou intermediários.

Usar um condicional para verificar a paridade do comprimento seria muito detalhado; portanto, obtemos os índices len(l)/2e ~len(l)/2:

• O primeiro é o piso (comprimento / 2) , que obtém o elemento do meio, se o comprimento for ímpar, ou o item esquerdo no par central, se o comprimento for par.
• A segunda é a inversão binária do comprimento da lista, avaliando como -1 - piso (comprimento / 2) . Devido à indexação negativa do Python, isso basicamente faz o mesmo que o primeiro índice, mas ao contrário do final da matriz.

Se a lista tiver um comprimento ímpar, esses índices apontarão para o mesmo valor. Se for de comprimento uniforme, eles apontarão para os dois itens centrais.

Agora que temos esses dois índices, encontramos esses valores na lista, somamos e dividimos por 2. A casa decimal à direita em /2.garante que seja a divisão flutuante em vez da divisão inteira.

O resultado é retornado implicitamente, pois esta é uma função lambda.

Experimente online!

Python3 - 31 30 bytes

Guardou um byte graças a @Dennis!

Eu não estava planejando uma resposta embutida, mas encontrei este módulo e achei muito legal, porque não fazia ideia de que ele existia.

from statistics import*;median

Experimente online aqui .

Na verdade , 1 byte

║

Experimente online!

Geléia , 9 bytes

L‘HịṢµ÷LS

Experimente online!

Explicação

Ainda estou pegando o jeito de Jelly ... não consegui encontrar os componentes internos para a mediana ou a média de uma lista, mas é muito conveniente para esse desafio que o Jelly permita que índices não inteiros sejam incluídos nas listas, nesse caso, ele retornará um par dos dois valores mais próximos. Isso significa que podemos trabalhar com metade do comprimento da entrada como índice e obter um par de valores quando precisarmos calculá-lo.

L          Get the length of the input.
 ‘         Increment it.
  H        Halve it. This gives us the index of the median for an odd-length list
           (Jelly uses 1-based indexing), and a half-integer between the two indices
           we need to average for even-length lists.
   ịṢ      Use this as an index into the sorted input. As explained above this will
           either give us the median (in case of an odd-length list) or a pair of
           values we'll now need to average.
     µ     Starts a monadic chain which is then applied to this median or pair...
      ÷L     Divide by the length. L treats atomic values like singleton lists.
        S    Sum. This also treats atomic values like singleton lists. Hence this
             monadic chain leaves a single value unchanged but will return the
             mean of a pair.

Flak cerebral , 914 + 1 = 915 bytes

([]){({}[()]<(([])<{({}[()]<([([({}<(({})<>)<>>)<><({}<>)>]{}<(())>)](<>)){({}())<>}{}({}<><{}{}>){{}<>(<({}<({}<>)<>>)<>({}<>)>)}{}({}<>)<>>)}{}<>{}>[()]){({}[()]<({}<>)<>>)}{}<>>)}{}([]<(()())>(<>))<>{(({})){({}[()])<>}{}}{}<>([{}()]{}<(())>){((<{}{}([[]]()){({}()()<{}>)}{}(({}){}<([]){{}{}([])}{}>)>))}{}{(<{}([[]]()()){({}()()<{}>)}{}({}{}<([]){{}{}([])}{}>)>)}{}([(({}<((((((()()()){}){}){}()){})[()()()])>)<(())>)](<>)){({}())<>}{}<>{}{}<>(({})){{}{}<>(<(())>)}{}(({}<>)<{(<{}([{}])>)}{}{(({})<((()()()()()){})>)({}(<>))<>{(({})){({}[()])<>}{}}{}<>([{}()]{})({}<({}<>)<>>((((()()()){}){}){}){})((()()()()()){})<>({}<>)(()()){({}[()]<([([({})](<()>))](<>())){({}())<>}{}<>{}{}<>(({})){{}{}<>(<(())>)}{}(({})<>)<>{(<{}([{}])>)}{}({}<>)<>({}<><({}<>)>)>)}{}({}(<>))<>([()]{()<(({})){({}[()])<>}{}>}{}<><{}{}>)<>(({}{}[(())])){{}{}(((<{}>)))}{}{}{(<{}<>([{}])><>)}{}<>}{}>){(<{}(((((()()()()())){}{})){}{})>)}{}

Requer que o -Asinalizador seja executado.

Experimente online!

Explicação

A espinha dorsal desse algoritmo é uma espécie de bolha que escrevi há algum tempo.

([]){({}[()]<(([])<{({}[()]<([([({}<(({})<>)<>>)<><({}<>)>]{}<(())>)](<>)){({}())<>}{}({}<><{}{}>){{}<>(<({}<({}<>)<>>)<>({}<>)>)}{}({}<>)<>>)}{}<>{}>[()]){({}[()]<({}<>)<>>)}{}<>>)}{}

Não me lembro como isso funciona, então não me pergunte. Mas sei que classifica a pilha e até funciona para negativos

Depois que tudo foi resolvido, encontro 2 vezes a mediana com o seguinte pedaço

([]<(()())>(<>))<>{(({})){({}[()])<>}{}}{}<>([{}()]{}<(())>)  #Stack height modulo 2
{((<{}{}          #If odd
 ([[]]())         #Push negative stack height +1
 {                #Until zero 
  ({}()()<{}>)    #add 2 to the stack height and pop one
 }{}              #Get rid of garbage
 (({}){}<         #Pickup and double the top value
 ([]){{}{}([])}{} #Remove everything on the stack
 >)               #Put it back down
>))}{}            #End if
{(<{}                     #If even
  ([[]]()())              #Push -sh + 2
  {({}()()<{}>)}{}        #Remove one value for every 2 in that value
  ({}{}<([]){{}{}([])}{}>)#Add the top two and remove everything under them
>)}{}                     #End if

Agora tudo o que resta é converter para ASCII

([(({}<((((((()()()){}){}){}()){})[()()()])>)<(())>)](<>)){({}())<>}{}<>{}{}<>(({})){{}{}<>(<(())>)}{}(({}<>)<
{(<{}([{}])>)}{}  #Absolute value (put "/2" beneath everything)

{                 #Until the residue is zero 
(({})<            #|Convert to base 10
((()()()()()){})  #|
>)                #|...
({}(<>))<>{(({})){({}[()])<>}{}}{}<>([{}()]{})
({}<({}<>)<>>((((()()()){}){}){}){})((()()()()()){})<>({}<>)
                  #|
(()()){({}[()]<([([({})](<()>))](<>())){({}())<>}{}<>{}{}<>(({})){{}{}<>(<(())>)}{}(({})<>)<>{(<{}([{}])>)}{}({}<>)<>({}<><({}<>)>)>)}{}({}(<>))<>([()]{()<(({})){({}[()])<>}{}>}{}<><{}{}>)<>(({}{}[(())])){{}{}(((<{}>)))}{}{}{(<{}<>([{}])><>)}{}<>
}{}               #|
>)
{(<{}(((((()()()()())){}{})){}{})>)}{}  #If it was negative put a minus sign

R, 6 bytes

median

Not surprising that R, a statistical programming language, has this built-in.

MATL, 4 bytes

.5Xq

This finds the 0.5-quantile, which is the median.

Try it online!

Pyth - 11 bytes

Finds the average of the middle item taken both backwards and forwards.

.O@R/lQ2_BS

Test Suite.

Octave, 38 bytes

@(x)mean(([1;1]*sort(x))(end/2+[0 1]))

This defines an anonymous function. Input is a row vector.

Try it online!

Explanation

            sort(x)                 % Sort input x, of length k
      [1;1]*                        % Matrix-multiply by column vector of two ones
                                    % This vertically concatenates the sort(x) with 
                                    % itself. In column-major order, this effectively 
                                    % repeats each entry of sort(x)
     (             )(end/2+[0 1])   % Select the entry at position end/2 and the next.
                                    % Entries are indexed in column-major order. Since
                                    % the array has 2*k elements, this picks the k-th 
                                    % and (k+1)-th. Because entries were repeated, for
                                    % odd k this takes the original (k+1)/2-th entry
                                    % (1-based indexing) twice. For even k this takes
                                    % the original (k/2)-th and (k/2+1)-th entries
mean(                            )  % Mean of the two selected entries

JavaScript, 57 52 bytes

v=>(v.sort((a,b)=>a-b)[(x=v.length)>>1]+v[--x>>1])/2

Sort the array numerically. If the array is an even length, find the 2 middle numbers and average them. If the array is odd, find the middle number twice and divide by 2.

Matlab/Octave, 6 bytes

A boring built-in:

median

Try it online!

Mathematica, 6 bytes

Median

As soon as I figure out Mthmtca, I'm posting a solution in it.

Perl 6, 31 bytes

*.sort[{($/=$_/2),$/-.5}].sum/2

Try it

Expanded:

*\     # WhateverCode lambda ( this is the parameter )

.sort\ # sort it

[{     # index into the sorted list using a code ref to calculate the positions

  (
    $/ = $_ / 2 # the count of elements divided by 2 stored in ｢$/｣
  ),            # that was the first index

  $/ - .5       # subtract 1/2 to get the second index

                # indexing operations round down to nearest Int
                # so both are effectively the same index if given
                # an odd length array

}]\

.sum / 2        # get the average of the two values

APL (Dyalog Unicode), 14 bytes

≢⊃2+/2/⊂∘⍋⌷÷∘2

Try it online!

This is a train. The original dfn was {(2+/2/⍵[⍋⍵])[≢⍵]÷2}.

The train is structured as follows

┌─┼───┐
≢ ⊃ ┌─┼───┐
    2 / ┌─┼───┐
    ┌─┘ 2 / ┌─┼─┐
    +       ∘ ⌷ ∘
           ┌┴┐ ┌┴┐
           ⊂ ⍋ ÷ 2

⊢ denotes the right argument.

⌷ index

• ⊂∘⍋ the indices which indexed into ⊢ results in ⊢ being sorted

• ÷∘2 into ⊢ divided by 2

2/ replicate this twice, so 1 5 7 8 becomes 1 1 5 5 7 7 8 8

2+/ take the pairwise sum, this becomes (1+1)(1+5)(5+5)(5+7)(7+7)(7+8)(8+8)

⊃ from this pick

• ≢ element with index equal to the length of ⊢

Previous solutions

{.5×+/(⍵[⍋⍵])[(⌈,⌊).5×1+≢⍵]}
{+/(2/⍵[⍋⍵]÷2)[0 1+≢⍵]}
{+/¯2↑(1-≢⍵)↓2/⍵[⍋⍵]÷2}
{(2+/2/⍵[⍋⍵])[≢⍵]÷2}
{(≢⍵)⊃2+/2/⍵[⍋⍵]÷2}
≢⊃2+/2/2÷⍨⊂∘⍋⌷⊢
≢⊃2+/2/⊂∘⍋⌷÷∘2

Common Lisp, 89

(lambda(s &aux(m(1-(length s)))(s(sort s'<)))(/(+(nth(floor m 2)s)(nth(ceiling m 2)s))2))

I compute the mean of elements at position (floor middle) and (ceiling middle), where middle is the zero-based index for the middle element of the sorted list. It is possible for middle to be a whole number, like 1 for an input list of size 3 such as (10 20 30), or a fraction for lists with an even numbers of elements, like 3/2 for (10 20 30 40). In both cases, we compute the expected median value.

(lambda (list &aux
             (m (1-(length list)))
             (list (sort list #'<)))
  (/ (+ (nth (floor m 2) list)
        (nth (ceiling m 2) list))
     2))

Vim, 62 bytes

I originally did this in V using only text manipulation until the end, but got frustrated with handling [X] and [X,Y], so here's the easy version. They're about the same length.

c$:let m=sort(")[(len(")-1)/2:len(")/2]
=(m[0]+m[-1])/2.0

Try it online!

Unprintables:

c$^O:let m=sort(^R")[(len(^R")-1)/2:len(^R")/2]
^R=(m[0]+m[-1])/2.0

Honorable mention:

• ^O takes you out of insert mode for one command (the let command).
• ^R" inserts the text that was yanked (in this case the list)

TI-Basic, 2 bytes

median(Ans

Very straightforward.

C#, 126 bytes

using System.Linq;float m(float[] a){var x=a.Length;return a.OrderBy(g=>g).Skip(x/2-(x%2==0?1:0)).Take(x%2==0?2:1).Average();}

Pretty straightforward, here with LINQ to order the values, skip half the list, take one or two values depending on even/odd and average them.

C++ 112 Bytes

Thanks to @original.legin for helping me save bytes.

#include<vector>
#include<algorithm>
float a(float*b,int s){std::sort(b,b+s);return(b[s/2-(s&1^1)]+b[s/2])/2;}

Usage:

    int main()
    {
        int n = 4;
        float e[4] = {1,4,3,2};
        std::cout<<a(e,n); /// Prints 2.5

        n = 9;
        float e1[9] = {1,2,3,4,5,6,7,8,9};
        std::cout<<a(e1,n); /// Prints 5

        n = 13;
        float e2[13] = {1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,-5,100000,1.3,1.4};
        std::cout<<a(e2,n); /// Prints 1.5

        return 0;
    }

J, ₁₆ 14 bytes

2%~#{2#/:~+\:~

Try it online!

In addition to BMO's array duplication trick, I found that we can add the whole array sorted in two directions. Then I realized that the two steps can be reversed, i.e. add the two arrays, then duplicate them and take the nth element.

How it works

2%~#{2#/:~+\:~
                Input: array of length n
       /:~      Sort ascending
           \:~  Sort descending
          +     Add the two element-wise
     2#         Duplicate each element
   #{           Take n-th element
2%~             Halve

Previous answers

J with stats addon, 18 bytes

load'stats'
median

Try it online!

Library function FTW.

median's implementation looks like this:

J, 31 bytes

-:@(+/)@((<.,>.)@(-:@<:@#){/:~)

Try it online!

How it works

-:@(+/)@((<.,>.)@(-:@<:@#){/:~)
         (<.,>.)@(-:@<:@#)       Find center indices:
                  -:@<:@#          Compute half of given array's length - 1
          <.,>.                    Form 2-element array of its floor and ceiling
                          {/:~   Extract elements at those indices from sorted array
-:@(+/)                          Sum and half

A bit of golfing gives this:

J, 28 bytes

2%~[:+/(<.,>.)@(-:@<:@#){/:~

Try it online!

J, 19 bytes

<.@-:@#{(/:-:@+\:)~

Explanation:

        (        )~   apply monadic argument twice to dyadic function 
         /:           /:~ = sort the list upwards
               \:     \:~ = sort the list downwards
           -:@+       half of sum of both lists, element-wise
<.@-:@#               floor of half of length of list
       {              get that element from the list of sums

JavaScript, 273 Bytes

function m(l){a=(function(){i=l;o=[];while(i.length){p1=i[0];p2=0;for(a=0;a<i.length;a++)if(i[a]<p1){p1=i[a];p2=a}o.push(p1);i[p2]=i[i.length-1];i.pop()}return o})();return a.length%2==1?l[Math.round(l.length/2)-1]:(l[Math.round(l.length/2)-1]+l[Math.round(l.length/2)])/2}

Java 7, 99 bytes

Golfed:

float m(Float[]a){java.util.Arrays.sort(a);int l=a.length;return l%2>0?a[l/2]:(a[l/2-1]+a[l/2])/2;}

Ungolfed:

float m(Float[] a)
{
    java.util.Arrays.sort(a);
    int l = a.length;
    return l % 2 > 0 ? a[l / 2] : (a[l / 2 - 1] + a[l / 2]) / 2;
}

Try it online

Pari/GP - 37 39 Bytes

Let a be a rowvector containing the values.

b=vecsort(a);n=#b+1;(b[n\2]+b[n-n\2])/2  \\ 39 byte              

n=1+#b=vecsort(a);(b[n\2]+b[n-n\2])/2    \\ obfuscated but only 37 byte

Since Pari/GP is interactive, no additional command is needed to display the result.

a=vector(8,r,random(999))           
n=1+#b=vecsort(a);w=(b[n\2]+b[n-n\2])/2      
print(a);print(b);print(w)       

Try it online!

Japt, 20 bytes

n gV=0|½*Ul)+Ug~V)/2

Test it online! Japt really lacks any built-ins necessary to create a really short answer for this challenge...

Explanation

n gV=0|½*Ul)+Ug~V)/2  // Implicit: U = input list
n                     // Sort U.
   V=0|½*Ul)          // Set variable V to floor(U.length / 2).
  g                   // Get the item at index V in U.
            +Ug~V     // Add to that the item at index -V - 1 in U.
                 )/2  // Divide by 2 to give the median.
                      // Implicit: output result of last expression

Java 8, 71 bytes

Parity is fun! Here's a lambda from double[] to Double.

l->{java.util.Arrays.sort(l);int s=l.length;return(l[s/2]+l[--s/2])/2;}

Nothing too complex going on here. The array gets sorted, and then I take the mean of two numbers from the array. There are two cases:

• If the length is even, then the first number is taken from just ahead of the middle of the array, and the second number is taken from the position before that by integer division. The mean of these numbers is the median of the input.
• If the length is odd, s and s-1 both divide to the index of the middle element. The number is added to itself and the result divided by two, yielding the original value.

Try It Online

SmileBASIC, 45 bytes

DEF M A
L=LEN(A)/2SORT A?(A[L-.5]+A[L])/2
END

Gets the average of the elements at floor(length/2) and floor(length/2-0.5) Very simple, but I was able to save 1 byte by moving things around:

DEF M A
SORT A    <- extra line break
L=LEN(A)/2?(A[L-.5]+A[L])/2
END

Husk, 10 bytes

½ΣF~e→←½OD

Try it online!

Explanation

This function uses that the median of $[a_1 \dots a_N]$ is the same as the median of $[a_1 \; a_1 \dots a_N \; a_N]$ which avoids the ugly distinction of odd-/even-length lists.

½ΣF~e→←½OD  -- example input: [2,3,4,1]
         D  -- duplicate: [2,3,4,1,2,3,4,1]
        O   -- sort: [1,1,2,2,3,3,4,4]
       ½    -- halve: [[1,1,2,2],[3,3,4,4]]
  F         -- fold the following
   ~        -- | compose the arguments ..
     →      -- | | last element: 2
      ←     -- | | first element: 3
    e       -- | .. and create list: [2,3]
            -- : [2,3]
 Σ          -- sum: 5
½           -- halve: 5/2

_{Unfortunately ½ for lists has the type [a] -> [[a]] and not [a] -> ([a],[a]) which doesn't allow F~+→← since foldl1 needs a function of type a -> a -> a as first argument, forcing me to use e.}

R without using the median builtin, 51 bytes

function(x,n=sum(x|1)+1)mean(sort(x)[n/2+0:1*n%%2])

Try it online!

GolfScript, 27 25 20 17 bytes

~..+$\,(>2<~+"/2"

Takes input as an array of integers on stdin. Outputs as an unreduced fraction. Try it online!

Explanation

The median of the array, as BMO's Husk answer explains, is equal to the median of an array twice as long where each element is repeated twice. So we concatenate the array to itself, sort, and take the mean of the middle two elements. If the length of the original array is $l$, the middle two elements of the doubled array are at indices $l-1$ and $l$.

~                  Evaluate input (converting string -> array)
 ..                Duplicate twice
   +               Concatenate two of the copies
    $              Sort the doubled array
     \,            Swap with the non-doubled array and get its length: l
       (           Decrement: l-1
        >          Array slice: all elements at index (l-1) and greater
         2<        Array slice: first two elements (originally at indices l-1 and l)
           ~       Dump array elements to stack
            +      Add
             "/2"  Push that string
                   Output all items on stack without separator

The output will be something like 10/2.