Problem:


Score : 300 points

Problem Statement

You have a pot and N ingredients. Each ingredient has a real number parameter called value, and the value of the i-th ingredient (1 \leq i \leq N) is v_i.

When you put two ingredients in the pot, they will vanish and result in the formation of a new ingredient. The value of the new ingredient will be (x + y) / 2 where x and y are the values of the ingredients consumed, and you can put this ingredient again in the pot.

After you compose ingredients in this way N-1 times, you will end up with one ingredient. Find the maximum possible value of this ingredient.

Constraints

2 \leq N \leq 50

1 \leq v_i \leq 1000

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
v_1 v_2 \ldots v_N

Output

Print a decimal number (or an integer) representing the maximum possible value of the last ingredient remaining.

Your output will be judged correct when its absolute or relative error from the judge's output is at most 10^{-5}.

Sample Input 1

2
3 4

Sample Output 1

3.5

If you start with two ingredients, the only choice is to put both of them in the pot. The value of the ingredient resulting from the ingredients of values 3 and 4 is (3 + 4) / 2 = 3.5.

Printing 3.50001, 3.49999, and so on will also be accepted.

Sample Input 2

3
500 300 200

Sample Output 2

375

You start with three ingredients this time, and you can choose what to use in the first composition. There are three possible choices:

Use the ingredients of values 500 and 300 to produce an ingredient of value (500 + 300) / 2 = 400. The next composition will use this ingredient and the ingredient of value 200, resulting in an ingredient of value (400 + 200) / 2 = 300.

Use the ingredients of values 500 and 200 to produce an ingredient of value (500 + 200) / 2 = 350. The next composition will use this ingredient and the ingredient of value 300, resulting in an ingredient of value (350 + 300) / 2 = 325.

Use the ingredients of values 300 and 200 to produce an ingredient of value (300 + 200) / 2 = 250. The next composition will use this ingredient and the ingredient of value 500, resulting in an ingredient of value (250 + 500) / 2 = 375.

Thus, the maximum possible value of the last ingredient remaining is 375.

Printing 375.0 and so on will also be accepted.

Sample Input 3

5
138 138 138 138 138

Sample Output 3

138



Sample input:
2
3 4


Sample output:
3.5

Submission status: Accepted

Solution code:
#from functools import reduce
N = int(input())
Xs_ = sorted(map(int,input().split()))
print(sum([Xs_[i]*(2**(-N+1)) if i == 0 else Xs_[i]* (2**(-N+i)) for i in range(N)]))

Submission status: Accepted

Solution code:

n = int(input())
V = list(map(int,input().split()))

V.sort(reverse=1)

bunbo = 2
ans = 0

for i in range(n):
    ans += V[i] / bunbo
    bunbo *= 2

print(ans + V[-1]/(bunbo/2))

Submission status: Accepted

Solution code:
# coding: utf-8
N = int(input())
V = list(map(int, input().split()))
V.sort()
ans = 0
for i in range(N):
    if i == 0:
        ans = V[i]
    else:
        ans = (ans + V[i]) / 2
print(ans)

Submission status: Accepted

Solution code:
n = int(input())
arr = [int(x) for x in input().split()]
arr.sort()

t = (arr[0] + arr[1]) / 2
for j in range(2, n):
  t = (t + arr[j]) / 2

print(t)

Submission status: Accepted

Solution code:
N = int(input())
v = list(map(int,input().split()))

v.sort()
nabe = v[0]

for i in v[1:]:
    nabe = (nabe + i)/2
    del v[:2]

print(nabe)

Submission status: Accepted

Solution code:
import sys

def main():
    input = sys.stdin.readline
    N = int(input())
    v = list(map(int, input().split()))
    
    #asc
    v.sort()
    
    s = 0
    pre = 0
    for i, v in enumerate(v):
        if i == 0:
            pre = v
        else:
            s = (pre + v) / 2
            pre = s
    
    print(s)
        
if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
num = int(input())

gu = list(map(int, input().split()))

gu.sort()

ans = gu[0]

for i in gu[1:]:
  ans = (ans + i) / 2



print(ans)

Submission status: Accepted

Solution code:
def main(sample_file = ''):

    """ convenient functions
    # for i, a in enumerate(iterable)
    # q, mod = divmod(a, b)
    # divmod(x, y) returns the tuple (x//y, x%y)
    # Higher-order function: reduce(operator.mul, xyz_count, 1)
    # manage median(s) using two heapq https://atcoder.jp/contests/abc127/tasks/abc127_f
    """

    """convenient decorator
    # @functools.lru_cache():
    # to facilitate use of recursive function
        # ex:
        # from functools import lru_cache
        # import sys
        # sys.setrecursionlimit(10**9)
        # @lru_cache(maxsize=None)
        # def fib(n):
        #     if n < 2:
        #         return n
        #     return fib(n-1) + fib(n-2)
        # print(fib(1000))
    """
    
    # import numpy as np
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product # https://docs.python.org/ja/3/library/itertools.html
    # accumulate() returns iterator! to get list: list(accumulate())
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  # prime factor
        b, e = 2, 0  # base, exponent
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        # TODO: How should I do when n - r is negative?
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict # https://docs.python.org/ja/3/library/collections.html#collections.deque
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest # https://docs.python.org/ja/3/library/heapq.html
    from copy import deepcopy, copy # https://docs.python.org/ja/3/library/copy.html
    import operator
    from operator import itemgetter #sort 
    # ex1: List.sort(key=itemgetter(1))
    # ex2: sorted(tuples, key=itemgetter(1,2))
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd # Deprecated since version 3.5: Use math.gcd() instead.
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)
    
    # first create factorial_list
    # fac_list = mod_factorial_list(n)
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    modpow = lambda a, n, p = MOD: pow(a, n, p) # Recursive function in python is slow!
    def modinv(a, p = MOD):
        # evaluate reciprocal using Fermat's little theorem:
        # a**(p-1) is identical to 1 (mod p) when a and p is coprime
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        # fac_list = modfactorial_list(100)
        # print(modcomb(100, 5, modfactorial_list(100)))
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something
        >>  else:
        >>      do something
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    # Graph: https://en.wikipedia.org/wiki/Directed_graph
    # Bellman-Ford: O(|V||E|). Use this if there exists an edge with negative length in the graph
    # After N steps, the shortest path has converded if there doesn't exist an cycle of edges with negative
    # Watch out: d[N] == d[2*N] doesn't necessarily mean the graph doesn't have negative cycle
    # ref: https://www.youtube.com/watch?v=1Z6ofKN03_Y

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    """ initialize variables and set inputs
    # initialize variables
        # to initialize list, use [0] * n
        # to initialize two dimentional array, use [[0] * N for _ in range(N)]
    # set inputs
        # put inputs between specific values (almost as quickly)
        # ex) S = [-INF] + [int(r()) for _ in range(A)] + [INF]
        # open(0).read() is sometimes useful:
        # ex) n, m, *x = map(int, open(0).read().split())
        #     min(x[::2]) - max(x[1::2])
        # ex2) *x, = map(int, open(0).read().split())
        #     don't forget to add comma after *x if only one variable is used
    # preprocessing
        # transpose = [x for x in zip(*data)]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [(1, 4, 7), (2, 5, 8), (3, 6, 9)]
        # flat = [flatten for inner in data for flatten in inner]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [1, 2, 3, 4, 5, 6, 7, 8, 9]
    # calculate and output
        # output pattern
        # ex1) print(*l) => when l = [2, 5, 6], printed 2 5 6
    """

    # functions to read input
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    R = lambda: list(map(int, r().split()))
    Rmap = lambda: map(int, r().split())
    Rfloat = lambda: list(map(float, r().split()))
    Rtuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    # single int: int(r())
    # single string: r()
    # single float: float(r())
    # line int: R()
    # line string: r().split()
    # line (str, int, int): [j if i == 0 else int(j) for i, j in enumerate(r().split())]
    # lines int: [R() for _ in range(n)]
    """

    # for test
    if sample_file:
        sys.stdin = open(sample_file)
        
    # ----------------------------------
    # main

    N = int(r())
    V = R()
    heapify(V)
    for _ in range(N-1):
        a = heappop(V)
        b = heappop(V)
        heappush(V, (a+b)/2)
    print(*V)
    
    
    

    # to finish code, use return instead of exit()
    # end of main
    # ----------------------------------

    """memo: how to use defaultdict of list
    # initialize
    Dic = defaultdict(list)
    # append / extend
    Dic[x].append(y)
    # three methods for loop: keys(), values(), items()
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    # to make binary digits text
    >>> a = 5
    >>> bin_str_a = format(a, '#06b')
    >>> print(bin_str_a)
    0b0101 # first 2 strings (='0b') indicates it is binary
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
N = int(input())
ing = list(map(int, input().split()))
ing.sort()
for i in range(N-1):
    ing[i+1] = (ing[i]+ing[i+1])*0.5
print(ing[N-1])

Submission status: Accepted

Solution code:
n = int(input())
v = list(map(int, input().split()))
v.sort()

for i in range(n-1):
  a, b = v[:2], v[2:]
  new = sum(a)/2
  v = [new] + b
  v.sort()
  
print(v[0])

Submission status: Accepted

Solution code:

n=int(input())
vList=list(map(int,input().split()))

vList.sort()
mixed = vList[0]
for i in range(n-1):
	mixed = (mixed + vList[i+1]) / 2
print(mixed)

Submission status: Accepted

Solution code:
n = int(input())
v = list(map(int,input().split()))

v.sort()

ans = v[0]

for i in v[1:]:
    ans = (ans + i) / 2

print(ans)

Submission status: Accepted

Solution code:
N = int(input())
v = list(map(int, input().split()))
v.sort()

x = v[0]

for i in range(1, N):
    x += v[i] * (2 ** (i - 1))

print(x / (2 ** (N - 1)))

Submission status: Accepted

Solution code:
def c_alchemist():
    from functools import reduce
    N = int(input())
    V = [int(i) for i in input().split()]
    return reduce(lambda x, y: (x + y) / 2, sorted(V))

print(c_alchemist())

Submission status: Accepted

Solution code:
a = int(input())
ar = list(map(int,input().split(" ")))
while len(ar) != 1:
    ar.sort()
    ar.append((ar[0] + ar[1]) / 2)
    del ar[0]
    del ar[0]
print(ar[0])

Submission status: Accepted

Solution code:
N = int(input())
v = input().split()
V = sorted(v, key = int)
S = int(V[0])
for i in range(N-1):
  S = (S + int(V[i+1])) / 2
print(S)

Submission status: Accepted

Solution code:
import sys
def input(): return sys.stdin.readline().strip()
n=int(input())
vv=sorted(map(int,input().split()))
from functools import reduce
print(reduce(lambda x,y:(x+y)/2, vv))

Submission status: Accepted

Solution code:
N = int(input())
V = [int(v) for v in input().split()]

V.sort()
ans = V[0] * ((1/2)**(N-1))
for n in range(1, N):
  ans += V[n] * ((1/2)**(N-n))

print(ans)

Submission status: Accepted

Solution code:
N=int(input())
v=list(map(int,input().split()))
v.sort()
sum=0

for i in range(N-1):
    v[i+1]=(v[i]+v[i+1])/2
    

print(v[N-1])

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-

import sys


n = int(sys.stdin.readline())
v = [int(x) for x in sys.stdin.readline().strip().split(" ")]

v = sorted(v)[::-1]
for _ in range(len(v) - 1):
    v1 = v.pop()
    v2 = v.pop()
    v3 = (v1 + v2) / 2
    v.append(v3)

print(v[0])

Submission status: Accepted

Solution code:
N=int(input())
value=sorted(list(map(int,input().split())))
while len(value)!=1:
  val=(value[0]+value[1])/2
  value.pop(0)
  value.pop(0)
  value.append(val)
  value=sorted(value)
print(value[0])

Submission status: Accepted

Solution code:
# Alchemist
N = int(input())
V = list(map(int, input().split()))

V = sorted(V) # 小さい順に並ぶ

V[0] = V[0]/(2**(N-1))
for i in range(1, N):
	V[i] = V[i]/(2**(N-i))
	
ans = sum(V)
print(ans)

Submission status: Accepted

Solution code:
n = int(input())
vLst = list(map(int, input().split()))
svLst = sorted(vLst)
cv = svLst.pop(0)
for v in svLst:
    cv = (cv + v) / 2
print(cv)

Submission status: Accepted

Solution code:
def main():
    N = int(input())
    V = list(map(int, input().split()))
    V.sort()
    ans = V[0]
    for i in range(1, N):
        ans = (ans + V[i]) / 2
    print(ans)


if __name__ == "__main__":
    main()

Submission status: Accepted

Solution code:
n=int(input())
l=list(map(int,input().split()))
l2=sorted(l)
for _ in range(n):
    if len(l2)==1:
        break
    a=l2.pop(0)
    b=l2.pop(0)
    l2.insert(0, (a+b)/2)
print(l2[0])

Submission status: Accepted

Solution code:
n=int(input())
it=list(map(int,input().split()))
it.sort()
a=it[0]
for i in range(1,n):
    a=(a+it[i])/2
print(a)

Submission status: Accepted

Solution code:
input()
vs=list(sorted(map(int, input().split(" "))))
s=vs[0]
for v in vs[1:]:
	s += v
	s /= 2.0
print("%.7f" % s)

Submission status: Accepted

Solution code:
from heapq import heappop, heappush

_ = int(input())
v = list(map(float, input().split()))

q = []
for vi in v:
    heappush(q, vi)

ans = heappop(q)
while q:
    ans += heappop(q)
    ans /= 2

print(ans)

Submission status: Accepted

Solution code:
N = int(input())
V = map(int, input().split())
V = sorted(V)
P = V[0]
for i in range(N-1):
  P += V[i+1]
  P = P/2
print(P)

Submission status: Accepted

Solution code:
N = int(input())
V = list(map(int, input().split()))

V.sort()
while len(V)>1:
  new_v = (V[0]+V[1])/2
  V = [new_v] + V[2:]

print(V[0])

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-


def main():
    n = int(input())
    v = sorted(list(map(int, input().split())))
    ans = (v[0] + v[1]) / 2

    for i in range(2, n):
        ans = (ans + v[i]) / 2

    print(ans)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import heapq
N = int(input())
V = list(map(int, input().split()))
 
heapq.heapify(V)
for i in range(N-2):
  heapq.heappush(V, (heapq.heappop(V)+heapq.heappop(V))/2)
print(sum(V)/2)

Submission status: Accepted

Solution code:
n =int(input())
v = list(map(int,input().split()))

v.sort()

for i in range(len(v)-1):
  v[1]=(v[1]+v[0])/2
  del v[0]
  
print(v[0])

Submission status: Accepted

Solution code:
a=int(input())
b=sorted(list(map(int, input().split())))
while len(b)>1:
  ave=(b[0]+b[1])/2
  del b[0]
  b[0]=ave
print(b[0])

Submission status: Accepted

Solution code:
n=int(input())
v=list(map(float,input().split()))
v.sort()
for i in range(n-1):
    v[i+1]=(v[i]+v[i+1])/2
print(v[n-1])

Submission status: Accepted

Solution code:
a = int(input())
b = list(map(int,input().split()))

b.sort()

for i in range(a-1):
  b[i+1] = (b[i] + b[i+1]) / 2

print(b[a-1])

Submission status: Accepted

Solution code:
N =int(input())
A = sorted([int(a) for a in input().split()])
if N  == 2:
  print(sum(A)/2)
else :
  ans=A[0]
  for i in (A):
    ans+= i
    anss = ans/2
    ans=anss
  print(anss)

Submission status: Accepted

Solution code:
N = int(input())
v = list(map(int, input().split()))
 
while len(v) != 1:
    v.sort(reverse = True)
    a = v.pop()
    b = v.pop()
    v.append((a+b)/2)
    
 
print(v[0])

Submission status: Accepted

Solution code:
N = int(input())
v = list(map(int, input().split()))
 
for i in range(N-1):
    v.sort(reverse = True)
    a = v.pop()
    b = v.pop()
    v.append((a+b)/2)
    
 
print(v[0])

Submission status: Accepted

Solution code:
N = int(input())
v = list(map(int, input().split()))
 
 
v.sort(reverse = True)
 
for i in range(N-1):
    a = v.pop()
    b = v.pop()
    v.append((a+b)/2)
    v.sort(reverse = True)
 
print(v[0])

Submission status: Accepted

Solution code:
N=int(input())
V=list(map(int,input().split()))
V.sort()
count=V[0]
for i in range(1,len(V)):
    count=(count+V[i])/2
print(count)

Submission status: Accepted

Solution code:
n=int(input())
v=list(map(int, input().split()))
vv=sorted(v)
for i in range(n-2):
    vv[i+1] = (vv[i]+vv[i+1]) / 2
print((vv[n-2]+vv[n-1])/2)

Submission status: Accepted

Solution code:

import bisect
import collections
import itertools


def getint(): return int(input())
def getints(): return list(map(int, input().split()))
def getint2d(rows): return [getints() for _ in range(rows)]
def getgrid(rows): return [input() for _ in range(rows)]
def array1d(n, value): return [value for _ in range(n)]
def array2d(n, m, value): return [array1d(m, value) for _ in range(n)]

n = getint()
values = list(sorted(getints()))

res = values[0]

for i in range(1, n):
    res = (res + values[i]) / 2.0

print(res)

Submission status: Accepted

Solution code:
n = int(input())
v = list(map(int, input().split()))
v.sort(reverse=True)

num = v.pop()

for i in range(n - 1):
    num = (v.pop() + num) / 2

print(num)

Submission status: Accepted

Solution code:
N = int(input())
S = list(map(int,input().split(" ")))
S.sort()

while True:
  if len(S)>1:
    num1,num2 =S.pop(0),S.pop(0)
    value=(num1+num2)/2
    S.insert(0,value)
  else:
    print(S.pop())
    break

Submission status: Accepted

Solution code:
n = int(input())
vs = [int(elem) for elem in input().split()]

vs = sorted(vs)
res = 0
for i, v in enumerate(vs):
  if i == 0:
    res = (v + vs[i+1]) / 2
  elif i < len(vs) - 1:
    res = (res + vs[i+1]) / 2
print(res)

Submission status: Accepted

Solution code:
N = int(input())
lst = sorted(list(map(int, input().split())))
while len(lst) > 1:
    lst[1] = (lst[0] + lst[1]) / 2
    lst = lst[1:]
print(lst[0])

Submission status: Accepted

Solution code:
n=input()
L=sorted(list(map(int,input().split())))
a=L[0]
for i in L:
    a=(a+i)/2
print(a)

Submission status: Accepted

Solution code:
n = int(input())
v = sorted(map(int, input().split()))

ans = v[0]
for i in range(1,n):
    ans = (ans + v[i]) / 2
print(ans)

Submission status: Accepted

Solution code:
n = int(input())
*p, = sorted(map(int,input().split()))
#print(p)
a = p[0]
for i in range(1,n):
  a = (a+p[i])/2
  #print(a)
print(a)

Submission status: Accepted

Solution code:
N = int(input())
v = [int(x) for x in input().split()]
v.sort()
result = v[0]
for x in v[1:]:
    result = (result+x)/2.0
print(result)

Submission status: Accepted

Solution code:
N = int(input())
v = sorted(list(map(int, input().split())))

worth = v[0]

for i in range(N-1) : 
    worth = (worth + v[i+1])/2
    
print(worth)

Submission status: Accepted

Solution code:
import numpy as np

N = int(input())
V = np.array(list(map(int,input().split())))
V = np.sort(V)

ans = V[0]

for i in V[1:]:
    ans += i
    ans = ans/2
    
print (ans)

Submission status: Accepted

Solution code:
n = int(input())
lis = sorted(map(int, input().split()))
ans = lis[0]
for i in lis[1:]:
    ans += i
    ans /= 2
print(ans)

Submission status: Accepted

Solution code:
N = int(input())
d = list(map(int,input().split()))

d.sort()

S = (d[0] + d[1])/2

for i in range(2,N):
  S = (S + d[i])/2

print(S)
#print(list(map(int,input().split())).sort(reverse=True))

Submission status: Accepted

Solution code:
N = int(input())
nums = list(map(int, input().split()))
nums.sort()
ans = nums[0]
for num  in nums[1:]:
  ans = (ans + num)/2
print(ans)

Submission status: Accepted

Solution code:
N = int(input())
u = list(map(int, input().split()))

for i in range(N-1):
  a = u.pop(u.index(min(u)))
  b = u.pop(u.index(min(u)))
  u.append((a + b) / 2)

print(u[0])

Submission status: Accepted

Solution code:
N = int(input())
V = [float(v) for v in input().split()]
V.sort(reverse=True)
for i in range(N):
    if len(V) == 1:
        print(V[0])
        exit()
    v1 = V.pop()
    v2 = V.pop()
    V.append((v1 + v2) / 2)

Submission status: Accepted

Solution code:
import numpy as np

N = int(input())
vn_list = input().split()

vn = np.sort(np.array(vn_list, dtype="float"))[::-1]
w = np.logspace(1, N, base=1/2, num = N)
w[N-1] = w[N-2]
result = np.dot(vn, w)
print(result)

Submission status: Accepted

Solution code:
N = int(input())
v_list = list(map(int, input().split()))

from heapq import *
que = []
heapify(que)

for v in v_list:
    heappush(que, v)

while len(que) != 1:
    a = heappop(que)
    b = heappop(que)
    heappush(que, (a+b)/2)
print(que.pop())

Submission status: Accepted

Solution code:
N = int(input())
V = list(map(int,input().split()))

V_ = sorted(V)

ans = 0

for i in range(N-1):  
    ans += V_[i+1]/2**(N-i-1)
    
ans += V_[0]/2**(N-1)

print(ans)

Submission status: Accepted

Solution code:
def solve(l):
    a = (l[0]+l[1])/2
    for i in range(2, len(l)):
        a = (a + l[i])/2
    return a

n = int(input())
l = sorted(list(map(int, input().split())))
print(solve(l))

Submission status: Accepted

Solution code:
def solve(string):
    n, *v = map(int, string.split())
    v = sorted(v, reverse=True)
    return str(sum(_v / 2**i for i, _v in enumerate(v[:-1], start=1)) + v[-1] / 2**(n - 1))


if __name__ == '__main__':
    print(solve('\n'.join([input(), input()])))

Submission status: Accepted

Solution code:
n=int(input())
a=list(map(int,input().split()))
b=sorted(a)
for i in range(1,n):
    b[i]=(b[i]+b[i-1])/2
print(b[-1])