Problem:


Score : 300 points

Problem Statement

There are N towns in a coordinate plane. Town i is located at coordinates (x_i, y_i). The distance between Town i and Town j is \sqrt{\left(x_i-x_j\right)^2+\left(y_i-y_j\right)^2}.

There are N! possible paths to visit all of these towns once. Let the length of a path be the distance covered when we start at the first town in the path, visit the second, third, \dots, towns, and arrive at the last town (assume that we travel in a straight line from a town to another). Compute the average length of these N! paths.

Constraints

2 \leq N \leq 8

-1000 \leq x_i \leq 1000

-1000 \leq y_i \leq 1000

\left(x_i, y_i\right) \neq \left(x_j, y_j\right) (if i \neq j)

(Added 21:12 JST) All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
:
x_N y_N

Output

Print the average length of the paths.
Your output will be judges as correct when the absolute difference from the judge's output is at most 10^{-6}.

Sample Input 1

3
0 0
1 0
0 1

Sample Output 1

2.2761423749

There are six paths to visit the towns: 1 → 2 → 3, 1 → 3 → 2, 2 → 1 → 3, 2 → 3 → 1, 3 → 1 → 2, and 3 → 2 → 1.

The length of the path 1 → 2 → 3 is \sqrt{\left(0-1\right)^2+\left(0-0\right)^2} + \sqrt{\left(1-0\right)^2+\left(0-1\right)^2} = 1+\sqrt{2}.

By calculating the lengths of the other paths in this way, we see that the average length of all routes is:

\frac{\left(1+\sqrt{2}\right)+\left(1+\sqrt{2}\right)+\left(2\right)+\left(1+\sqrt{2}\right)+\left(2\right)+\left(1+\sqrt{2}\right)}{6} = 2.276142...

Sample Input 2

2
-879 981
-866 890

Sample Output 2

91.9238815543

There are two paths to visit the towns: 1 → 2 and 2 → 1. These paths have the same length.

Sample Input 3

8
-406 10
512 859
494 362
-955 -475
128 553
-986 -885
763 77
449 310

Sample Output 3

7641.9817824387



Sample input:
3
0 0
1 0
0 1


Sample output:
2.2761423749

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 = r_int()
    XY = [R() for i in range(N)]
    cnt = 0
    s = 0
    for i in range(N):
        for j in range(N):
            if i != j:
                s += sqrt((XY[i][0]-XY[j][0])**2+(XY[i][1]-XY[j][1])**2)
                cnt += 1
    print(s/cnt*(N-1))
    # 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:
import itertools
n = int(input())
t = 1
for i in range(1,n+1):
  t *= i
L = []
for i in range(n):
  L.append(list(map(int,input().split())))
seq = []
for i in range(n):
  seq.append(i)
K = list(itertools.permutations(seq))
ans = 0
keiro = []
for i in range(n):
  T = [0 for j in range(n)]
  keiro.append(T)
for i in range(n):
  for j in range(n):
    keiro[i][j] = ((L[i][0]-L[j][0])**2+(L[i][1]-L[j][1])**2)**0.5
for i in range(len(K)):
  cur = 0
  for j in range(len(K[i])-1):
    cur += keiro[K[i][j]][K[i][j+1]]
  ans += cur
print(ans/t)

Submission status: Accepted

Solution code:
n = int(input())
a = [[int(i) for i in input().split()] for _ in range(n)]
dp = {}
ans = 0
for i in range(n):
    for k in range(i+1,n):
        dp[(i,k)] = (((a[i][0]-a[k][0])**2 + (a[i][1]-a[k][1])**2)**0.5)
        ans += dp[(i,k)]
print(ans*2/n)

Submission status: Accepted

Solution code:
n = int(input())
xy = [[int(i) for i in input().split()]for j in range(n)]

ans = 0

for i in range(n):
    for j in range(i+1,n):
        ans += ((xy[i][0] - xy[j][0]) ** 2 + (xy[i][1] - xy[j][1]) ** 2) ** 0.5
        
print(ans*4/(n*2))

Submission status: Accepted

Solution code:
import math


def solve(n, x_list, y_list):
    d_total = 0.0
    for i in range(n - 1):
        for j in range(i + 1, n):
            d_total += math.sqrt((x_list[i] - x_list[j]) ** 2 + (y_list[i] - y_list[j]) ** 2)
    return d_total * 2 / n


def main():
    n = int(input())
    x_list = [0] * n
    y_list = [0] * n
    for i in range(n):
        x, y = map(int, input().split())
        x_list[i] = x
        y_list[i] = y
    res = solve(n, x_list, y_list)
    print(res)


def test():
    assert abs(solve(3, [0, 1, 0], [0, 0, 1]) - 2.2761423749) < 0.000001
    assert abs(solve(2, [-879, -866], [981, 890]) - 91.9238815543) < 0.000001
    assert abs(solve(
        8, [-406, 512, 494, -955, 128, -986, 763, 449], [10, 859, 362, -475, 553, -885, 77, 310]
    ) - 7641.9817824387) < 0.000001


if __name__ == "__main__":
    test()
    main()

Submission status: Accepted

Solution code:
import math
import itertools

N = int(input())
XY = [list(map(int,input().split())) for _ in range(N)]

t = 2*math.factorial(N-1)

ans = 0
for p1,p2 in itertools.combinations(XY,2):
    x1,y1 = p1
    x2,y2 = p2
    l = ((x1-x2)**2+(y1-y2)**2)**.5
    ans += l*t
ans /= math.factorial(N)
print(ans)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline

import itertools
import math

def main():
    N = int(input())
    X =[]
    Y =[]
    for _ in range(N):
        x, y = [int(x) for x in input().split()]
        X.append(x)
        Y.append(y)

    jun = list(itertools.permutations(range(N)))
    to = 0
    for i in jun:
        for j in range(N - 1):
            to += math.sqrt((X[i[j + 1]] - X[i[j]]) ** 2 + (Y[i[j + 1]] - Y[i[j]]) ** 2)

    print(to / (len(jun)))







if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
N = int(input())
place = []
for _ in range(N):
    place.append(tuple(map(int, input().split())))

length = 0
for i in range(N):
    for j in range(i):
        length += ((place[i][0] - place[j][0]) ** 2 + (place[i][1] - place[j][1]) ** 2) ** (1 / 2)

print(length * 2 / N)

Submission status: Accepted

Solution code:
def d(x,y):
    return ((x[0]-y[0])**2+(x[1]-y[1])**2)**(1/2)

import itertools
ans=0
k=1
n= int(input())
xy=[list(map(int,input().split())) for i in range(n)]
l=[i for i in range(n)]
for v in itertools.permutations(l, n):
    for i in range(n-1):
        ans+=d(xy[v[i]],xy[v[i+1]])
for i in range(1,n+1):
    k*=i
print(ans/k)

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(10000000)
import itertools


def calc_distance(cord1, cord2):
    x1, y1 = cord1
    x2, y2 = cord2

    return ((x1 - x2) ** 2 + (y1 - y2) ** 2) ** 0.5


def main():
    N = int(input())
    cords = []
    for _ in range(N):
        x, y = map(int,input().split())
        cords.append((x, y))
    
    n_lists = [i for i in range(N)]
    sum_distance = 0
    num = 0
    for order in itertools.permutations(n_lists):
        distance = 0
        for i in range(1, N):
            from_, to_ = order[i - 1], order[i]
            distance += calc_distance(cords[from_], cords[to_])
        sum_distance += distance
        num += 1
    
    sum_distance /= num
    print(sum_distance)

    




if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
N = int(input())
city = []

for i in range(N):
    city.append(list(map(int, input().split())))

sum = 0

for i in range(N):
    for j in range(N):
        if i > j:
            sum += ((city[i][0]-city[j][0])**2 + (city[i][1]-city[j][1])**2) ** (1/2)

ave = 2 * sum / N
print(ave)

Submission status: Accepted

Solution code:
# C
from itertools import permutations
import numpy as np
n = int(input())
machis = []
for _ in range(n):
    x, y = list(map(int, input().split()))
    machis.append((x, y))
kumi = permutations(machis)

nagasa = []
for k in list(kumi):
    kwa = 0
    for i in range(len(k)-1):
        x, y = k[i]
        nx, ny = k[i+1]
        kwa += np.sqrt((x-nx)**2 + (y-ny)**2)
    nagasa.append(kwa)
print(np.mean(nagasa))

Submission status: Accepted

Solution code:
import itertools
import math

def makelist(n, m):
    return [[0 for _ in range(m)] for _ in range(n)]


N = int(input())
hoge = [0]*N
for i in range(N):
    x, y = list(map(int, input().split()))
    hoge[i] = (x, y)

lsts = list(itertools.permutations(range(N)))

ans = 0
b = len(lsts)

for lst in lsts:
    lst = list(lst)

    for i in range(N-1):
        (x1, y1) = hoge[lst[i]]
        (x2, y2) = hoge[lst[i+1]]
        s = math.pow(x1-x2, 2)
        t = math.pow(y1-y2, 2)

        ans += math.sqrt(s + t)

ans /= b

print(ans)

Submission status: Accepted

Solution code:
import math

N = int(input())
T = [tuple(map(int, input().split())) for i in range(N)]

S = 0
for i in range(N - 1):
    for j in range(i, N):
        S += math.sqrt((T[i][0] - T[j][0]) ** 2 + (T[i][1] - T[j][1]) ** 2)
print(S * 2 / N)

Submission status: Accepted

Solution code:
N = int(input())
xy = [list(map(int, input().split())) for _ in range(N)]

import math

dist = [[0] * N for _ in range(N)]
for i in range(N - 1):
    xi, yi = xy[i]
    for j in range(i + 1, N):
        xj, yj = xy[j]
        dist[i][j] = math.sqrt((xi - xj) ** 2 + (yi - yj) ** 2)
        dist[j][i] = dist[i][j]

import itertools

ans = 0
cases = list(itertools.permutations(range(N)))
for case in cases:
    for idx in range(N - 1):
        ans += dist[case[idx]][case[idx + 1]]
ans /= len(cases)

print(ans)

Submission status: Accepted

Solution code:
def d(a,b,c,d):
    return ((a-b)**2+(c-d)**2)**(1/2)

n = int(input())
s = []
for i in range(n):
    s.append([int(x) for x in input().split()])
f = 0
for dis in s:
    for ris in s:
        f += d(dis[0], ris[0], dis[1], ris[1])

print(str(f/n))

Submission status: Accepted

Solution code:
#!/usr/bin/env python3
import sys, itertools, math


def solve(N: int, x: "List[int]", y: "List[int]"):
    f = 1
    for i in range(2, N+1):
        f *= i
    sm = 0
    for (s, t) in itertools.combinations(range(N), 2):
        sm += math.sqrt((x[s] - x[t])**2 + (y[s] - y[t])**2) * f / N * 2
    print(sm / f)
    return


# Generated by 1.1.5 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    x = [int()] * (N)  # type: "List[int]"
    y = [int()] * (N)  # type: "List[int]"
    for i in range(N):
        x[i] = int(next(tokens))
        y[i] = int(next(tokens))
    solve(N, x, y)

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import itertools
import math

n = int(input())

x = []
y = []
for i in range(n):
    xi, yi = map(int, input().split())
    x.append(xi)
    y.append(yi)

def calcdist(x0, y0, x1, y1):
    return math.sqrt((x0 - x1)**2 + (y0 - y1)**2)

dist_sum = 0
for order in itertools.permutations(range(n), n):
    for i in range(n-1):
        dist_sum += calcdist(x[order[i]], y[order[i]], x[order[i+1]], y[order[i+1]])

print(dist_sum / math.factorial(n))

Submission status: Accepted

Solution code:
import itertools


def average_distance(N, points):
    order = list(itertools.permutations(points))
    distance = []
    for ord in order:
        d = 0
        for i in range(len(ord) - 1):
            d += ((ord[i][0] - ord[i + 1][0]) ** 2 + (ord[i][1] - ord[i + 1][1]) ** 2) ** (1 / 2)
        distance.append(d)
    return sum(distance) / len(distance)


N = int(input())
town = []
for i in range(N):
    town.append(list(map(int, input().split())))
res = average_distance(N, town)
print(res)

Submission status: Accepted

Solution code:
import itertools
import math

n = int(input())
m = []
items = []
for i in range(n):
    m.append([int(x) for x in input().split(' ')])
    items.append(i)

#print(m)

total = 0
count = 0
for perms in itertools.permutations(items):
    #print(perms)
    d = 0
    for i in range(n - 1):
        dx = m[perms[i]][0] - m[perms[i + 1]][0]
        dy = m[perms[i]][1] - m[perms[i + 1]][1]
        d += math.sqrt(dx * dx + dy * dy)
    #print(d)
    total += d
    count += 1

print(total / count)

Submission status: Accepted

Solution code:
import itertools
n=int(input())
xy=[[int(i) for i in input().split()] for _ in range(n)]
l=list(itertools.permutations(range(n)))
sum = 0
for lis in l:
    for i in range(n-1):
        sum += ((xy[lis[i]][0] - xy[lis[i+1]][0])**2 + (xy[lis[i]][1] - xy[lis[i+1]][1])**2)**(1/2)
print(sum/len(l))

Submission status: Accepted

Solution code:
import math
N = int(input())
sum = math.factorial(N)
X = [0] * N
Y = [0] * N
ans = 0
for i in range(N):
    X[i], Y[i] = map(int,input().split())
for i in range(N):
    x1 = X[i]
    y1 = Y[i]
    for j in range(i+1,N):
        x2 = X[j]
        y2 = Y[j]
        ans += (((x1-x2)**2+(y1-y2)**2)**(1/2)) * (sum//N) * 2
print(ans/sum)

Submission status: Accepted

Solution code:
N = int(input())
L = [tuple(map(int, input().split())) for n in range(N)]
Roads = []
for n in range(N):
    for m in range(n + 1, N):
        distance = ((L[n][0] - L[m][0]) ** 2 + (L[n][1] - L[m][1]) ** 2) ** 0.5
        Roads.append(distance)
mean = sum(Roads) / len(Roads)
print(mean * (N - 1))

Submission status: Accepted

Solution code:
n = int(input())
xy = [list(map(int, input().split())) for _ in range(n)]
import math

ans = 0
for a in xy:
  t = 0
  for b in xy:
    if a == b:
      continue
    t += math.sqrt((b[1] - a[1])**2 + (b[0] - a[0]) **2)
  ans += t  
print(ans/n)

Submission status: Accepted

Solution code:
import itertools
n = int(input())
p = [list(map(int,input().split())) for _ in range(n)]
order = list(itertools.permutations(range(n)))
length = 0

for o_list in order:
  start_x,start_y = p[o_list[0]]
  for o in o_list[1:]:
    x,y = p[o]
    length += ((start_x-x)**2+(start_y-y)**2)**(1/2)
    start_x,start_y = x,y
print(length/len(order))

Submission status: Accepted

Solution code:
#!/usr/bin/env python3
from collections import defaultdict,deque
from heapq import heappush, heappop
from bisect import bisect_left, bisect_right
import sys, random, itertools, math
sys.setrecursionlimit(10**5)
input = sys.stdin.readline
sqrt = math.sqrt
def LI(): return list(map(int, input().split()))
def LF(): return list(map(float, input().split()))
def LI_(): return list(map(lambda x: int(x)-1, input().split()))
def II(): return int(input())
def IF(): return float(input())
def LS(): return list(map(list, input().split()))
def S(): return list(input().rstrip())
def IR(n): return [II() for _ in range(n)]
def LIR(n): return [LI() for _ in range(n)]
def FR(n): return [IF() for _ in range(n)]
def LFR(n): return [LI() for _ in range(n)]
def LIR_(n): return [LI_() for _ in range(n)]
def SR(n): return [S() for _ in range(n)]
def LSR(n): return [LS() for _ in range(n)]
mod = 1000000007
inf = float('INF')

#solve
def solve():
    n = II()
    xy = LIR(n)
    full = itertools.permutations(range(n), n)
    tmp = 0
    ans = 0
    for fu in full:
        i = 0
        bx, by = 0, 0
        for f in fu:
            if i == 0:
                bx, by = xy[f][0], xy[f][1]
                i = 1
                continue
            x, y = xy[f][0], xy[f][1]
            ans += sqrt((bx - x) ** 2 + (by - y) ** 2)
        tmp += 1
    print(ans/tmp)

    return


#main
if __name__ == '__main__':
    solve()

Submission status: Accepted

Solution code:
n=int(input())
x=[0]*n
y=[0]*n
for i in range(n):
  x[i],y[i]=map(int,input().split())
count=0
for i in range(n):
  for j in range(i+1,n):
    count+=((x[i]-x[j])**2+(y[i]-y[j])**2)**0.5
print(count*2/n)

Submission status: Accepted

Solution code:
from math import sqrt

n = int(input())

points = [list(map(int, input().split())) for _ in range(n)]


sum_r = 0
for i in range(n):
    for j in range(i+1, n):
        a = points[i]
        b = points[j]
        sum_r += sqrt(pow(a[0]-b[0], 2) + pow(a[1] - b[1], 2))

print(sum_r*2/n)

Submission status: Accepted

Solution code:
#!/snap/bin/pypy3
from itertools import permutations
from math import sqrt, factorial


def main():
    n = int(input())

    points = [tuple(map(float, input().split())) for _ in range(n)]

    total_distance = 0.0
    for sample in permutations(range(n), n):
        total_distance += sum(sqrt((points[sample[i]][0] - points[sample[i + 1]][0])**2 + (points[sample[i]][1] - points[sample[i + 1]][1])**2) for i in range(n - 1))

    print(total_distance / factorial(n))


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import math
n=int(input())
xy=[]

for i in range(n):
  xy.append(list(map(int,input().split())))

sum=0
count=0
for i in range(len(xy)):
  for j in range(len(xy)):
    if i==j:
      continue
    sum+=math.sqrt((xy[i][0]-xy[j][0])**2+(xy[i][1]-xy[j][1])**2)
  count+=1
print(sum/count)