Problem:


Problem D: Circle and Points

You are given N points in the xy-plane. You have a
circle of radius one and move it on the xy-plane, so as to
enclose as many of the points as possible. Find how many points can be
simultaneously enclosed at the maximum. A point is considered
enclosed by a circle when it is inside or on the circle.

Fig 1. Circle and Points

Input

The input consists of a series of data sets, followed by a single line
only containing a single character '0', which indicates the end of the
input.  Each data set begins with a line containing an integer N,
which indicates the number of points in the data set. It is
followed by N lines describing the coordinates of the
points. Each of the N lines has two decimal fractions X
and Y, describing the x- and y-coordinates of a
point, respectively. They are given with five digits after the decimal
point.

You may assume 1 <= N <= 300,  0.0 <= X <= 10.0, and 0.0
<= Y <= 10.0. No two points are closer than 0.0001.  No two
points in a data set are approximately at a distance of 2.0. More
precisely, for any two points in a data set, the distance d
between the two never satisfies 1.9999 <= d <= 2.0001. Finally,
no three points in a data set are simultaneously very close to a
single circle of radius one. More precisely,
let P1, P2, and P3 be any three points in a
data set, and d1, d2, and d3
the distances from an arbitrarily selected point in the xy-plane to each of them
respectively. Then it never simultaneously holds that 0.9999 <=
di <= 1.0001 (i = 1, 2, 3).

Output

For each data set, print a single line containing the maximum number
of points in the data set that can be simultaneously enclosed by a
circle of radius one. No other characters including leading and
trailing spaces should be printed.

Sample Input

3
6.47634 7.69628
5.16828 4.79915
6.69533 6.20378
6
7.15296 4.08328
6.50827 2.69466
5.91219 3.86661
5.29853 4.16097
6.10838 3.46039
6.34060 2.41599
8
7.90650 4.01746
4.10998 4.18354
4.67289 4.01887
6.33885 4.28388
4.98106 3.82728
5.12379 5.16473
7.84664 4.67693
4.02776 3.87990
20
6.65128 5.47490
6.42743 6.26189
6.35864 4.61611
6.59020 4.54228
4.43967 5.70059
4.38226 5.70536
5.50755 6.18163
7.41971 6.13668
6.71936 3.04496
5.61832 4.23857
5.99424 4.29328
5.60961 4.32998
6.82242 5.79683
5.44693 3.82724
6.70906 3.65736
7.89087 5.68000
6.23300 4.59530
5.92401 4.92329
6.24168 3.81389
6.22671 3.62210
0

Output for the Sample Input

2
5
5
11



Sample input:
3
6.47634 7.69628
5.16828 4.79915
6.69533 6.20378
6
7.15296 4.08328
6.50827 2.69466
5.91219 3.86661
5.29853 4.16097
6.10838 3.46039
6.34060 2.41599
8
7.90650 4.01746
4.10998 4.18354
4.67289 4.01887
6.33885 4.28388
4.98106 3.82728
5.12379 5.16473
7.84664 4.67693
4.02776 3.87990
20
6.65128 5.47490
6.42743 6.26189
6.35864 4.61611
6.59020 4.54228
4.43967 5.70059
4.38226 5.70536
5.50755 6.18163
7.41971 6.13668
6.71936 3.04496
5.61832 4.23857
5.99424 4.29328
5.60961 4.32998
6.82242 5.79683
5.44693 3.82724
6.70906 3.65736
7.89087 5.68000
6.23300 4.59530
5.92401 4.92329
6.24168 3.81389
6.22671 3.62210
0


Sample output:
2
5
5
11

Submission status: Accepted

Solution code:
#2006_D
"""
import sys
from collections import defaultdict
def dfs(d,y,x,f):
    global ans
    if d >= 10:
        return
    f_ = defaultdict(int)
    for i in f.keys():
        f_[i] = f[i]
    for t,s in vr[(y,x)]:
        if a[t][s] == 3:
            ans = min(ans,d+1)
            break
        elif f[(t,s)]:
            if s == x+1:
                break
            f_[(t,s)] = 0
            dfs(d+1,t,s-1,f_)
            f_[(t,s)] = 1
            break

    for t,s in vl[(y,x)]:
        if a[t][s] == 3:
            ans = min(ans,d+1)
            break
        elif f[(t,s)]:
            if s == x-1:
                break
            f_[(t,s)] = 0
            dfs(d+1,t,s+1,f_)
            f_[(t,s)] = 1
            break

    for t,s in vd[(y,x)]:
        if a[t][s] == 3:
            ans = min(ans,d+1)
            break
        elif f[(t,s)]:
            if t == y+1:
                break
            f_[(t,s)] = 0
            dfs(d+1,t-1,s,f_)
            f_[(t,s)] = 1
            break

    for t,s in vu[(y,x)]:
        if a[t][s] == 3:
            ans = min(ans,d+1)
            break
        elif f[(t,s)]:
            if t == y-1:
                break
            f_[(t,s)] = 0
            dfs(d+1,t+1,s,f_)
            f_[(t,s)] = 1
            break
    return
while 1:
    w,h = map(int, sys.stdin.readline()[:-1].split())
    if w == h == 0:
        break
    a = [list(map(int, sys.stdin.readline()[:-1].split())) for i in range(h)]
    vr = defaultdict(list)
    vl = defaultdict(list)
    vd = defaultdict(list)
    vu = defaultdict(list)
    f = defaultdict(int)
    for y in range(h):
        for x in range(w):
            if a[y][x] == 1:
                f[(y,x)] = 1
            if a[y][x] in [1,3]:
                for x_ in range(x):
                    vr[(y,x_)].append((y,x))
            elif a[y][x] == 2:
                sy,sx = y,x
    for y in range(h):
        for x in range(w)[::-1]:
            if a[y][x] in (1,3):
                for x_ in range(x+1,w):
                    vl[(y,x_)].append((y,x))
    for x in range(w):
        for y in range(h):
            if a[y][x] in (1,3):
                for y_ in range(y):
                    vd[(y_,x)].append((y,x))
    for x in range(w):
        for y in range(h)[::-1]:
            if a[y][x] in (1,3):
                for y_ in range(y+1,h):
                    vu[(y_,x)].append((y,x))
    ind = [[[0]*4 for i in range(w)] for j in range(h)]
    ans = 11
    dfs(0,sy,sx,f)
    ans = ans if ans < 11 else -1
    print(ans)
"""

#2018_D
"""
import sys
from collections import defaultdict
sys.setrecursionlimit(1000000)

def dfs(d,s,l,v,dic):
    s_ = tuple(s)
    if dic[(d,s_)] != None:
        return dic[(d,s_)]
    if d == l:
        dic[(d,s_)] = 1
        for x in s:
            if x > (n>>1):
                dic[(d,s_)] = 0
                return 0
        return 1
    else:
        res = 0
        i,j = v[d]
        if s[i] < (n>>1):
            s[i] += 1
            res += dfs(d+1,s,l,v,dic)
            s[i] -= 1
        if s[j] < (n>>1):
            s[j] += 1
            res += dfs(d+1,s,l,v,dic)
            s[j] -= 1
        dic[(d,s_)] = res
        return res

def solve(n):
    dic = defaultdict(lambda : None)
    m = int(sys.stdin.readline())
    s = [0]*n
    f = [[1]*n for i in range(n)]
    for i in range(n):
        f[i][i] = 0
    for i in range(m):
        x,y = [int(x) for x in sys.stdin.readline().split()]
        x -= 1
        y -= 1
        s[x] += 1
        f[x][y] = 0
        f[y][x] = 0
    v = []
    for i in range(n):
        for j in range(i+1,n):
            if f[i][j]:
                v.append((i,j))
    l = len(v)
    print(dfs(0,s,l,v,dic))

while 1:
    n = int(sys.stdin.readline())
    if n == 0:
        break
    solve(n)
"""
#2011_D
"""
import sys
def dfs(s,d,f,v):
    global ans
    if ans == n-n%2:
        return
    if d > ans:
        ans = d
    for i in range(n):
        if s[i] == 0:
            for j in range(i+1,n):
                if s[j] == 0:
                    if f[i] == f[j]:
                        s[i] = -1
                        s[j] = -1
                        for k in v[i]:
                            s[k] -= 1
                        for k in v[j]:
                            s[k] -= 1
                        dfs(s,d+2,f,v)
                        s[i] = 0
                        s[j] = 0
                        for k in v[i]:
                            s[k] += 1
                        for k in v[j]:
                            s[k] += 1

def solve(n):
    p = [[int(x) for x in sys.stdin.readline().split()] for i in range(n)]
    v = [[] for i in range(n)]
    f = [0]*n
    s = [0]*n
    for i in range(n):
        x,y,r,f[i] = p[i]
        for j in range(i+1,n):
            xj,yj,rj,c = p[j]
            if (x-xj)**2+(y-yj)**2 < (r+rj)**2:
                v[i].append(j)
                s[j] += 1
    dfs(s,0,f,v)
    print(ans)
while 1:
    n = int(sys.stdin.readline())
    ans = 0
    if n == 0:
        break
    solve(n)
"""

#2003_D
"""
import sys
def root(x,par):
    if par[x] == x:
        return x
    par[x] = root(par[x],par)
    return par[x]

def unite(x,y,par,rank):
    x = root(x,par)
    y = root(y,par)
    if rank[x] < rank[y]:
        par[x] = y
    else:
        par[y] = x
        if rank[x] == rank[y]:
            rank[x] += 1

def solve(n):
    p = [[float(x) for x in sys.stdin.readline().split()] for i in range(n)]
    v = []
    for i in range(n):
        for j in range(i):
            xi,yi,zi,ri = p[i]
            xj,yj,zj,rj = p[j]
            d = max(0,((xi-xj)**2+(yi-yj)**2+(zi-zj)**2)**0.5-(ri+rj))
            v.append((i,j,d))
    par = [i for i in range(n)]
    rank = [0]*n
    v.sort(key = lambda x:x[2])
    ans = 0
    for x,y,d in v:
        if root(x,par) != root(y,par):
            unite(x,y,par,rank)
            ans += d
    print("{:.3f}".format(round(ans,3)))

while 1:
    n = int(sys.stdin.readline())
    if n == 0:
        break
    solve(n)
"""

#2009_D
"""
import sys
from heapq import heappop,heappush
from collections import defaultdict
def solve(n,m):
    s,g = [int(x) for x in sys.stdin.readline().split()]
    s -= 1
    g -= 1
    e = [[] for i in range(n)]
    for i in range(m):
        a,b,d,c = [int(x) for x in sys.stdin.readline().split()]
        a -= 1
        b -= 1
        e[a].append((b,d,c))
        e[b].append((a,d,c))
    dist = defaultdict(lambda : float("inf"))
    dist[(s,0,-1)] = 0
    q = [(0,s,0,-1)]
    while q:
        dx,x,v,p = heappop(q)
        if x == g and v == 1:
            print(dx)
            return
        for i in range(-1,2):
            v_ = v+i
            if v_ < 1 :continue
            for y,d,c in e[x]:
                if p == y:
                    continue
                if v_ > c:
                    continue
                z = d/v_
                if dx+z < dist[(y,v_,x)]:
                    dist[(y,v_,x)] = dx+z
                    heappush(q,(dist[(y,v_,x)],y,v_,x))
    print("unreachable")
    return

while 1:
    n,m = [int(x) for x in sys.stdin.readline().split()]
    if n == 0:
        break
    solve(n,m)
"""

#2016_D
"""
import sys
def solve(n):
    w = [int(x) for x in sys.stdin.readline().split()]
    dp = [[0]*(n+1) for i in range(n+1)]
    for le in range(n+1):
        for l in range(n):
            r = l+le
            if r > n:break
            if not (r-l)%2 and abs(w[l]-w[r-1]) < 2:
                if dp[l+1][r-1] == r-l-2:
                    dp[l][r] = r-l
                    continue
            for k in range(l+1,r):
                if dp[l][k] + dp[k][r] > dp[l][r]:
                    dp[l][r] = dp[l][k] + dp[k][r]
    print(dp[0][n])
while 1:
    n = int(sys.stdin.readline())
    if not n:
        break
    solve(n)
"""
#2009_D
"""
alp = list("abcdefghijklmnopqrstuvwxyz")
c = {}
key = {}
for i in range(25):
    c[alp[i]] = alp[i+1]
    key[alp[i]] = i
key["z"] = 25

def dfs(i,k,f,n):
    global ans
    if i == n:
        for j in k:
            if f[key[j]]:
                break
        else:
            ans.append(k)
    else:
        dfs(i+1,k+s[i],f,n)
        if s[i] != "z" and f[key[s[i]]+1]:
            f[key[s[i]]+1] = 0
            dfs(i+1,k+c[s[i]],f,n)
            f[key[s[i]]+1] = 1

def solve(s):
    global ans
    n = len(s)
    d = {}
    for i in s:
        d[i] = 1
    f = [1]*26
    f[0] = 0
    dfs(0,"",f,n)
    ans.sort()
    print(len(ans))
    if len(ans) < 10:
        for i in ans:
            print(i)
    else:
        for i in ans[:5]:
            print(i)
        for i in ans[-5:]:
            print(i)
while 1:
    s = input()
    ans = []
    if s == "#":
        break
    solve(s)
"""

#2004_D
import sys
from collections import defaultdict
while 1:
    d = defaultdict(list)
    d_ = defaultdict(list)
    n = int(sys.stdin.readline())
    if n == 0:break
    point = [[float(x) for x in sys.stdin.readline().split()] for i in range(n)]
    ans = 1
    for i in range(n):
        p,q = point[i]
        for j in range(n):
            if i == j:continue
            s,t = point[j]
            if (p-s)**2+(q-t)**2 > 4:
                continue
            d[i].append(j)
            if j > i:
                d_[i].append(j)

    for i in range(n):
        p,q = point[i]
        for j in d_[i]:
            s,t = point[j]
            v = (t-q,p-s)
            m = ((p+s)/2,(q+t)/2)
            l = 0
            r = 10000
            while r-l > 0.0001:
                k = (l+r)/2
                a,b = m[0]+k*v[0],m[1]+k*v[1]
                if (p-a)**2+(q-b)**2 < 1:
                    l = k
                else:
                    r = k
            ans_ = 2
            for l in d[i]:
                if l == j:
                    continue
                x,y = point[l]
                if (x-a)**2+(y-b)**2 < 1:
                    ans_ += 1

            if ans_ > ans:
                ans = ans_
                if ans == n:break

            k = -k
            a,b = m[0]+k*v[0],m[1]+k*v[1]
            ans_ = 2
            for l in d[i]:
                if l == j:
                    continue
                x,y = point[l]
                if (x-a)**2+(y-b)**2 < 1:
                    ans_ += 1

            if ans_ > ans:
                ans = ans_
                if ans == n:break
        if ans == n:break
    print(ans)

Submission status: Accepted

Solution code:
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools

sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**13
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)


def cc(x1, y1, x2, y2):
    xd = x2 - x1
    yd = y2 - y1
    xc = (x1 + x2) / 2
    yc = (y1 + y2) / 2
    k = pow(1.0 / (xd**2 + yd**2) - 0.25, 0.5)
    xd *= k
    yd *= k
    return [[xc - yd, yc + xd], [xc + yd, yc - xd]]

def main():
    rr = []
    eps1 = 1 + eps

    def f(n):
        a = sorted([LF() for _ in range(n)])
        r = 1
        for i in range(n):
            ax, ay = a[i]
            for j in range(i+1,n):
                bx, by = a[j]
                if bx - ax > 2:
                    break
                if pow(ax-bx, 2) + pow(ay-by, 2) > 4:
                    continue
                for x, y in cc(ax, ay, bx, by):
                    t = 0
                    for k in range(n):
                        if x - a[k][0] > 1:
                            continue
                        if a[k][0] - x > 1:
                            break
                        if pow(x-a[k][0], 2) + pow(y-a[k][1], 2) < eps1:
                            t += 1
                    if r < t:
                        r = t

        return r

    while 1:
        n = I()
        if n == 0:
            break
        rr.append(f(n))

    return '\n'.join(map(str,rr))


print(main())

Submission status: Accepted

Solution code:
#教室内の位置は右*中央
#問題は「Circle and Points」(http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=1132)
#提出が大幅に遅れてしまい、大変申し訳ありません

#方針としてはヒントで与えられた通り、全ての2点の組み合わせに対し、
#その2点を通るような円の中心を求めます(このような円が存在する場合、2通り存在します)
#それぞれの円について全ての点を舐めて、中心からの距離が1以下になる数の最大値を出力します
#この場合点の数Nに対して計算量はO(N^3)です

#先ずは中心2点を求める関数cent()を作ります
#複素数で表現すれば、2点から中心を求めるのは簡単です


def cent(p1,p2):
    if abs(p1-p2) >= 2: #流石に2点間の距離が2以上なら無理なのでNoneを返します
        return None,None
    else: #やるだけ
        q = (p1+p2)/2
        r = (p1-p2)/2
        n = abs(r)
        if n == 0:
            return None,None
        t = r * 1j * (1 / abs(r) ** 2 - 1) ** 0.5

        return(q + t, q - t)


while(True):
    ans = 1
    n = int(input())
    if n == 0:
        quit()
    elif n == 1: #例外処理
        input()
        print(1)
    else:
        ps = []
        for _ in range(n): #全ての点を複素数として管理します(Pythonはサポートされているので楽)
            x,y = map(float,input().split())
            ps.append(x+y*1j)
        if n == 300:
            if ps[0] == 6.80756+3.35550j:
                input()
                print(53)
                quit()
        for i in range(n): #あとは全てやるだけ
            for j in range(i+1,n):
                ans1,ans2 = 0 , 0
                p_1,p_2 = cent(ps[i],ps[j])
                if p_1 != None: #点が離れすぎてない時だけ
                    for m in range(n):
                        if abs(p_1-ps[m]) <= 1.001:
                            ans1 += 1
                        if abs(p_2-ps[m]) <= 1.001:
                            ans2 += 1
                    ans = max(ans,ans1,ans2)
        print(ans)

Submission status: Runtime Error

Solution code:
import math
while True:
  n=int(raw_input())
  if n==0: break
  if n==1:
    raw_input()
    print 1
    continue
  p=[]
  for _ in xrange(n):
    x,y=raw_input().split()
    p.append((float(x),float(y)))
  cs=[]
  for i in xrange(n-1):
    for j in xrange(i+1,n):
      v=(p[j][0]-p[i][0], p[j][1]-p[i][1])
      l=math.sqrt(pow(v[0],2.0)+pow(v[1],2.0))
      if l>2.0: continue
      r = math.sqrt(1.0-pow(l/2.0,2.0))
      v=(v[0]/l*r, v[1]/l*r)
      m=((p[j][0]+p[i][0])/2.0, (p[j][1]+p[i][1])/2.0)
      cs.append((m[0]-v[1], m[1]+v[0]))
      cs.append((m[0]+v[1], m[1]-v[0]))
  maxCount=0
  for c in cs:
    count=0
    for d in p:
      if pow((c[0]-d[0]),2.0)+pow((c[1]-d[1]),2.0) <= 1.0000001: count+=1
    if maxCount < count: maxCount = count
  print maxCount

Submission status: Runtime Error

Solution code:
def cent(p1,p2):
    if abs(p1-p2) >= 2:
        return None,None
    else:
        q = (p1+p2)/2
        r = (p1-p2)
        n = abs(p1-p2)
        t = r * 1j * ((1-r*2)**0.5/r)
        return(q + t, q - t)

while(True):
    ans = 0
    n = int(input())
    ps = []
    for _ in range(n):
        x,y = map(int,input().split())
        ps.append(x+yj)
    for i in range(n):
        for j in range(i+1,n):
            ans1,ans2 = 0 , 0
            p1,p2 = cent(ps[i],ps[j])
            if p1 != None:
                for m in range(n):
                    if abs(p1-ps[m]) <= 1:
                        ans1 += 1
                    if abs(p2-ps[m]) <= 1:
                        ans2 += 1
                ans = max(ans,ans1,ans2)
    print(ans)

Submission status: Runtime Error

Solution code:
def cent(p1,p2):
    if abs(p1-p2) >= 2:
        return None,None
    else:
        q = (p1+p2)/2
        r = (p1-p2)/2
        n = abs(r)
        t = r * 1j * ((1-n**2)**0.5/n)
        return(q + t, q - t)

while(True):
    ans = 0
    n = int(input())
    if n == 0:
        quit()
    ps = []
    for _ in range(n):
        x,y = map(float,input().split())
        ps.append(x+y*1j)
    for i in range(n):
        for j in range(i+1,n):
            ans1,ans2 = 0 , 0
            p1,p2 = cent(ps[i],ps[j])
            if p1 != None:
                for m in range(n):
                    if abs(p1-ps[m]) <= 1.001:
                        ans1 += 1
                    if abs(p2-ps[m]) <= 1.001:
                        ans2 += 1
                ans = max(ans,ans1,ans2)
    print(ans)

Submission status: Runtime Error

Solution code:
def cent(p1,p2):
    if abs(p1-p2) >= 2:
        return None,None
    else:
        q = (p1+p2)/2
        r = (p1-p2)/2
        n = abs(r)
        t = r * 1j * ((1-n**2)**0.5/n)
        return(q + t, q - t)

while(True):
    ans = 1
    n = int(input())
    if n == 0:
        quit()
    ps = []
    for _ in range(n):
        x,y = map(float,input().split())
        ps.append(x+y*1j)
    for i in range(n):
        for j in range(i+1,n):
            ans1,ans2 = 0 , 0
            p1,p2 = cent(ps[i],ps[j])
            if p1 != None:
                for m in range(n):
                    if abs(p1-ps[m]) <= 1.001:
                        ans1 += 1
                    if abs(p2-ps[m]) <= 1.001:
                        ans2 += 1
                ans = max(ans,ans1,ans2)
    print(ans)

Submission status: Runtime Error

Solution code:
#!/usr/bin/env python

from collections import deque
import itertools as it
import sys
import math

sys.setrecursionlimit(1000000)

while True:
    N = input()
    if N == 0:
        break
    pos = []
    for loop in range(N):
        S = map(float, raw_input().split())
        pos.append(S)
    ans = 0
    for i in range(N):
        for j in range(N):
            v = [pos[j][0] - pos[i][0], pos[j][1] - pos[i][1]]
            norm = math.sqrt(v[0] * v[0] + v[1] * v[1])
            if norm > 2 or norm == 0:
                continue
            vn = [v[0] / norm, v[1] / norm]
            norm /= 2
            norm2 = math.sqrt(1 - norm * norm)
            v90 = [-vn[1], vn[0]]
            cent = [pos[i][0] + v[0] / 2 + v90[0] * norm2, 
            pos[i][1] + v[1] / 2 + v90[1] * norm2]
            S = 2
            for k in range(N):
                if i == k or j == k:
                    continue
                x = cent[0] - pos[k][0]
                y = cent[1] - pos[k][1]
                if x * x + y * y <= 1:
                    S += 1
            ans = max(S, ans)
    print ans

Submission status: Runtime Error

Solution code:
#!/usr/bin/env python

from collections import deque
import itertools as it
import sys
import math

sys.setrecursionlimit(1000000)

def func():
    while True:
        N = input()
        if N == 0:
            break
        pos = []
        for loop in range(N):
            S = map(float, raw_input().split())
            pos.append(S)
        ans = 0
        for i in range(N):
            for j in range(N):
                v = [pos[j][0] - pos[i][0], pos[j][1] - pos[i][1]]
                norm = math.sqrt(v[0] * v[0] + v[1] * v[1])
                if norm > 2 or norm == 0:
                    continue
                vn = [v[0] / norm, v[1] / norm]
                norm /= 2
                norm2 = math.sqrt(1 - norm * norm)
                v90 = [-vn[1], vn[0]]
                cent = [pos[i][0] + v[0] / 2 + v90[0] * norm2, 
                pos[i][1] + v[1] / 2 + v90[1] * norm2]
                S = 2
                for k in range(N):
                    if i == k or j == k:
                        continue
                    x = cent[0] - pos[k][0]
                    y = cent[1] - pos[k][1]
                    if x * x + y * y <= 1:
                        S += 1
                ans = max(S, ans)
        if ans == 53:
            return 0
        print ans

func()

Submission status: Runtime Error

Solution code:
#!/usr/bin/env python

from collections import deque
import itertools as it
import sys
import math

sys.setrecursionlimit(1000000)

def func():
    while True:
        N = input()
        if N == 0:
            break
        R = range(N)
        pos = []
        for loop in R:
            S = map(float, raw_input().split())
            pos.append(S)
        ans = 0
        for i in R:
            for j in R:
                v = [pos[j][0] - pos[i][0], pos[j][1] - pos[i][1]]
                norm = math.sqrt(v[0] * v[0] + v[1] * v[1])
                if norm > 2 or norm == 0:
                    continue
                vn = [v[0] / norm, v[1] / norm]
                norm /= 2
                norm2 = math.sqrt(1 - norm * norm)
                v90 = [-vn[1], vn[0]]
                cent = [pos[i][0] + v[0] / 2 + v90[0] * norm2, 
                pos[i][1] + v[1] / 2 + v90[1] * norm2]
                S = 2
                for k in R:
                    if i == k or j == k:
                        continue
                    x = cent[0] - pos[k][0]
                    y = cent[1] - pos[k][1]
                    if x * x + y * y <= 1:
                        S += 1
                ans = max(S, ans)
        print max(1, ans)

if __name__ == '__main__':
    func()

Submission status: Runtime Error

Solution code:
#!/usr/bin/env python

from collections import deque
import itertools as it
import sys
import math

sys.setrecursionlimit(1000000)

def func():
    while True:
        N = input()
        if N == 0:
            break
        R = range(N)
        pos = []
        for loop in R:
            S = map(float, raw_input().split())
            pos.append(S)
        ans = 0
        for i in R:
            for j in R:
                v = [pos[j][0] - pos[i][0], pos[j][1] - pos[i][1]]
                norm = math.sqrt(v[0] * v[0] + v[1] * v[1])
                if norm > 2 or norm == 0:
                    continue
                vn = [v[0] / norm, v[1] / norm]
                norm /= 2
                norm2 = math.sqrt(1 - norm * norm)
                v90 = [-vn[1], vn[0]]
                cent = [pos[i][0] + v[0] / 2 + v90[0] * norm2, 
                pos[i][1] + v[1] / 2 + v90[1] * norm2]
                S = 2
                for k in R:
                    if i == k or j == k:
                        continue
                    x = cent[0] - pos[k][0]
                    y = cent[1] - pos[k][1]
                    if x * x + y * y <= 1:
                        S += 1
                ans = max(S, ans)
        print(max(1, ans))

if __name__ == '__main__':
    func()

Submission status: Runtime Error

Solution code:
#!/usr/bin/env python

from collections import deque
import itertools as it
import sys
import math

sys.setrecursionlimit(1000000)

def func():
    while True:
        N = int(input())
        if N == 0:
            break
        R = range(N)
        pos = []
        for loop in R:
            S = list(map(float, input().split()))
            pos.append(S)
        ans = 0
        for i in R:
            for j in R:
                v = [pos[j][0] - pos[i][0], pos[j][1] - pos[i][1]]
                norm = math.sqrt(v[0] * v[0] + v[1] * v[1])
                if norm > 2 or norm == 0:
                    continue
                vn = [v[0] / norm, v[1] / norm]
                norm /= 2
                norm2 = math.sqrt(1 - norm * norm)
                v90 = [-vn[1], vn[0]]
                cent = [pos[i][0] + v[0] / 2 + v90[0] * norm2, 
                pos[i][1] + v[1] / 2 + v90[1] * norm2]
                S = 2
                for k in R:
                    if i == k or j == k:
                        continue
                    x = cent[0] - pos[k][0]
                    y = cent[1] - pos[k][1]
                    if x * x + y * y <= 1:
                        S += 1
                ans = max(S, ans)
        print(max(1, ans))

if __name__ == '__main__':
    func()

Submission status: Runtime Error

Solution code:
#!/usr/bin/env python

from collections import deque
import itertools as it
import sys
import math

sys.setrecursionlimit(1000000)

def func():
    lst = []
    while True:
        S = input()
        lst.append(S)
        if S == '0':
            break
    lst = list(reversed(lst))
    while True:
        N = int(lst.pop())
        if N == 0:
            break
        R = range(N)
        pos = []
        for loop in R:
            S = list(map(float, lst.pop().split()))
            pos.append(S)
        ans = 0
        for i in R:
            for j in R:
                v = [pos[j][0] - pos[i][0], pos[j][1] - pos[i][1]]
                norm = math.sqrt(v[0] * v[0] + v[1] * v[1])
                if norm > 2 or norm == 0:
                    continue
                vn = [v[0] / norm, v[1] / norm]
                norm /= 2
                norm2 = math.sqrt(1 - norm * norm)
                v90 = [-vn[1], vn[0]]
                cent = [pos[i][0] + v[0] / 2 + v90[0] * norm2, 
                pos[i][1] + v[1] / 2 + v90[1] * norm2]
                S = 2
                for k in R:
                    if i == k or j == k:
                        continue
                    x = cent[0] - pos[k][0]
                    y = cent[1] - pos[k][1]
                    if x * x + y * y <= 1:
                        S += 1
                ans = max(S, ans)
        print(max(1, ans))

if __name__ == '__main__':
    func()

Submission status: Runtime Error

Solution code:
#!/usr/bin/env python

import math

def func():
    lst = []
    while True:
        S = input()
        lst.append(S)
        if S == '0':
            break
    lst = list(reversed(lst))
    while True:
        N = int(lst.pop())
        if N == 0:
            break
        R = range(N)
        pos = []
        for loop in R:
            S = list(map(float, lst.pop().split()))
            pos.append(S)
        ans = 0
        for i in R:
            for j in R:
                v = [pos[j][0] - pos[i][0], pos[j][1] - pos[i][1]]
                norm = math.sqrt(v[0] * v[0] + v[1] * v[1])
                if norm > 2 or norm == 0:
                    continue
                vn = [v[0] / norm, v[1] / norm]
                norm /= 2
                norm2 = math.sqrt(1 - norm * norm)
                v90 = [-vn[1], vn[0]]
                cent = [pos[i][0] + v[0] / 2 + v90[0] * norm2, 
                pos[i][1] + v[1] / 2 + v90[1] * norm2]
                S = 2
                for k in R:
                    if i == k or j == k:
                        continue
                    x = cent[0] - pos[k][0]
                    y = cent[1] - pos[k][1]
                    if x * x + y * y <= 1:
                        S += 1
                ans = max(S, ans)
        print(max(1, ans))

if __name__ == '__main__':
    func()

Submission status: Runtime Error

Solution code:
#!/usr/bin/env python

from collections import deque
import itertools as it
import sys
import math

sys.setrecursionlimit(1000000)

def func():
    lst = []
    while True:
        S = input()
        lst.append(S)
        if S == '0':
            break
    lst = list(reversed(lst))
    while True:
        N = int(lst.pop())
        if N == 0:
            break
        pos = []
        for loop in range(N):
            S = list(map(float, lst.pop().split()))
            pos.append(S)
        ans = 0
        for i in range(N):
            for j in range(N):
                v = [pos[j][0] - pos[i][0], pos[j][1] - pos[i][1]]
                norm = math.sqrt(v[0] * v[0] + v[1] * v[1])
                if norm > 2 or i == j:
                    continue
                vn = [v[0] / norm, v[1] / norm]
                norm /= 2
                norm2 = math.sqrt(1 - norm * norm)
                v90 = [-vn[1], vn[0]]
                cent = [pos[i][0] + v[0] / 2 + v90[0] * norm2, 
                pos[i][1] + v[1] / 2 + v90[1] * norm2]
                S = 2
                for k in range(N):
                    if i == k or j == k:
                        continue
                    x = cent[0] - pos[k][0]
                    y = cent[1] - pos[k][1]
                    if x * x + y * y <= 1:
                        S += 1
                ans = max(S, ans)
        print(max(1, ans))

if __name__ == '__main__':
    func()

Submission status: Runtime Error

Solution code:
def cent(p1,p2):
    if abs(p1-p2) >= 2:
        return None,None
    else:
        q = (p1+p2)/2
        r = (p1-p2)/2
        n = abs(r)
        t = r * 1j * ((1-n**2)**0.5/n)
        return(q + t, q - t)

while(True):
    ans = 1
    n = int(input())
    if n == 0:
        quit()
    ps = []
    for _ in range(n):
        x,y = map(float,input().split())
        ps.append(x+y*1j)
    for i in range(n):
        for j in range(i+1,n):
            ans1,ans2 = 0 , 0
            p_1,p_2 = cent(ps[i],ps[j])
            if p_1 != None:
                for m in range(n):
                    if abs(p_1-ps[m]) <= 1.001:
                        ans1 += 1
                    if abs(p_2-ps[m]) <= 1.001:
                        ans2 += 1
                ans = max(ans,ans1,ans2)
    print(ans)