def digit_expansion(n, prec):
context = Context(prec=prec + 2)
sqrt = str(context.sqrt(n))
total = 0
#delete last two decimal places to avoid rounding infelicities
for d in sqrt[:-2]:
if d != '.':
total += int(d)
return total
def cont_frac(N):
context = Context(prec=1000)
val = Decimal(context.sqrt(N))
rep = [floor(val)]
ctr = 1
while ctr <= 1000:
val = Decimal(
context.divide(1, (context.subtract(val, Decimal(floor(val))))))
rep.append(floor(val))
ctr += 1
return rep
def cont_frac(N):
context = Context(prec=1000)
val = Decimal(context.sqrt(N))
init_val = floor(val)
rep = [init_val]
ctr = 1
while floor(val) != 2 * init_val:
val = Decimal(
context.divide(1, (context.subtract(val, Decimal(floor(val))))))
rep.append(floor(val))
ctr += 1
return rep
def fundamental_solution(N):
context = Context(prec=1000)
val = Decimal(context.sqrt(N))
rep = [floor(val)]
val = Decimal(
context.divide(1, (context.subtract(val, Decimal(floor(val))))))
rep.append(floor(val))
ctr = 1
h_base = [0, 1]
k_base = [1, 0]
h_1 = rep[0] * h_base[-1] + h_base[-2]
k_1 = rep[0] * k_base[-1] + k_base[-2]
if check_sol(h_1, k_1, N):
return h_1, k_1
h_2 = rep[1] * h_1 + h_base[-1]
k_2 = rep[1] * k_1 + k_base[-1]
if check_sol(h_2, k_2, N):
return h_2, k_2
H = [h_1, h_2]
K = [k_1, k_2]
h = h_2
k = k_2
ind = 3
frac = Fraction(int(h), int(k))
while not (check_sol(frac.numerator, frac.denominator, N)):
val = Decimal(
context.divide(1, (context.subtract(val, Decimal(floor(val))))))
rep.append(floor(val))
#val = rep[ind-1]
h = long(long(floor(val)) * H[-1] + H[-2])
k = long(long(floor(val)) * K[-1] + K[-2])
frac = Fraction(long(h), long(k))
H.append(frac.numerator)
K.append(frac.denominator)
ind += 1
return h, k
from decimal import Decimal, Context, ROUND_FLOOR, setcontext C = Context(rounding=ROUND_FLOOR) setcontext(C) x1, y1, x2, y2 = map(Decimal, input().split()) r_2 = (x2 - x1)**2 + (y2 - y1)**2 print(C.sqrt(r_2))
from decimal import Decimal, Context, ROUND_FLOOR, setcontext
from sys import float_info
# NOTE: sqrtする際の誤差をround_floorで切り捨てるので、eで補完する
# ref: https://marco-note.net/abc-191-work-log/
C = Context(rounding=ROUND_FLOOR)
setcontext(C)
# NOTE: pythonの計算機イプシロン
# ref: https://qiita.com/ikuzak/items/1332625192daab208e22
e = Decimal(str(float_info.epsilon))
X, Y, R = map(Decimal, input().split())
zero = Decimal("0")
ans = 0
for x in range(int(X - R), int(X + R) + 1):
y2_ = R**2 - (X - x)**2
if y2_ >= zero:
y_ = C.sqrt(y2_ + e)
y_min = Y - y_
y_max = Y + y_
ans += (int(y_max.quantize(zero)) - int(y_min.quantize(zero)))
print(ans)
