def solution():
DIGITS = 100
MULTIPLIER = 100**DIGITS
result = sum(
sum(int(c) for c in str(common.sqrt(i * MULTIPLIER))[:DIGITS])
for i in range(100) if common.sqrt(i)**2 != i)
return str(result)
def solution(): goal = 2000000 end = common.sqrt(goal) + 1 gen = ((w, h) for w in range(1, end) for h in range(1, end)) func = lambda wh: abs(num_rectangles(*wh) - goal) result = min(gen, key=func) return str(result[0] * result[1])
def floor(self): temp = common.sqrt(self.b * self.b * self.d) if self.b < 0: temp = -(temp + 1) temp += self.a if temp < 0: temp -= self.c - 1 return temp // self.c
def divisorCount(n):
count = 1
end = common.sqrt(n)
for i in itertools.count(2):
if i > end:
break
if n % i == 0:
j = 0
while True:
n //= i
j += 1
if n % i != 0:
break
count *= j * 2 + 1
end = common.sqrt(n)
if n != 1:
count *= 3
return count
def stdev(X,axis=1):
assert(dim(X)==2)
assert(axis==1)
X_T = matrix_transpose(X)
m = mean(X,axis=1)
R = []
for j in range(shape(X)[1]):
R.append(sqrt(mean(square(minus(X_T[j],m[j])))))
return R
def _corr(A,i,j):
assert(dim(A)==2)
m,n = shape(A)
A_T = matrix_transpose(A)
X,Y = A_T[i],A_T[j] # X,Y = col(A,i),col(A,j)
mean_X,mean_Y = mean(X),mean(Y)
X_ = [k-mean_X for k in X]
Y_ = [k-mean_Y for k in Y]
numerator = mean(multiply(X_,Y_))
# print(sqrt(mean(square(X_))))
denominator = sqrt(mean(square(X_)))*sqrt(mean(square(Y_)))
if denominator == 0:
return 0
else:
r = (numerator)/(denominator)
return r
def solution():
ceiling = 50000000
primes = common.list_primes(common.sqrt(ceiling))
sums = {0}
for i in range(2, 5):
newsums = set()
for p in primes:
q = p**i
if q > ceiling:
break
for x in sums:
if x + q <= ceiling:
newsums.add(x + q)
sums = newsums
return str(len(sums))
def is_prime(x): if x < 0: raise ValueError() elif x in (0, 1): return False else: end = common.sqrt(x) for p in primes: if p > end: break if x % p == 0: return False for i in range(primes[-1] + 2, end + 1, 2): if x % i == 0: return False return True
def solution():
x0 = 3
y0 = 1
x = x0
y = y0
while True:
sqrt = common.sqrt(y**2 * 8 + 1)
if sqrt % 2 == 1: # Is odd
blue = (sqrt + 1) // 2 + y
if blue + y > 10**12:
return str(blue)
nextx = x * x0 + y * y0 * 8
nexty = x * y0 + y * x0
x = nextx
y = nexty
def solution():
ceiling = 1500000
triples = set()
for s in range(3, common.sqrt(ceiling) + 1, 2):
for t in range(s - 2, 0, -2):
if fractions.gcd(s, t) == 1:
a = s * t
b = (s * s - t * t) // 2
c = (s * s + t * t) // 2
if a + b + c <= ceiling:
triples.add((a, b, c))
ways = [0] * (ceiling + 1)
for triple in triples:
sigma = sum(triple)
for i in range(sigma, len(ways), sigma):
ways[i] += 1
result = ways.count(1)
return str(result)
