def main():
limit = 1500000
sumCount = {}
# We have a+b+c = 2m^2 + 2mn > 2m^2, so we need only test check m up to floor(sqrt(limit/2))
for m in range(1,math.floor(math.sqrt(limit/2))):
# m,n have different parity
n = 1+(m%2)
while n<m:
#Establishing coprimality condition
if gcd.main(m,n) == 1:
#Taking care of nonprimitive triples
sidelength = 2*m*m+2*m*n
mult = 1
while sidelength*mult <= limit:
sumCount[mult*(2*m*m+2*m*n)]= 1+sumCount.get(mult*(2*m*m+2*m*n),0)
mult += 1
n += 2
total = 0
for i in sumCount:
if sumCount.get(i) == 1:
total += 1
return total
def main(frac_floor1, frac_floor2, frac_ceil1, frac_ceil2, d):
#solves the defined problem
#as given, frac_floor1 = 1, frac_floor2 = 3, frac_ceil1 = 1, frac_ceil2 = 2, d = 12000
frac_num = 0
#will count number of irreducible fractions
for b in range(2, (d + 1)):
#want to check all denominators 2 to d
for a in range((((b * frac_floor1) // frac_floor2) + 1),
((((b * frac_ceil1) - 1) // frac_ceil2) + 1)):
#see above calculations for cap and floor on a
#TEST
print('a=', a, 'b=', b)
#TEST
#BOUNDS ARE INCORRECT
if gcd.main(a, b) == 1:
#i.e. if a/b is an irreducible fraction, then add one to the fraction count
frac_num += 1
return frac_num
def main( x ): count = 1 #since 1 will always be relatively prime to an integer for i in range( 2, x ): #checks all integers >= 2 and less than x. if gcd(x,i) is one (i.e. if i and x are coprime), then increments count if gcd.main( x, i ) == 1: count += 1 return count
def main(x):
#finds all primitive pythagorean triples of sum < x
#based on Euclid's formula as explained on https://en.wikipedia.org/wiki/Pythagorean_triple
trip_list = []
m = 1
n = 1
while (2 * (m**2) + 2 * m * n) < x:
#sum of a,b,c to be generated
m += 1
#increments m
n_max = min(m, ((x - (2 * (m**2))) // (2 * m) + 1))
#finds cap for search of n to keep total length below x
#REPLACED
# n_max = m
#REPLACED
for n in range(1, n_max):
#search through n < n_max
if ((m % 2 == 1) or (n % 2 == 1)) and ((m % 2 == 0) or
(n % 2 == 0)):
#must have one even and one odd to get primitive triple
if gcd.main(m, n) == 1:
#need m,n to be coprime to get primitive triple
a = ((m**2) - (n**2))
b = (2 * m * n)
c = ((m**2) + (n**2))
#calculates the triple
trip_list.append([a, b, c])
#adds triple to the list
n = 1
#needed so while loop doesn't end early
return trip_list
def main(x, y, cap):
#solves the defined problem for fraction to the left of x/y for d<= cap
#as defined, x = 3, y = 7, cap = 10**6
best = [1, 0]
#will store answer
desired = x / y
#the number that we want to get close to
for b in range(2, cap + 1):
#checks all divisors 2 -> d
a = (x * b - 1) // y
#finds the highest integer a for which a/b is less than x/y
if a != 0:
#necessary since gcd function will break if a = 0
if gcd.main(a, b) == 1:
#need a,b to be coprime for fraction to be irreducible
#TEST
# print('a=',a,'b=',b)
#TEST
diff = desired - (a / b)
#calculates the difference between x/y and a/b. will always be positive since it is assured that a/b < x/y
if diff < best[0]:
#i.e. if best a/b found so far
best[0] = diff
best[1] = [a, b]
#stores the best values found so far
return best
from gcd import main
from pyannotate_runtime import collect_types
if __name__ == '__main__':
collect_types.init_types_collection()
with collect_types.collect():
main()
collect_types.dump_stats('type_info.json')