def countRT(p, limit): # counts right triangles OPQ where Q is to the left of OP # for a right angle, Q must lie on line perpendicular to OP # get the shortest integer vector on that line in the counter-clockwise direction # count how many times we can add it to P before going out of bounds if p[1] == 0: return limit dx, dy = reduceFrac(*p) return min(p[0] // dy, (limit - p[1]) // dx)
def countRT(p,
limit): # counts right triangles OPQ where Q is to the left of OP
# for a right angle, Q must lie on line perpendicular to OP
# get the shortest integer vector on that line in the counter-clockwise direction
# count how many times we can add it to P before going out of bounds
if p[1] == 0: return limit
dx, dy = reduceFrac(*p)
return min(p[0] // dy, (limit - p[1]) // dx)
def main(): # this is a terrible question def seq(): for d in range(11, 100): da, db = d // 10, d % 10 if db > 0 and da != db: for n in range(10, d): na, nb = n // 10, n % 10 if nb > 0 and na != nb and (da == na and n * db == nb * d or da == nb and n * db == na * d or db == na and n * da == nb * d or db == nb and n * da == na * d): yield n, d n, d = 1, 1 for a, b in seq(): n, d = a * n, b * d n, d = reduceFrac(n, d) return d
def main():
# this is a terrible question
def seq():
for d in range(11, 100):
da, db = d // 10, d % 10
if db > 0 and da != db:
for n in range(10, d):
na, nb = n // 10, n % 10
if nb > 0 and na != nb and (
da == na and n * db == nb * d
or da == nb and n * db == na * d
or db == na and n * da == nb * d
or db == nb and n * da == na * d):
yield n, d
n, d = 1, 1
for a, b in seq():
n, d = a * n, b * d
n, d = reduceFrac(n, d)
return d
