On 22/10/2010 13:33, Baba wrote:
On Oct 22, 8:07 am, Dennis Lee Bieber<wlfr...@ix.netcom.com> wrote:
On Thu, 21 Oct 2010 03:51:07 -0700 (PDT), Baba<raoul...@gmail.com>
declaimed the following in gmane.comp.python.general:
Hi everyone
i need a hint regarding the following exercise question:
"Write a program that generates all Pythagorean triples whose small
sides are no larger than n.
Try it with n<= 200."
what is "n" ? i am guessing that it is a way to give a bound to the
triples to be returned but i can't figure out where to fit in "n".
a^a + b^b = c^c is the condition to satisfy and i need to use loops
Well, I'd interpret it to mean that
a<= 200
AND
b<= 200
since c is the hypotenuse, which by definition is longer than either of
the sides.
The brute force approach is a nested set of "for" loops, running
1-200 (remember that (x)range(200) runs 0-199<G>).
The alternative is to study the information at
http://www.math.uic.edu/~fields/puzzle/triples.html
and filtering out entries where the first two components are>200...
Looking at the middle term "2*m*n" would have to be less than 201, and
the first term "n*n-m*m"< 201
In Python, this can all be done in a one-liner...
[(n*n - m*m, 2*m*n, n*n + m*m) for n in xrange(2,101) for m in
xrange(1,n) if 2*m*n< 201 and n*n-m*m< 201]
Converting this to a clean set of nested loops and nice lines of
output is a different matter.
Oh, and DO study the link I gave so you can cite it when you turn in
this intriguing formulation... after all, no need for math.sqrt<G>
--
Wulfraed Dennis Lee Bieber AF6VN
wlfr...@ix.netcom.com HTTP://wlfraed.home.netcom.com/
Hi Wulfraed,
only a has an upper limit of 200
Really? The quote you gave included "whose small sides are no larger
than n". Note: "sides", plural.
the program needs to output the following triple for a == 200: (200 ,
609,641)
so at this stage my problem is: how to set the upper limit for b in a
smart way?
My solution below is not efficient i believe.
import math
for a in range (190,200):
for b in range (a,a*a):
csqrd = a * a + b * b
csqrt = math.sqrt(csqrd)
for c in range (1, csqrd):
if c * c == a * a + b * b and math.floor(csqrt) == csqrt:
print (a,b,c)
--
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