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Find all Pythagorean triangles with length or height less than or equal to 20
Pythagorean triangles are right angle triangles whose sides comply with the following equation:
a * a + b * b = c * c
where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides. Find all such triangles where a, b and c are non-zero integers with a and b less than or equal to 20. Sort your results by the size of the hypotenuse. The expected answer is:
a * a + b * b = c * c
where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides. Find all such triangles where a, b and c are non-zero integers with a and b less than or equal to 20. Sort your results by the size of the hypotenuse. The expected answer is:
[3, 4, 5]
[6, 8, 10]
[5, 12, 13]
[9, 12, 15]
[8, 15, 17]
[12, 16, 20]
[15, 20, 25]
python
from math import sqrt
a = 1
ret = []
while a <= 20:
b = 1
while b <= 20:
c = sqrt((a**2)+(b**2))
if int(c) == c and sorted([a,b,int(c)]) not in ret:
ret.append(sorted([a,b,int(c)]))
b +=1
a +=1
print ret
or if you wanna get snarky..
print sorted(set([tuple(sorted((a,b,int(sqrt((a**2)+(b**2)))))) for a in xrange(1,21) for \
b in xrange(1,21) if int(sqrt((a**2)+(b**2))) == sqrt((a**2)+(b**2))]))
a = 1
ret = []
while a <= 20:
b = 1
while b <= 20:
c = sqrt((a**2)+(b**2))
if int(c) == c and sorted([a,b,int(c)]) not in ret:
ret.append(sorted([a,b,int(c)]))
b +=1
a +=1
print ret
or if you wanna get snarky..
print sorted(set([tuple(sorted((a,b,int(sqrt((a**2)+(b**2)))))) for a in xrange(1,21) for \
b in xrange(1,21) if int(sqrt((a**2)+(b**2))) == sqrt((a**2)+(b**2))]))
fsharp
let getGoodTri (a,b) =
let h = int(System.Math.Sqrt(float(a*a + b*b)))
if a*a + b*b = h*h then Some(a,b,h)
else None
seq{ for i in 1..20 do yield! seq{for j in i..20 do yield i,j} } |> Seq.choose(getGoodTri) |> Seq.sortBy(fun (_,_,c) -> c);;
let h = int(System.Math.Sqrt(float(a*a + b*b)))
if a*a + b*b = h*h then Some(a,b,h)
else None
seq{ for i in 1..20 do yield! seq{for j in i..20 do yield i,j} } |> Seq.choose(getGoodTri) |> Seq.sortBy(fun (_,_,c) -> c);;
Greatest Common Divisor
Find the largest positive integer that divides two given numbers without a remainder. For example, the GCD of 8 and 12 is 4.
python
def gcd_recursive(i, j):
if min(i, j) == 0:
return max(i, j)
else:
return gcd_recursive(min(i, j), abs(i - j))
def gcd_iterative(i, j):
while min(i, j) != 0:
i, j = min(i, j), abs(i - j)
return max(i, j)
if __name__ == "__main__":
print gcd_recursive(8, 12)
print gcd_iterative(8, 12)
if min(i, j) == 0:
return max(i, j)
else:
return gcd_recursive(min(i, j), abs(i - j))
def gcd_iterative(i, j):
while min(i, j) != 0:
i, j = min(i, j), abs(i - j)
return max(i, j)
if __name__ == "__main__":
print gcd_recursive(8, 12)
print gcd_iterative(8, 12)
from fractions import gcd
print gcd(8, 12)
print gcd(8, 12)
fsharp
let rec gcd x y =
if y = 0 then x
else gcd y (x % y)
if y = 0 then x
else gcd y (x % y)
