Python Primitive Pythagorean triple code not working

Question

Currently trying to find all primitve pytagorean triples up to some number n, using the formula a = m^2-n^2, b = 2mn, c = m^2 + n^2. Here is the code:

    def prim(k):
        primlist=[]
        for m in range(1,k):
            for n in range(m+1,k+1):
                if m**2+n**2>k:
                    break
                if m%2==1 and n%2==1:
                    break
               if n**2-m**2==0 or 2*m*n ==0 or n**2+m**2==0:
                    break

                if gcd(m,n)!=1:
                    break


                primlist.append([n**2-m**2,2*m*n,n**2+m**2])
        return primlist
    print(prim(100))

We expect to find all pythagorean triples, however some are missing, for example 20,21,29. Theres 16 with c under 100 however we only get 6. Cheers

SO is there to ask specific questions, not to fix broken code or get homework done. Please update your question with what you have already tried and your suspicions why your code doesn't work. — Vroomfondel, Dec 07 '17 at 14:37
@Vroomfondel There's nothing wrong with this question. The OP has posted a MCVE, and adequately described the expected output and the actual output. — PM 2Ring, Dec 07 '17 at 15:05
Well I've put the code which i cant find a problem with, and have also said what the problem is, i cant put suspicions if i didn't know where the code was going wrong in the first place. — Sam Corrigan, Dec 07 '17 at 15:07

PM 2Ring · Accepted Answer · 2017-12-07T14:57:04.590

Apart from the first condition, where m & n are too large, you don't want to break out of the inner loop, simply continue on to the next iteration.

The following tests are completely superfluous, since with your m and n they can never be true.

if n**2-m**2==0 or 2*m*n ==0 or n**2+m**2==0:

so I've removed them from the code. You didn't supply a gcd function, or import one from the standard library, so I've supplied my own.

def gcd(a, b):
    '''  Greatest common divisor of a & b '''
    while b:
        a, b = b, a % b
    return a

def prim(k):
    primlist=[]
    for m in range(1,k):
        for n in range(m+1,k+1):
            if m**2 + n**2 > k:
                break
            if m%2==1 and n%2==1:
                continue
            if gcd(m,n)!=1:
                continue

            primlist.append([n**2 - m**2, 2*m*n, n**2 + m**2])
    return primlist

print(prim(100))

output

[[3, 4, 5], [15, 8, 17], [35, 12, 37], [63, 16, 65], [5, 12, 13], [21, 20, 29], [45, 28, 53], [77, 36, 85], [7, 24, 25], [55, 48, 73], [9, 40, 41], [33, 56, 65], [65, 72, 97], [11, 60, 61], [39, 80, 89], [13, 84, 85]]

FWIW, here's a more efficient (and slightly more Pythonic) way to write that code. Rather than building a list, we make a generator. That way we can just print or consume the triples, and of course we can easily collect them into a list by doing, eg list(prim(100)).

def gcd(a, b):
    '''  Greatest common divisor of a & b '''
    while b:
        a, b = b, a % b
    return a

def prim(k):
    for m in range(1, k):
        for n in range(m+1, k+1):
            m2, n2 = m * m, n * n
            if m2 + n2 > k:
                break
            if m % 2 and n % 2:
                continue
            if gcd(m, n) > 1:
                continue

            yield n2 - m2, 2*m*n, n2 + m2

for i, t in enumerate(prim(100), 1):
    print(i, t)

output

1 (3, 4, 5)
2 (15, 8, 17)
3 (35, 12, 37)
4 (63, 16, 65)
5 (5, 12, 13)
6 (21, 20, 29)
7 (45, 28, 53)
8 (77, 36, 85)
9 (7, 24, 25)
10 (55, 48, 73)
11 (9, 40, 41)
12 (33, 56, 65)
13 (65, 72, 97)
14 (11, 60, 61)
15 (39, 80, 89)
16 (13, 84, 85)

Python Primitive Pythagorean triple code not working

1 Answers1