Problem p03006 (python)

Fixed submission:
#!/usr/bin/env python3
import sys
from collections.abc import Iterable
from math import *
from itertools import *
from collections import *
from functools import *
from operator import *
try:
    from math import gcd
except Exception:
    from fractions import gcd


def solve(N: int, x: "List[int]", y: "List[int]"):
    ds = []
    for i in range(N):
        for j in range(N):
            if i == j:
                continue
            dx = x[j] - x[i]
            dy = y[j] - y[i]
            ds.append((dx, dy))

    return 1 if N == 1 else (N - max(Counter(ds).values()))


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    x = [int()] * (N)  # type: "List[int]" 
    y = [int()] * (N)  # type: "List[int]" 
    for i in range(N):
        x[i] = int(next(tokens))
        y[i] = int(next(tokens))
    result = solve(N, x, y)
    print(result)

if __name__ == '__main__':
    main()

Buggy submission (verdict: Runtime Error):
#!/usr/bin/env python3
import sys
from collections.abc import Iterable
from math import *
from itertools import *
from collections import *
from functools import *
from operator import *
try:
    from math import gcd
except Exception:
    from fractions import gcd


def solve(N: int, x: "List[int]", y: "List[int]"):
    ds = []
    for i in range(N):
        for j in range(i + 1, N):
            dx = x[j] - x[i]
            dy = y[j] - y[i]
            ds.append((dx, dy))

    return N - max(Counter(ds).values())


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    x = [int()] * (N)  # type: "List[int]" 
    y = [int()] * (N)  # type: "List[int]" 
    for i in range(N):
        x[i] = int(next(tokens))
        y[i] = int(next(tokens))
    result = solve(N, x, y)
    print(result)

if __name__ == '__main__':
    main()

Buggy submission (verdict: Runtime Error):
#!/usr/bin/env python3
import sys
from collections.abc import Iterable
from math import *
from itertools import *
from collections import *
from functools import *
from operator import *
try:
    from math import gcd
except Exception:
    from fractions import gcd


def solve(N: int, x: "List[int]", y: "List[int]"):
    rem = {}
    for i in range(N-1):
        for j in range(i + 1, N):
            dx = x[i] - x[j]
            dy = y[i] - y[j]

            found = False
            for dx2, dy2  in rem.keys():
                if dx * dy2 == dy * dx2:
                    rem[(dx2, dy2)].add(j)
                    found = True
            if not found:
                rem[(dx, dy)] = set()
                rem[(dx, dy)].add(j)
    
    return N - max([len(v) for k, v in rem.items()])


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    x = [int()] * (N)  # type: "List[int]" 
    y = [int()] * (N)  # type: "List[int]" 
    for i in range(N):
        x[i] = int(next(tokens))
        y[i] = int(next(tokens))
    result = solve(N, x, y)
    print(result)

if __name__ == '__main__':
    main()

Buggy submission (verdict: Runtime Error):
#!/usr/bin/env python3
import sys
from collections.abc import Iterable
from math import *
from itertools import *
from collections import *
from functools import *
from operator import *
try:
    from math import gcd
except Exception:
    from fractions import gcd


def solve(N: int, x: "List[int]", y: "List[int]"):
    acc = {}
    for i in range(N):
        for j in range(i+1, N):
            dx = x[i] - x[j]
            dy = y[i] - y[j]
            c = gcd(dx, dy)
            tmp = (dx // c, dy // c)
            acc.setdefault(tmp, set()).add(j)
    return N - max([len(s) for s in acc.values()])


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    x = [int()] * (N)  # type: "List[int]" 
    y = [int()] * (N)  # type: "List[int]" 
    for i in range(N):
        x[i] = int(next(tokens))
        y[i] = int(next(tokens))
    result = solve(N, x, y)
    if isinstance(result, Iterable) and not isinstance(result, str):
        result = '\n'.join([str(v) for v in result])
    print(result)

if __name__ == '__main__':
    main()

Buggy submission (verdict: Runtime Error):
#!/usr/bin/env python3
import sys
from collections.abc import Iterable
from math import *
from itertools import *
from collections import *
from functools import *
from operator import *
try:
    from math import gcd
except Exception:
    from fractions import gcd


def solve(N: int, x: "List[int]", y: "List[int]"):
    acc = []
    for i in range(N):
        for j in range(i+1, N):
            dx = x[i] - x[j]
            dy = y[i] - y[j]
            c = gcd(dx, dy)
            acc.append((dx // c, dy // c))
    c = Counter(acc)
    v, (p, q) = max([(v, k) for k, v in c.items()])
    return max(N - v, 1)


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    x = [int()] * (N)  # type: "List[int]" 
    y = [int()] * (N)  # type: "List[int]" 
    for i in range(N):
        x[i] = int(next(tokens))
        y[i] = int(next(tokens))
    result = solve(N, x, y)
    if isinstance(result, Iterable) and not isinstance(result, str):
        result = '\n'.join([str(v) for v in result])
    print(result)

if __name__ == '__main__':
    main()