Problem p02574 (python)

Fixed submission:
from math import gcd


def eratosthenes(n):
    prime = []
    data = [i + 1 for i in range(1, n)]
    while True:
        p = data[0]
        if n <= p ** 2:
            return prime + data
        prime.append(p)
        data = [e for e in data if e % p != 0]
    return data


def factorize(N):  # 素因数分解
    for p in prime_list:
        if p * p > N:
            break
        if N % p == 0 and (p in num):
            print('setwise coprime')
            exit()
        while N % p == 0:
            N //= p
            num.add(p)
    if N > 1:
        if N in num:
            print('setwise coprime')
            exit()
        num.add(N)


n = int(input())
a = list(map(int, input().split()))

ans = 0
for ai in a:
    ans = gcd(ans, ai)
if ans != 1:
    print('not coprime')
    exit()

prime_list = eratosthenes(10 ** 6)
num = set()
for ai in a:
    factorize(ai)
else:
    print('pairwise coprime')

Buggy submission (verdict: Runtime Error):
from math import gcd

n = int(input())
a = list(map(int, input().split()))

# 解説AC(a*loga)
ans = 0
cnt = [0] * (max(a) + 1)
for ai in a:
    ans = gcd(ans, ai)
    cnt[ai] += 1

if ans != 1:
    print('not coprime')
elif any(sum(cnt[i::i]) > 1 for i in range(max(a) + 1)):
    print('setwise coprime')
else:
    print('pairwise coprime')

Buggy submission (verdict: Runtime Error):
from math import gcd


class Eratosthenes(): # エラトステネスの篩
    def __init__(self, N) # 素数リスト生成 O(n*log(log n))
        is_prime = [0, 0] + [1] * (N - 1)
        for i in range(int(N**0.5) + 1):
            if is_prime[i] == 0:
                continue
            for j in range(i * 2, N + 1, i):
                is_prime[j] = 0
        self.prime_list = [i for i, pi in enumerate(is_prime) if pi == 1]


    def factor(self, NUM):  # 高速素因数分解 O(log num)
        PRIME = set()
        for p in self.prime_list:
            if p * p > NUM:
                break
            while NUM % p == 0:
                NUM //= p
                PRIME.add(p)
        if NUM > 1:
            PRIME.add(NUM)
        return PRIME


n = int(input())
a = list(map(int, input().split()))

ans = 0
for ai in a:
    ans = gcd(ans, ai)
if ans != 1:
    print('not coprime')
    exit()

era = Eratosthenes(max(a))
num = set()
for ai in a:
    prime = era.factor(ai)
    if len(prime & num) > 0:
        print('setwise coprime')
        break
    num |= prime
else:
    print('pairwise coprime')

Buggy submission (verdict: Runtime Error):
from math import gcd


class Eratosthenes: # エラトステネスの篩
    def __init__(self, N) # 素数リスト生成 O(n*log(log n))
        is_prime = [0, 0] + [1] * (N - 1)
        for i in range(int(N**0.5) + 1):
            if is_prime[i] == 0:
                continue
            for j in range(i * 2, N + 1, i):
                is_prime[j] = 0
        self.prime_list = [i for i, pi in enumerate(is_prime) if pi == 1]


    def factor(self, NUM):  # 高速素因数分解 O(log num)
        PRIME = set()
        for p in self.prime_list:
            if p * p > NUM:
                break
            while NUM % p == 0:
                NUM //= p
                PRIME.add(p)
        if NUM > 1:
            PRIME.add(NUM)
        return PRIME


n = int(input())
a = list(map(int, input().split()))

ans = 0
for ai in a:
    ans = gcd(ans, ai)
if ans != 1:
    print('not coprime')
    exit()

era = Eratosthenes(max(a))
num = set()
for ai in a:
    prime = era.factor(ai)
    if len(prime & num) > 0:
        print('setwise coprime')
        break
    num |= prime
else:
    print('pairwise coprime')

Buggy submission (verdict: Runtime Error):
from math import gcd


class Eratosthenes: # エラトステネスの篩
    def __init__(self, N) # 素数リスト生成 O(n*log(log n))
        is_prime = [0, 0] + [1] * (N - 1)
        for i in range(int(N**0.5) + 1):
            if is_prime[i] == 0:
                continue
            for j in range(i * 2, N + 1, i):
                is_prime[j] = 0
        self.prime_list = [i for i, pi in enumerate(is_prime) if pi == 1]


    def factor(self, NUM):  # 高速素因数分解 O(log num)
        PRIME = set()
        for p in self.prime_list:
            if p * p > NUM:
                break
            while NUM % p == 0:
                NUM //= p
                PRIME.add(p)
        if NUM > 1:
            PRIME.add(NUM)
        return PRIME


n = int(input())
a = list(map(int, input().split()))

ans = 0
for ai in a:
    ans = gcd(ans, ai)
if ans != 1:
    print(‘not coprime’)
    exit()

era = Eratosthenes(max(a))
num = set()
for ai in a:
    prime = era.factor(ai)
    if len(prime & num) > 0:
        print(‘setwise coprime’)
        break
    num |= prime
else:
    print(‘pairwise coprime’)

Buggy submission (verdict: Runtime Error):
from math import gcd


def eratosthenes(n):
    prime = []
    data = [i for i in range(n - 1)]
    while True:
        p = data[0]
        if n <= p ** 2:
            return prime + data
        prime.append(p)
        data = [e for e in data if e % p != 0]
    return data


def factorize(N):  # 素因数分解
    prime = set()
    for p in prime_list:
        if p * p > N:
            break
        while N % p == 0:
            N //= p
            prime.add(p)
    if N > 1:
        prime.add(N)
    return prime


n = int(input())
a = list(map(int, input().split()))

ans = 0
for ai in a:
    ans = gcd(ans, ai)
if ans != 1:
    print('not coprime')
    exit()

prime_list = eratosthenes(10 ** 6)
num = set()
for ai in a:
    prime = factorize(ai)
    if len(prime & num) > 0:
        print('setwise coprime')
        break
    num |= prime
else:
    print('pairwise coprime')