Problem p02690 (python)

Fixed submission:
import math

X = int(input())

def decompose(n):
	result = []
	half = math.floor(math.sqrt(n))
	i = 2
	while i <= half:
		if n % i == 0:
			result.append(i)
			n //= i
			half = math.floor(math.sqrt(n))
		else:
			i += 1
	if n > 1:
		result.append(n)
	return result

facts = decompose(X)

fact_table = {}
for f in facts:
	if f not in fact_table:
		fact_table[f] = 1
	else:
		fact_table[f] += 1

facts = list(fact_table.items())
facts.sort()

def bisearch_smallest(f, s, e = None):
	if e == None:
		e = s - 1
		s = 0
	else:
		e -= 1
	
	while s < e:
		m = (s + e) // 2
		if f(m):
			e = m
		else:
			s = m + 1
	
	if s == e and f(s):
		return s
	else:
		return -1

def find(num, n):
	if n >= len(facts):
		m = bisearch_smallest(lambda A: 5 * A ** 4 - 5 * (A - num) ** 4 >= 0, 0, 10 ** 9)
		i = bisearch_smallest(lambda A: A ** 5 - (A - num) ** 5 <= X, 0, m + 1)
		j = bisearch_smallest(lambda A: A ** 5 - (A - num) ** 5 >= X, m - 1, 10 ** 9)
		
		if i ** 5 - (i - num) ** 5 == X:
			return i, i - num
		if j ** 5 - (j - num) ** 5 == X:
			return j, j - num
	else:
		f, c = facts[n]
		for i in range(c + 1):
			ret = find(num, n + 1)
			if ret != None:
				return ret
			num *= f
	return None

A, B = find(1, 0)


print(A, B)

Buggy submission (verdict: Runtime Error):
import math

X = int(input())

def decompose(n):
	result = []
	half = math.floor(math.sqrt(n))
	i = 2
	while i <= half:
		if n % i == 0:
			result.append(i)
			n //= i
			half = math.floor(math.sqrt(n))
		else:
			i += 1
	if n > 1:
		result.append(n)
	return result

facts = decompose(X)

fact_table = {}
for f in facts:
	if f not in fact_table:
		fact_table[f] = 1
	else:
		fact_table[f] += 1

facts = list(fact_table.items())
facts.sort()

def bisearch_smallest(f, s, e = None):
	if e == None:
		e = s - 1
		s = 0
	else:
		e -= 1
	
	while s < e:
		m = (s + e) // 2
		if f(m):
			e = m
		else:
			s = m + 1
	
	if s == e and f(s):
		return s
	else:
		return -1

def find(num, n):
	if n >= len(facts):
		m = bisearch_smallest(lambda A: 5 * A ** 4 - (A - num) ** 4 >= 0, 0, 10 ** 9)
		i = bisearch_smallest(lambda A: A ** 5 - (A - num) ** 5 <= X, 0, m + 1)
		j = bisearch_smallest(lambda A: A ** 5 - (A - num) ** 5 >= X, m - 1, 10 ** 9)
		
		if i ** 5 - (i - num) ** 5 == X:
			return i, i - num
		if j ** 5 - (j - num) ** 5 == X:
			return j, j - num
	else:
		f, c = facts[n]
		for i in range(c + 1):
			ret = find(num, n + 1)
			if ret != None:
				return ret
			num *= f
	return None

A, B = find(1, 0)


print(A, B)

Buggy submission (verdict: Runtime Error):
import math

X = int(input())

def decompose(n):
	result = []
	half = math.floor(math.sqrt(n))
	i = 2
	while i <= half:
		if n % i == 0:
			result.append(i)
			n //= i
			half = math.floor(math.sqrt(n))
		else:
			i += 1
	if n > 1:
		result.append(n)
	return result

facts = decompose(X)

fact_table = {}
for f in facts:
	if f not in fact_table:
		fact_table[f] = 1
	else:
		fact_table[f] += 1

facts = list(fact_table.items())
facts.sort()

def find(num, n):
	if n >= len(facts):
#		print(num)
		A = 1
		while True:
			B = A - num
			x = A ** 5 - B ** 5
#			print(">", A, B, x)
			if x == X:
				return A, B
			elif x > X:
				break
			A += 1
	else:
		f, c = facts[n]
		for i in range(c + 1):
			ret = find(num, n + 1)
			if ret != None:
				return ret
			num *= f
	return None

A, B = find(1, 0)


print(A, B)