[Python] Inline vs Function-based Swapping (First Missing Positive)

I am trying to solve this leetcode problem: First Missing Positive. However, I am facing a problem while performing the swap.

I referred to the solution here.

So instead of having a helper function like this to perform the swap,

class Solution:
def firstMissingPositive(self, nums: List[int]) -> int:
def swap_elements(index1, index2):
nums[index1], nums[index2] = nums[index2], nums[index1]

list_length = len(nums)

for i in range(list_length):
while 1 <= nums <= list_length and nums != nums[nums - 1]:
swap_elements(i, nums - 1)

for i in range(list_length):
if i + 1 != nums:
return i + 1

return list_length + 1


I tried to perform an inline swap like this

class Solution:
def firstMissingPositive(self, nums: List[int]) -> int:
list_length = len(nums)

for i in range(list_length):
while 1 <= nums <= list_length and nums != nums[nums - 1]:
nums, nums[nums - 1] = nums[nums - 1], nums

for i in range(list_length):
if i + 1 != nums:
return i + 1

return list_length + 1


Both approaches use the same logic, but the second does not work for some inputs.

Example: Given the input [3,4,-1,1], the first approach will change the nums like this

[-1, 4, 3, 1] --> [-1, 1, 3, 4] --> [1, -1, 3, 4]

but the second approach will cause an infinite while loop

[-1, 4, 3, 1] --> [4, 1, 3, 1] --> [4, 4, 3, 1] --> [4, 1, 3, 1] --> [4, 4, 3, 1]...

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