Python program using python class improves speed?

Question

I'm doing another Leetcode "1202. Smallest String With Swaps". The code below managed 35/36 cases but exceeded time for one.

from collections import defaultdict

class Solution:

    def smallestStringWithSwaps(self, s, pairs):

        nofNode = len(s)
        parents = list(range(nofNode))
        def findParent(child):
            if child == parents[child]: return child
            else:
                return findParent(parents[child])
        def union(a, b):
            parents[findParent(a)] = findParent(b)

        for a, b in pairs:
            union(a, b)
        for i in range(nofNode):
            parents[i] = findParent(parents[i])
        dic = defaultdict(list)
        for i in range(nofNode):
            dic[findParent(i)].append(s[i])
        for key in dic.keys():
            dic[key].sort(reverse=True)
        res = []
        for i in range(nofNode):
            res.append(dic[findParent(i)].pop())

        return ''.join(res)

The way to resolve this is to create a class and move the functions into a class. Also move the parents (python list) into the class.

from collections import defaultdict

class Solution:

    def smallestStringWithSwaps(self, s, pairs):

        class UF:
            def __init__(self, n): self.p = list(range(n))

            def union(self, x, y): self.p[self.findParent(x)] = self.findParent(y)

            def findParent(self, x):
                if x != self.p[x]: self.p[x] = self.findParent(self.p[x])
                return self.p[x]

        uf = UF(len(s))
        for a, b in pairs:
            uf.union(a, b)
        for i in range(len(s)):
            uf.p[i] = uf.findParent(uf.p[i])
        dic = defaultdict(list)
        for i in range(len(s)):
            dic[uf.findParent(i)].append(s[i])
        for key in dic.keys():
            dic[key].sort(reverse=True)
        res = []
        for i in range(len(s)):
            res.append(dic[uf.findParent(i)].pop())

        return ''.join(res)

Why does using a class solves improve the timing ?

Thanks !