**Problem Statement:**

You are given two strings of the same length s1 and s2 and a string baseStr.

We say s1[i] and s2[i] are equivalent characters.

For example, if s1 = "abc" and s2 = "cde", then we have 'a' == 'c', 'b' == 'd', and 'c' == 'e'.

Equivalent characters follow the usual rules of any equivalence relation:

**Reflexivity:** 'a' == 'a'.

**Symmetry:** 'a' == 'b' implies 'b' == 'a'.

**Transitivity:** 'a' == 'b' and 'b' == 'c' implies 'a' == 'c'.

For example, given the equivalency information from s1 = "abc" and s2 = "cde", "acd" and "aab" are equivalent strings of baseStr = "eed", and "aab" is the lexicographically smallest equivalent string of baseStr.

Return the lexicographically smallest equivalent string of baseStr by using the equivalency information from s1 and s2.

**Example 1:**

**Input:** s1 = "parker", s2 = "morris", baseStr = "parser"

**Output:** "makkek"

**Explanation:** Based on the equivalency information in s1 and s2, we can group their characters as [m,p], [a,o], [k,r,s], [e,i].

The characters in each group are equivalent and sorted in lexicographical order.

So the answer is "makkek".

**Example 2:**

**Input:** s1 = "hello", s2 = "world", baseStr = "hold"

**Output:** "hdld"

**Explanation:** Based on the equivalency information in s1 and s2, we can group their characters as [h,w], [d,e,o], [l,r].

So only the second letter 'o' in baseStr is changed to 'd', the answer is "hdld".

**Example 3:**

**Input:** s1 = "leetcode", s2 = "programs", baseStr = "sourcecode"

**Output:** "aauaaaaada"

**Explanation:** We group the equivalent characters in s1 and s2 as [a,o,e,r,s,c], [l,p], [g,t] and [d,m], thus all letters in baseStr except 'u' and 'd' are transformed to 'a', the answer is "aauaaaaada".

**Constraints:**

- 1 <= s1.length, s2.length, baseStr <= 1000
- s1.length == s2.length
- s1, s2, and baseStr consist of lowercase English letters.

**Solution:**

**Algorithm:**

- Initialize parent array with 26 elements, each element is its index.
- Iterate through s1 and s2, find the parent of each character, if they are not the same, set the parent of the larger one to the smaller one.
- Iterate through baseStr, find the parent of each character, and append the character to the result.
- Return the result.
**Code:**

```
1. Initialize parent array with 26 elements, each element is its index.
2. Iterate through s1 and s2, find the parent of each character, if they are not the same, set the parent of the larger one to the smaller one.
3. Iterate through baseStr, find the parent of each character, and append the character to the result.
4. Return the result.
```

**Time Complexity:**

O(n), where n is the length of baseStr.

**Space Complexity:**

O(1), we only use constant extra space

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