## 990. Satisfiability of Equality Equations

Given an array equations of strings that represent relationships between variables, each string `equations[i]` has length `4` and takes one of two different forms: `"a==b"` or `"a!=b"`.  Here, `a` and `b` are lowercase letters (not necessarily different) that represent one-letter variable names.

Return `true` if and only if it is possible to assign integers to variable names so as to satisfy all the given equations.

Example 1:

```Input: ["a==b","b!=a"]
Output: false
Explanation: If we assign say, a = 1 and b = 1, then the first equation is satisfied, but not the second.  There is no way to assign the variables to satisfy both equations.
```

Example 2:

```Input: ["b==a","a==b"]
Output: true
Explanation: We could assign a = 1 and b = 1 to satisfy both equations.
```

Example 3:

```Input: ["a==b","b==c","a==c"]
Output: true
```

Example 4:

```Input: ["a==b","b!=c","c==a"]
Output: false
```

Example 5:

```Input: ["c==c","b==d","x!=z"]
Output: true
```

Note:

1. `1 <= equations.length <= 500`
2. `equations[i].length == 4`
3. `equations[i]` and `equations[i]` are lowercase letters
4. `equations[i]` is either `'='` or `'!'`
5. `equations[i]` is `'='`

## Rust Solution

``````struct Solution;

struct UnionFind {
parent: Vec<usize>,
n: usize,
}

impl UnionFind {
fn new(n: usize) -> Self {
let parent = (0..n).collect();
UnionFind { parent, n }
}

fn find(&mut self, i: usize) -> usize {
let j = self.parent[i];
if i == j {
j
} else {
let k = self.find(j);
self.parent[i] = k;
k
}
}

fn union(&mut self, i: usize, j: usize) {
let i = self.find(i);
let j = self.find(j);
if i != j {
self.parent[i] = j;
self.n -= 1;
}
}
}

impl Solution {
fn equations_possible(equations: Vec<String>) -> bool {
let mut uf = UnionFind::new(26);
let mut pairs: Vec<(usize, usize)> = vec![];
for equation in equations {
let s: Vec<char> = equation.chars().collect();
let i = (s as u8 - b'a') as usize;
let j = (s as u8 - b'a') as usize;
if s == '=' {
uf.union(i, j);
} else {
pairs.push((i, j));
}
}
for pair in pairs {
let i = pair.0;
let j = pair.1;
if uf.find(i) == uf.find(j) {
return false;
}
}
true
}
}

#[test]
fn test() {
let equations = vec_string!["a==b", "b!=a"];
let res = false;
assert_eq!(Solution::equations_possible(equations), res);
let equations = vec_string!["b==a", "a==b"];
let res = true;
assert_eq!(Solution::equations_possible(equations), res);
let equations = vec_string!["a==b", "b==c", "a==c"];
let res = true;
assert_eq!(Solution::equations_possible(equations), res);
let equations = vec_string!["a==b", "b!=c", "c==a"];
let res = false;
assert_eq!(Solution::equations_possible(equations), res);
let equations = vec_string!["c==c", "b==d", "x!=z"];
let res = true;
assert_eq!(Solution::equations_possible(equations), res);
}
``````

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