990. Satisfiability of Equality Equations

You are given an array of strings equations that represent relationships between variables where each string equations[i] is of length 4 and takes one of two different forms: "xi==yi" or "xi!=yi".Here, xi and yi are lowercase letters (not necessarily different) that represent one-letter variable names.

Return true if it is possible to assign integers to variable names so as to satisfy all the given equations, or false otherwise.

Example 1:

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

Constraints:

• 1 <= equations.length <= 500
• equations[i].length == 4
• equations[i][0] is a lowercase letter.
• equations[i][1] is either '=' or '!'.
• equations[i][2] is '='.
• equations[i][3] is a lowercase letter.

class Solution {
    public boolean equationsPossible(String[] equations) {
        int[] pa = new int[26];
        for(int i = 0; i < 26; i++) pa[i] = i;
        for(String s: equations) {
            if(s.charAt(1) == '=') pa[find(pa, s.charAt(0) - 'a')] = find(pa, s.charAt(3) - 'a');
        }
        for(String s: equations) {
            if(s.charAt(1) == '!') {
                if(find(pa, s.charAt(0) - 'a') == find(pa, s.charAt(3) - 'a')) return false;
            }
        }
        return true;
    }
    public int find(int[] pa, int n) {
        if(n != pa[n]) pa[n] = find(pa, pa[n]);
        return pa[n];
    }
}

https://leetcode.com/problems/satisfiability-of-equality-equations/discuss/234486/JavaC%2B%2BPython-Easy-Union-Find

union find can be used here, make all "==" as union, then search the "!" euqation and return false if they still have same parents.