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Java-based LeetCode algorithm problem solutions, regularly updated

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package g0901_1000.s0990_satisfiability_of_equality_equations;

// #Medium #Array #String #Graph #Union_Find #2022_03_31_Time_5_ms_(24.79%)_Space_43.5_MB_(18.67%)

import java.util.HashMap;

/**
 * 990 - Satisfiability of Equality Equations\.
 *
 * Medium
 *
 * 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: "x_i==y_i" or "x_i!=y_i".Here, x_i and y_i 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.
**/
public class Solution {
    private int[] par;

    public boolean equationsPossible(String[] equations) {
        int counter = 0;
        HashMap map = new HashMap<>();
        for (String str : equations) {
            char ch = str.charAt(0);
            if (!map.containsKey(ch)) {
                map.put(ch, counter);
                counter++;
            }
            ch = str.charAt(3);
            if (!map.containsKey(ch)) {
                map.put(ch, counter);
                counter++;
            }
        }
        par = new int[counter];
        for (int i = 0; i < par.length; i++) {
            par[i] = i;
        }
        for (String str : equations) {
            String oper = str.substring(1, 3);
            if (oper.equals("==")) {
                int px = find(map.get(str.charAt(0)));
                int py = find(map.get(str.charAt(3)));
                if (px != py) {
                    par[px] = py;
                }
            }
        }
        for (String str : equations) {
            String oper = str.substring(1, 3);
            if (oper.equals("!=")) {
                int px = find(map.get(str.charAt(0)));
                int py = find(map.get(str.charAt(3)));
                if (px == py) {
                    return false;
                }
            }
        }
        return true;
    }

    private int find(int x) {
        if (par[x] == x) {
            return x;
        }
        par[x] = find(par[x]);
        return par[x];
    }
}