Decide Whether Letter-Variable Equalities and Inequalities Are Consistent

### Problem Each four-character equation has the form `x==y` or `x!=y`, with lowercase single-letter variables that may be the same letter. Return whether integer values can be assigned to the variables so every equation is satisfied. ```cpp class Solution { public: bool equationsPossible(vector<string>& equations); }; ``` ### Examples **Example 1:** ```text Input: equations = ["a==b","b==c","a!=c"] Output: false Explanation: The equalities force a,b,and c to share one value, contradicting a!=c. ``` **Example 2:** ```text Input: equations = ["a!=b","b!=c","a==c"] Output: true Explanation: Assign a=c=0 and b=1. ``` ### Constraints - `1 <= equations.length <= 500`. - Each string has length4: lowercase variable, `=` or `!`, `=`, lowercase variable. ### Contract considerations The function returns satisfiability, not an arbitrary assignment. Repeated relations are permitted by the supplied format. ```hint Read the boundary condition Equalities form equivalence classes; an inequality is impossible only when both ends fall in one class. ``` ### Boundary reminders The function returns satisfiability, not an arbitrary assignment. Repeated relations are permitted by the supplied format.