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This approach uses the Union-Find data structure to manage connectivity between variables. The core idea is to group variables that are known to be equal using '=='. After processing all such equations, we then check the '!=' equations to ensure that connected variables (i.e., variables that are in the same component) are not incorrectly marked as not equal.
Steps:
Time Complexity: O(n * α(n)) where n is the number of equations, and α is the inverse Ackermann function.
Space Complexity: O(1) as we are using a fixed-size array of 26 characters.
1var equationsPossible = function(equations) {
2 let parent = new Array(26).fill(0).map((_, index) =>
The JavaScript implementation uses a similar approach with an array initialized with character indices to act as parents. We apply the union-find operations to resolve connectivity driven by '==', verify discrepancies noted in inequalities, and return falsity if conflicts are found.
Another method is to visualize the problem as a graph and determine if the '==' relations create valid partitions without violating '!=' conditions. This is managed using a BFS approach.
Steps:
Time Complexity: O(n) where n is the number of equations as each one is processed once during graph building and inequality checks.
Space Complexity: O(1) as it uses a fixed-size 26x26 adjacency matrix.
This C solution constructs an undirected graph for the equality constraints and checks inequality constraints using a BFS traversal. If any graph component contains both nodes linked by a '!=' relation, it returns false. The operation checks conflicts and resets visitation states for independent inequality checks.