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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.
1class Solution {
2 public int find(int[] parent, int x) {
3 if (parent[x] != x) {
In the Java implementation, the logic matches closely with the other languages. Integer arrays are used to keep track of the connected components. The methods find and unionSet manage the equality constraints, and the inequality constraints are verified thereafter.
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.
The Python graph implementation uses lists of lists for creating adjustable connectivity maps, engaging queues to seek connections and enforce separations via BFS processing. Each inequality discovered in the same component steps up incongruence resolutions, returning false when conflicts emerge.