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This approach uses a Union-Find (Disjoint Set Union, DSU) structure to detect cycles and check for nodes with two parents. The goal is to handle two situations: a node having two parents, and a cycle existing in the graph. We iterate through the edges to identify a node with two parents and mark the offending edge. Then, we use the Union-Find structure to track cycles and find the redundant connection based on the identified edges.
Time Complexity: O(n), where n is the number of edges.
Space Complexity: O(n), for storing the parent and rank arrays.
1class UnionFind {
2 constructor(size) {
3 this.parent = Array.from({ length: size }, (_, index) => index);
4 this.rank = Array(size).fill(1);
5 }
6
7 find(x) {
8 if (this.parent[x] !== x) {
9 this.parent[x] = this.find(this.parent[x]);
10 }
11 return this.parent[x];
12 }
13
14 union(x, y) {
15 let rootX = this.find(x);
16 let rootY = this.find(y);
17 if (rootX === rootY) return false;
18 if (this.rank[rootX] > this.rank[rootY]) {
19 this.parent[rootY] = rootX;
20 } else if (this.rank[rootX] < this.rank[rootY]) {
21 this.parent[rootX] = rootY;
22 } else {
23 this.parent[rootY] = rootX;
24 this.rank[rootX]++;
25 }
26 return true;
27 }
28}
29
30var findRedundantDirectedConnection = function(edges) {
31 const n = edges.length;
32 const parent = Array.from({ length: n + 1 }, (_, index) => index);
33 let can1 = null, can2 = null;
34
35 for (const [u, v] of edges) {
36 if (parent[v] !== v) {
37 can1 = [parent[v], v];
38 can2 = [u, v];
39 v = 0;
40 } else {
41 parent[v] = u;
42 }
43 }
44
45 const uf = new UnionFind(n + 1);
46 for (const [u, v] of edges) {
47 if (v === 0) continue;
48 if (!uf.union(u, v)) return can1 || [u, v];
49 }
50 return can2;
51};
52The JavaScript approach involves creating a Union-Find structure tailored to capture duplicate parent incidents and explore the resultant edge arrangements to ensure consistent tree hierarchy by advanced cycle detection and union handling for non-unique parentage correction.
In this method, we focus on identifying two scenarios: an edge creating a cycle in the graph and a node with two parents. With graph traversal, primarily cross-check with parent pointers and DFS for cycle confirmation, fine-tuning insights to pinpoint a last array occurrence redundant connection.
Time Complexity: O(n^2) with recursive verification.
Space Complexity: O(n), memoizing visited nodes.
1
The Python script leverages DFS walkthrough simplification to evaluate node links and rank suitable output arrays. Using inner loops partnered with recursive cycle validation, it correctly adjudicates offending connections.