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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.
The Java implementation maps nodes with potential redundant edges and explores which connection among candidates could feasibly be removed to preserve tree properties while applying Union-Find for cycle detection, ensuring correct upstream connections converge towards a union of sets strategy.
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#include <stdio.h>
2#include <stdlib.h>
3#include <stdbool.h>
4
5void dfs(int* parent, bool* visited, bool* cycle, int current) {
6 visited[current] = true;
7 int next = parent[current];
8 if (next != 0) {
9 if (!visited[next]) {
10 dfs(parent, visited, cycle, next);
11 } else {
12 *cycle = true;
13 }
14 }
15}
16
17int* findRedundantDirectedConnection(int** edges, int edgesSize, int* edgesColSize, int* returnSize) {
18 int n = edgesSize;
19 int* parent = (int*)calloc(n + 1, sizeof(int));
20
21 for (int i = 0; i < n; ++i) {
22 int u = edges[i][0], v = edges[i][1];
23 if (parent[v] != 0) {
24 int* can1 = (int*)malloc(sizeof(int) * 2);
25 int* can2 = (int*)malloc(sizeof(int) * 2);
26 can1[0] = parent[v];
27 can1[1] = v;
28 can2[0] = u;
29 can2[1] = v;
30 parent[v] = 0;
31 bool cycle = false;
32 for (int j = 0; j <= n; j++) {
33 if (parent[j] == 0) continue;
34 bool* visited = (bool*)calloc(n + 1, sizeof(bool));
35 dfs(parent, visited, &cycle, j);
36 free(visited);
37 if (cycle) break;
38 }
39 if (cycle) return can1;
40 else return can2;
41 }
42 parent[v] = u;
43 }
44
45 bool cycle = false;
46 for (int j = 0; j <= n; j++) {
47 if (parent[j] == 0) continue;
48 bool* visited = (bool*)calloc(n + 1, sizeof(bool));
49 dfs(parent, visited, &cycle, j);
50 free(visited);
51 if (cycle) {
52 int u = parent[j], v = j;
53 int* result = (int*)malloc(sizeof(int) * 2);
54 result[0] = u;
55 result[1] = v;
56 return result;
57 }
58 }
59
60 return NULL;
61}
62Utilizing DFS, this C code ensures settings target node connections and traces for potential overlapping cycles, using indications to determine redundancy. Understanding traversal in view of directed graph properties is fundamental to isolating missteps.