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MinimumDegreeOfAConnectedTrio.java
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MinimumDegreeOfAConnectedTrio.java
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package Leetcode;
import java.util.HashMap;
import java.util.Map;
/**
* @author kalpak
*
* You are given an undirected graph. You are given an integer n which is the number of nodes in the graph and an array edges,
* where each edges[i] = [ui, vi] indicates that there is an undirected edge between ui and vi.
*
* A connected trio is a set of three nodes where there is an edge between every pair of them.
*
* The degree of a connected trio is the number of edges where one endpoint is in the trio, and the other is not.
*
* Return the minimum degree of a connected trio in the graph, or -1 if the graph has no connected trios.
*
* Example 1:
* Input: n = 6, edges = [[1,2],[1,3],[3,2],[4,1],[5,2],[3,6]]
* Output: 3
* Explanation: There is exactly one trio, which is [1,2,3]. The edges that form its degree are bolded in the figure above.
*
*
* Example 2:
* Input: n = 7, edges = [[1,3],[4,1],[4,3],[2,5],[5,6],[6,7],[7,5],[2,6]]
* Output: 0
*
* Explanation: There are exactly three trios:
* 1) [1,4,3] with degree 0.
* 2) [2,5,6] with degree 2.
* 3) [5,6,7] with degree 2.
*
*
* Constraints:
*
* 2 <= n <= 400
* edges[i].length == 2
* 1 <= edges.length <= n * (n-1) / 2
* 1 <= ui, vi <= n
* ui != vi
* There are no repeated edges.
*
*/
public class MinimumDegreeOfAConnectedTrio {
public static int minTrioDegree(int n, int[][] edges) {
int result = Integer.MAX_VALUE;
Map<Integer, Integer> degrees = new HashMap<>(); // vertex, degree
boolean[][] isEdge = new boolean[n + 1][n + 1];
for (int[] edge : edges) {
degrees.put(edge[0], degrees.getOrDefault(edge[0], 0) + 1);
degrees.put(edge[1], degrees.getOrDefault(edge[1], 0) + 1);
isEdge[edge[0]][edge[1]] = true;
isEdge[edge[1]][edge[0]] = true;
}
for (int[] edge : edges) {
for (int i = 1; i <= n; i++) {
if (isEdge[i][edge[0]] && isEdge[i][edge[1]]) {
// we have successfully found a connected trio.
// These three vertices would each share an edge with the 2 other vertices, that's 2 * 3 = 6 edges (degrees).
// subtract 6 because we do not count inner edges of a trio.
int degree = degrees.get(i) + degrees.get(edge[0]) + degrees.get(edge[1]) - 6;
result = Math.min(result, degree);
}
}
}
return result == Integer.MAX_VALUE ? -1 : result;
}
public static void main(String[] args) {
int n = 6;
int[][] edges = new int[][]{{1,2},{1,3},{3,2},{4,1},{5,2},{3,6}};
System.out.println(minTrioDegree(n, edges));
}
}