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.
Code :
int minTrioDegree(int n, vector<vector<int>>& edges) {
vector<set<int>> al(n + 1);
vector<int> cnt(n + 1);
int res = INT_MAX;
for (auto &e: edges) {
al[min(e[0], e[1])].insert(max(e[0], e[1]));
++cnt[e[0]];
++cnt[e[1]];
}
for (auto t1 = 1; t1 <= n; ++t1)
for (auto it2 = begin(al[t1]); it2 != end(al[t1]); ++it2)
for (auto it3 = next(it2); it3 != end(al[t1]); ++it3)
if (al[*it2].count(*it3))
res = min(res, cnt[t1] + cnt[*it2] + cnt[*it3] - 6);
return res == INT_MAX ? -1 : res;
}