We want to split a group of n people (labeled from 1 to n) into two groups of any size. Each person may dislike some other people, and they should not go into the same group.
Given the integer n and the array dislikes where dislikes[i] = [ai, bi] indicates that the person labeled ai does not like the person labeled bi, return true if it is possible to split everyone into two groups in this way.
Example 1:
Input: n = 4, dislikes = [[1,2],[1,3],[2,4]] Output: true Explanation: group1 [1,4] and group2 [2,3].
Example 2:
Input: n = 3, dislikes = [[1,2],[1,3],[2,3]] Output: false
Example 3:
Input: n = 5, dislikes = [[1,2],[2,3],[3,4],[4,5],[1,5]] Output: false
Constraints:
1 <= n <= 20000 <= dislikes.length <= 104dislikes[i].length == 21 <= dislikes[i][j] <= nai < bidislikes are unique.class Solution {
public:
bool possibleBipartition(int N, vector<vector<int>> &edges)
{
vector<vector<int>> adj(N + 1); // adjacency matrix
vector<int> color(N + 1, 0);
vector<bool> explored(N + 1, false);
for (auto &edge: edges) {
adj[edge[0]].push_back(edge[1]);
adj[edge[1]].push_back(edge[0]);
}
queue<int> q;
for (int i = 1; i <= N; ++i) {
if (!explored[i]) {
color[i] = 1;
q.push(i);
while (!q.empty()) {
int u = q.front();
q.pop();
if (explored[u]) continue;
explored[u] = true;
for (auto v: adj[u]) {
if (color[v] == color[u])
return false;
color[v] = -color[u];
q.push(v);
}
}
}
}
return true;
}
};