# Possible Bipartition Problem

## Description

LeetCode Problem 886.

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] = [a_i, b_i] indicates that the person labeled a_i does not like the person labeled b_i, return true if it is possible to split everyone into two groups in this way.

Example 1:

``````1
2
3
Input: n = 4, dislikes = [[1,2],[1,3],[2,4]]
Output: true
Explanation: group1 [1,4] and group2 [2,3].
``````

Example 2:

``````1
2
Input: n = 3, dislikes = [[1,2],[1,3],[2,3]]
Output: false
``````

Example 3:

``````1
2
Input: n = 5, dislikes = [[1,2],[2,3],[3,4],[4,5],[1,5]]
Output: false
``````

Constraints:

• 1 <= n <= 2000
• 0 <= dislikes.length <= 10^4
• dislikes[i].length == 2
• 1 <= dislikes[i][j] <= n
• a_i < b_i
• All the pairs of dislikes are unique.

``````1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
class Solution {
public:
bool possibleBipartition(int N, vector<vector<int>>& dislikes) {
int m = dislikes.size();
if (m == 0)
return true;

vector<vector<int>> edges(N+1, vector<int>());

for (auto &x : dislikes) {
edges[x].push_back(x);
edges[x].push_back(x);
}

vector<int> color(N+1, -1);
queue<int> q;
int curr;
for (int i = 1; i <= N; i ++) {
if (color[i] == -1) {
q.push(i);
color[i] = 0;
while (!q.empty()) {
curr = q.front();
q.pop();
for (auto j : edges[curr]) {
if (color[curr] == color[j])
return false;
if (color[j] == -1) {
color[j] = 1 - color[curr];
q.push(j);
}
}
}
}
}
return true;
}
};
``````