886. Possible Bipartition ¶

Problem

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:

Input: n = 4, dislikes = [[1,2],[1,3],[2,4]]
Output: true
Explanation: The first group has [1,4], and the second group has [2,3].

Example 2:

Input: n = 3, dislikes = [[1,2],[1,3],[2,3]]
Output: false
Explanation: We need at least 3 groups to divide them. We cannot put them in two groups.

Constraints:

1 <= n <= 2000
0 <= dislikes.length <= 10⁴
dislikes[i].length == 2
1 <= a_i < b_i <= n
All the pairs of dislikes are unique.