#886
Medium Algorithms Possible bipartition
Depth-First Search Breadth-First Search Union-Find Graph Theory
52.4% acceptance
Feb 22, 2026
4901
120
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.
Solution
Rust
Time O(n * m)
Space O(n * m)
/*
* 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: 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 <= ai < bi <= n
* All the pairs of dislikes are unique.
*/
use std::collections::VecDeque;
impl Solution {
pub fn possible_bipartition(n: i32, dislikes: Vec<Vec<i32>>) -> bool {
let n = n as usize;
let mut adj = vec![vec![]; n + 1];
for d in &dislikes {
adj[d[0] as usize].push(d[1] as usize);
adj[d[1] as usize].push(d[0] as usize);
}
let mut color = vec![0i32; n + 1];
for start in 1..=n {
if color[start] != 0 { continue; }
color[start] = 1;
let mut q = VecDeque::new();
q.push_back(start);
while let Some(u) = q.pop_front() {
for &v in &adj[u] {
if color[v] == 0 {
color[v] = -color[u];
q.push_back(v);
} else if color[v] == color[u] {
return false;
}
}
}
}
true
}
}