#785
Medium Algorithms Is graph bipartite
Depth-First Search Breadth-First Search Union-Find Graph Theory
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Feb 21, 2026
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There is an undirected graph with n nodes, where each node is numbered between 0 and n - 1. You are given a 2D array graph, where graph[u] is an array of nodes that node u is adjacent to. More formally, for each v in graph[u], there is an undirected edge between node u and node v. The graph has the following properties:
There are no self-edges (graph[u] does not contain u).
There are no parallel edges (graph[u] does not contain duplicate values).
If v is in graph[u], then u is in graph[v] (the graph is undirected).
The graph may not be connected, meaning there may be two nodes u and v such that there is no path between them.
A graph is bipartite if the nodes can be partitioned into two independent sets A and B such that every edge in the graph connects a node in set A and a node in set B.
Return true if and only if it is bipartite.
Solution
Rust
Time O(n³)
Space O(n)
/*
* There is an undirected graph with n nodes, where each node is numbered between 0 and n - 1. You are given a 2D array graph, where graph[u] is an array of nodes that node u is adjacent to. More formally, for each v in graph[u], there is an undirected edge between node u and node v. The graph has the following properties:
* There are no self-edges (graph[u] does not contain u).
* There are no parallel edges (graph[u] does not contain duplicate values).
* If v is in graph[u], then u is in graph[v] (the graph is undirected).
* The graph may not be connected, meaning there may be two nodes u and v such that there is no path between them.
* A graph is bipartite if the nodes can be partitioned into two independent sets A and B such that every edge in the graph connects a node in set A and a node in set B.
* Return true if and only if it is bipartite.
* Example 1:
* Input: graph = [[1,2,3],[0,2],[0,1,3],[0,2]]
* Output: false
* Explanation: There is no way to partition the nodes into two independent sets such that every edge connects a node in one and a node in the other.
* Example 2:
* Input: graph = [[1,3],[0,2],[1,3],[0,2]]
* Output: true
* Explanation: We can partition the nodes into two sets: {0, 2} and {1, 3}.
* Constraints:
* graph.length == n
* 1 <= n <= 100
* 0 <= graph[u].length < n
* 0 <= graph[u][i] <= n - 1
* graph[u] does not contain u.
* All the values of graph[u] are unique.
* If graph[u] contains v, then graph[v] contains u.
*/
impl Solution {
pub fn is_bipartite(graph: Vec<Vec<i32>>) -> bool {
let n = graph.len();
let mut color = vec![-1i32; n];
for start in 0..n {
if color[start] != -1 { continue; }
let mut queue = std::collections::VecDeque::new();
queue.push_back(start);
color[start] = 0;
while let Some(u) = queue.pop_front() {
for &v in &graph[u] {
let v = v as usize;
if color[v] == -1 {
color[v] = 1 - color[u];
queue.push_back(v);
} else if color[v] == color[u] {
return false;
}
}
}
}
true
}
}