## 785. Is Graph Bipartite?

Given an undirected `graph`, return `true` if and only if it is bipartite.

Recall that a graph is bipartite if we can split its set of nodes into two independent subsets A and B, such that every edge in the graph has one node in A and another node in B.

The graph is given in the following form: `graph[i]` is a list of indexes `j` for which the edge between nodes `i` and `j` exists. Each node is an integer between `0` and `graph.length - 1`. There are no self edges or parallel edges: `graph[i]` does not contain `i`, and it doesn't contain any element twice.

Example 1:

```Input: graph = [[1,3],[0,2],[1,3],[0,2]]
Output: true
Explanation: We can divide the vertices into two groups: {0, 2} and {1, 3}.

```

Example 2:

```Input: graph = [[1,2,3],[0,2],[0,1,3],[0,2]]
Output: false
Explanation: We cannot find a way to divide the set of nodes into two independent subsets.
```

Constraints:

• `1 <= graph.length <= 100`
• `0 <= graph[i].length < 100`
• `0 <= graph[i][j] <= graph.length - 1`
• `graph[i][j] != i`
• All the values of `graph[i]` are unique.
• The graph is guaranteed to be undirected

## Rust Solution

``````struct Solution;
use std::collections::HashSet;

struct Graph {
edges: Vec<HashSet<usize>>,
nodes: Vec<i32>,
n: usize,
}

impl Graph {
fn new(n: usize) -> Self {
let edges: Vec<HashSet<usize>> = vec![HashSet::new(); n];
let nodes: Vec<i32> = vec![0; n];
Graph { edges, nodes, n }
}

fn insert_edge(&mut self, u: usize, v: usize) {
self.edges[u].insert(v);
}

fn dfs(&mut self, u: usize, color: i32) -> bool {
if self.nodes[u] == 0 {
self.nodes[u] = color;
for v in self.edges[u].clone() {
if !self.dfs(v, -color) {
return false;
}
}
} else {
return self.nodes[u] == color;
}
true
}
}

impl Solution {
fn is_bipartite(graph: Vec<Vec<i32>>) -> bool {
let n = graph.len();
let mut g = Graph::new(n);
for u in 0..n {
for &v in &graph[u] {
g.insert_edge(u, v as usize);
}
}
for u in 0..n {
if g.nodes[u] == 0 && !g.dfs(u, 1) {
return false;
}
}
true
}
}

#[test]
fn test() {
let graph = vec![vec![1, 3], vec![0, 2], vec![1, 3], vec![0, 2]];
let res = true;
assert_eq!(Solution::is_bipartite(graph), res);
let graph = vec![vec![1, 2, 3], vec![0, 2], vec![0, 1, 3], vec![0, 2]];
let res = false;
assert_eq!(Solution::is_bipartite(graph), res);
let graph = vec![
vec![],
vec![2, 4, 6],
vec![1, 4, 8, 9],
vec![7, 8],
vec![1, 2, 8, 9],
vec![6, 9],
vec![1, 5, 7, 8, 9],
vec![3, 6, 9],
vec![2, 3, 4, 6, 9],
vec![2, 4, 5, 6, 7, 8],
];
let res = false;
assert_eq!(Solution::is_bipartite(graph), res);
}
``````

Having problems with this solution? Click here to submit an issue on github.
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "https://rustgym.com/leetcode/785", "fetch_time": 1631965892000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2021-39/segments/1631780056392.79/warc/CC-MAIN-20210918093220-20210918123220-00367.warc.gz", "warc_record_offset": 550023818, "warc_record_length": 4295, "token_count": 906, "char_count": 2636, "score": 3.921875, "int_score": 4, "crawl": "CC-MAIN-2021-39", "snapshot_type": "longest", "language": "en", "language_score": 0.6963783502578735, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00002-of-00064.parquet"}