<p>We want to split a group of <code>n</code> people (labeled from <code>1</code> to <code>n</code>) into two groups of <strong>any size</strong>. Each person may dislike some other people, and they should not go into the same group.</p>

<p>Given the integer <code>n</code> and the array <code>dislikes</code> where <code>dislikes[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that the person labeled <code>a<sub>i</sub></code> does not like the person labeled <code>b<sub>i</sub></code>, return <code>true</code> <em>if it is possible to split everyone into two groups in this way</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

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

<p><strong class="example">Example 2:</strong></p>

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

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 2000</code></li>
	<li><code>0 &lt;= dislikes.length &lt;= 10<sup>4</sup></code></li>
	<li><code>dislikes[i].length == 2</code></li>
	<li><code>1 &lt;= a<sub>i</sub> &lt; b<sub>i</sub> &lt;= n</code></li>
	<li>All the pairs of <code>dislikes</code> are <strong>unique</strong>.</li>
</ul>

class Solution {//考察二分图的判定
public:
    bool ok =true;
    vector<bool> color;
    vector<bool> visited;
    //主函数
    bool possibleBipartition(int n, vector<vector<int>>& dislikes) {
        this->color=vector<bool>(n+1);
        this->visited=vector<bool>(n+1);
        vector<vector<int>> graph = buildGraph(n, dislikes);
        for(int v=1; v<=n; v++){
            if(!visited[v]){
                traverse(graph,v);
            }
        }
        return ok;
    }
    vector<vector<int>> buildGraph(int n , vector<vector<int>>& dislikes){
        vector<vector<int>> graph(n+1);
        for( int i=1; i<=n; i++){
            vector<int> tmp;
            graph[i]= tmp;
        }
        for(vector<int> edge : dislikes){
            int v= edge[1];
            int w= edge[0];
            //无向图相当于双向图
            graph[v].push_back(w);//v->w
            graph[w].push_back(v);//w->v
        }
        return graph;
    }
    void traverse(vector<vector<int>>& graph, int v){
        if(!ok){
            return;
        }
        visited[v]=true;
        for(int w : graph[v]){
            if(!visited[w]){
                color[w] =! color[v];
                traverse(graph, w);
            }
            else{
                if(color[w]== color[v]){
                    ok =false;
                }
            }
        }
    }
};
76890