<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>

# 785. Is Graph Bipartite?
#BFS
class Solution:
    def possibleBipartition(self, n: int, dislikes: List[List[int]]) -> bool:
        dislikeMap = defaultdict(list)
        colored = defaultdict(int)      #default as 0
        
        for x, y in dislikes:
            dislikeMap[x].append(y)  
            dislikeMap[y].append(x)  
            
        def bfs(node):
            nonlocal result
            
            queue = deque([i])
            while(queue):
                cur = queue.popleft()
                neighborColor = -colored[cur]       # map和colored配合

                for neighbor in dislikeMap[cur]:
                    if(colored[neighbor] == 0):
                        colored[neighbor] = neighborColor
                        queue.append(neighbor)

                    elif(colored[neighbor] != neighborColor):
                        result = False
                        break
        
        result = True
        for i in range(1, n + 1):  #[1, n] #每个node都看一遍
            if(result == False): break #优化用
                
            if(colored[i] == 0):
                colored[i] = 1
                bfs(i)
                

        return result
    
#DFS
class Solution:
    def possibleBipartition(self, n: int, dislikes: List[List[int]]) -> bool:
        dislikeMap = defaultdict(list)
        colored = defaultdict(int)      #default as 0
                                        #无论什么都能用defaultdict(int) 作为indegree/outdegree，下面for-loop做相对应处理就行
        for x, y in dislikes:
            dislikeMap[x].append(y)  
            dislikeMap[y].append(x)  
            
        #和785. Is Graph Bipartite 完全一样的code
        result = True 
            
        def dfs(i):
            nonlocal result
            if(not result): return
            
            neighborColor = -colored[i]
            
            for neighbor in dislikeMap[i]:
                if(colored[neighbor] == 0):
                    colored[neighbor] = neighborColor
                    dfs(neighbor)

                elif(colored[neighbor] != neighborColor):
                    result = False
                    return
        
        
        for i in range(1, n + 1):  #[1, n]
            if(colored[i] == 0):
                colored[i] = 1
                dfs(i)
        
        return result
23000