886. Possible Bipartition

Problem Link

Description

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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.

Solution

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Python3

class Solution:
    def possibleBipartition(self, n: int, dislikes: List[List[int]]) -> bool:
        graph = defaultdict(list)
 
        for a, b in dislikes:
            graph[a].append(b)
            graph[b].append(a)
        
        color = {}
 
        def go(node):
            for hate in graph[node]:
                if hate not in color:
                    color[hate] = -color[node]
                    if not go(hate):
                        return False
                else:
                    if color[hate] == color[node]:
                        return False
            
            return True
 
        for node in range(1, n + 1):
            if node not in color:
                color[node] = 1
                if not go(node):
                    return False
        
        return True