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886. Possible Bipartition

Difficulty Topics

Description

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: group1 [1,4] and group2 [2,3].

Example 2:

Input: n = 3, dislikes = [[1,2],[1,3],[2,3]]
Output: false

Example 3:

Input: n = 5, dislikes = [[1,2],[2,3],[3,4],[4,5],[1,5]]
Output: false

 

Constraints:

  • 1 <= n <= 2000
  • 0 <= dislikes.length <= 104
  • dislikes[i].length == 2
  • 1 <= dislikes[i][j] <= n
  • ai < bi
  • All the pairs of dislikes are unique.

Solution

possible-bipartition.py
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