Is graph bipartite?

Time: O(|V|+|E|); Space: O(|V|); medium

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

Recall that a graph is bipartite if we can split it’s 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:

  • The graph looks like this:

    0----1
|    |
|    |
3----2

  • 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:

  • The graph looks like this:

    0----1
| \  |
|  \ |
3----2

  • We cannot find a way to divide the set of nodes into two independent subsets.

Constraints:

  • graph will have length in range [1, 100].

  • graph[i] will contain integers in range [0, graph.length - 1].

  • graph[i] will not contain i or duplicate values.

  • The graph is undirected: if any element j is in graph[i], then i will be in graph[j].

[1]:

class Solution1(object):
    """
    Time: O(|V|+|E|)
    Space: O(|V|)
    """
    def isBipartite(self, graph):
        """
        :type graph: List[List[int]]
        :rtype: bool
        """
        color = {}

        for node in range(len(graph)):
            if node in color:
                continue
            stack = [node]
            color[node] = 0

            while stack:
                curr = stack.pop()
                for neighbor in graph[curr]:
                    if neighbor not in color:
                        stack.append(neighbor)
                        color[neighbor] = color[curr] ^ 1
                    elif color[neighbor] == color[curr]:
                        return False

        return True

[2]:

s = Solution1()

graph = [[1,3], [0,2], [1,3], [0,2]]
assert s.isBipartite(graph) == True

graph = [[1,2,3], [0,2], [0,1,3], [0,2]]
assert s.isBipartite(graph) == False