Is Graph Bipartite?.py

'''
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: [[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: [[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.

 

Note:

    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].


'''

class Solution(object):
    def isBipartite(self, graph):
        """
        :type graph: List[List[int]]
        :rtype: bool
        """
        color = {}
        
        for i in xrange(len(graph)):
            if i not in color:
                color[i] = 0
            if not self.paint(i, graph, color):
                return False
            
        return True
    
    def paint(self, pos, graph, color):
        for x in graph[pos]:
            if x in color:
                if color[pos] == color[x]:
                    return False
            else:
                color[x] = 1 - color[pos]
                if not self.paint(x, graph, color):
                    return False
        return True