Bipartite

Determine if an undirected graph is bipartite. A bipartite graph is one in which the nodes can be divided into two groups such that no nodes have direct edges to other nodes in the same group.

Examples

1  --   2

    /   

3  --   4

is bipartite (1, 3 in group 1 and 2, 4 in group 2).

1  --   2

    /   |

3  --   4

is not bipartite.

Assumptions

• The graph is represented by a list of nodes, and the list of nodes is not null.

M1: BFS

用map记录每个节点是否visited，0和1表示两种不同颜色

time: O(n + e), space: O(n)

/**
 * public class GraphNode {
 *   public int key;
 *   public List<GraphNode> neighbors;
 *   public GraphNode(int key) {
 *     this.key = key;
 *     this.neighbors = new ArrayList<GraphNode>();
 *   }
 * }
 */
public class Solution {
  public boolean isBipartite(List<GraphNode> graph) {
    // write your solution here
    Map<GraphNode, Integer> visited = new HashMap<>();
    for(GraphNode node : graph) {
      if(!BFS(node, visited)) {
        return false;
      }
    }
    return true;
  }
  
  public boolean BFS(GraphNode node, Map<GraphNode, Integer> visited) {
    if(visited.containsKey(node)) {
      return true;
    }
    Queue<GraphNode> q = new LinkedList<>();
    q.offer(node);
    visited.put(node, 0);
    while(!q.isEmpty()) {
      GraphNode cur = q.poll();
      int curColor = visited.get(cur);
      int neiColor = curColor == 0 ? 1 : 0;
      for(GraphNode nei : cur.neighbors) {
        if(!visited.containsKey(nei)) {
          visited.put(nei, neiColor);
          q.offer(nei);
        } else if(visited.get(nei) != neiColor) {
            return false;
          }
        }
      }
    return true;
  }
}