[LeetCode] Problem 785 - Is Graph Bipartite?

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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

No.1

Input: [[1,3], [0,2], [1,3], [0,2]]

Output: true

Explanation:
The graph looks like this:

1
2
3
4
0----1
|    |
|    |
3----2

We can divide the vertices into two groups: {0, 2} and {1, 3}.

No.2

Input: [[1,2,3], [0,2], [0,1,3], [0,2]]

Output: false

Explanation:
The graph looks like this:

1
2
3
4
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].

Code

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public boolean isBipartite(int[][] graph) {
    int[] color = new int[graph.length];

    for (int i = 0; i < color.length; i++) {
        if (color[i] == 0) {
            if (!dfs(graph, color, i, 1))
                return false;
        }
    }

    return true;
}

private boolean dfs(int[][] graph, int[] color, int s, int c) {
    if (color[s] != 0)
        return color[s] == c;

    color[s] = c;

    for (int neighbor : graph[s]) {
        if (!dfs(graph, color, neighbor, -c))
            return false;
    }

    return true;
}