Given a connected graph, check if the graph is bipartite or not. A bipartite graph is possible if the graph coloring is possible using two colors such that vertices in a set are colored with the same color. Note that it is possible to color a cycle graph with even cycle using two colors. For example, see the following graph.
It is not possible to color a cycle graph with an odd cycle using two colors.
- Use a color array which stores 0 or 1 for every node which denotes opposite colors.
- Call the function DFS from any node.
- If the node u has not been visited previously, then assign !color[v] to color[u] and call DFS again to visit nodes connected to u.
- If at any point, color[u] is equal to !color[v], then the node is bipartite.
- Modify the DFS function such that it returns a boolean value at the end.
Below is the implementation of the above approach:
Graph is Bipartite
Time Complexity: O(N)
Auxiliary Space: O(N)
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- Check if a graph is strongly connected | Set 1 (Kosaraju using DFS)
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Improved By : RishiAgrawal