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We can use DFS for cycle detection and i don't think there is any better way to represent it apart from what we usually do for lower order trees ( using pointers ) unless you need to address certain special properties.

You can use a graph to represent it. And then run a DFS on it for cycle detection.

in c this will be your datastructure: node{int val; node* child_nodes; int child_count} and use DFS for cycle detection

imagine child_nodes as an array of node and child_counts to be the length of that array so you can refer to the ith child as child_nodes[i-1] something similar to a two dimension array which is nothing but array of arrays

You can use DFS with backedge approach. Backedge is, you have pointer from your new node to already visited node.

Please some one post the code to traverse in postorder and check for cycle