Distinct Colors

I`ve solved yet another very funny CSES task - it looks very similar to another task called "Reachable Nodes" (my solution for it). The only difference is that we asked to count not unique nodes but colors of nodes. What can go wrong?

And this is where funny part begins - my patched solution got crashes. gdb didn`t showed nothing interesting. However I remember scary cryptic command to show stack usage:

print (char *)_environ - (char *)$sp
$1 = 8384904

Very close to default 8Mb (check ulimit -s). Wait, WHAT? Do we really have stack exhausting? Lets check - 8 * 1024 * 1024 = 8388608 bytes. Tree can have 200000 nodes. 8388608 / 200000 = ~42 bytes for each recursive DFS call. Seems to be true - in each call we store return address + stack frame RBP + 3 registers holding args (this, indexes of node and parent) - so at least 5 * 8 = 40 bytes. It`s so happened that some tests contain tree with very long stem from root till end, so yes - recursive DFS cannot visit all nodes in such tree. Solution is simple - we can emulate recursion with std::stack. As bonus for all nodes in stack we can use single bit mask to save space

Another unpleasant observation is that trees in tests ain't BINARY trees. When one picture is worth a thousand words:

Degree of node 2 is 4. This is main reason why function dfs has separate branch for processing joint nodes with only 2 descendants - bcs initially method is_fork returned only left and right

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