Why the node split when inserting into 2-3-4 tree?
In the depicted 2-3-4 tree below (from Data Structures & Algorithm in Java, 2nd ed), why does inserting 99 cause the node split of 83/92/104 when it seems like 99 could've been inserted into the right child (the C child, into the spot immediately after 97) without any splitting done?
Solution
Inserting 99 into C would be OK in that it would maintain all the invariants, but the algorithm is simpler in general if insert always expands 4-nodes on the way down. Then there will always be room for any needed lifting and rotations. It may help to compare the case where C is already a 4-node itself.
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