<p>In the depicted 2-3-4 tree below (from Data Structures & Algorithm in Java, 2nd ed), why does inserting <code>99</code> cause the node split of <code>83/92/104</code> when it seems like <code>99</code> could've been inserted into the right child (the <code>C</code> child, into the spot immediately after <code>97</code>) without any splitting done?</p> <p><img src="https://i.stack.imgur.com/BzMzQ.png" alt="enter image description here"></p>

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?

enter image description here

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.