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The principal advantage of splitting full nodes ( 4 - nodes with 3 keys ) on a way down during insertion of a new key
The principal advantage of splitting full nodes nodes with keys on a way down during insertion of a new key lies in the fact that if the appropriate leaf turns out to be full, its split will never cause a chain reaction of splits because the leafs parent will always have a room for an extra key. If the parent is full before the insertion, it is split before the leaf is reached. This is the same case for the insertion algorithm employed for trees!
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