At most how many keys can be inserted in the children of the leftmost node (with the separator key e) in the middle level without splitting that node?
Consider the following B+ tree:
3 keys. Let us denote the leaf nodes n1, n2, n3, n4 and the mid-level nodes m1, m2. Since we need to find the maximal number of keys that can be inserted in the children of m1 before it gets split, we should try to insert as many as possible keys without affecting any splits.
We can insert 1 key into n1. Adding 1 key to n2 splits this node into n21 and n22. A separator key moves up to m1 filling up the remaining free space there. The node n21 is going to be full, but n22 will have one free spot, which we can fill in with one additional key. After that, any addition to the leaves of m1 will necessarily generate a 4th child and thus will cause splitting of m1.
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