In a B+ - tree where each node can hold at most four key values, a root to…

Answer: 33

Key insight: inserting 23 causes the leaf to overflow and split; the smallest key of the new right leaf is copied up, which then causes the parent to overflow and split, producing a new internal node whose smallest key is 33.

1. Locate the leaf: the leaf with entries 20, 22, 25, 26 lies under the parent with keys 7, 19, 33, 44, in the interval [19, 33).

2. Insert 23 into that leaf, producing entries 20, 22, 23, 25, 26. This exceeds the leaf capacity of 4, so the leaf splits.

3. Split result (typical split into 3 and 2): left leaf = [20, 22, 23], right leaf = [25, 26]. The smallest key of the right leaf, 25, is copied up into the parent as a separator.

4. Inserting 25 into the parent (which was 7, 19, 33, 44) creates 7, 19, 25, 33, 44, which overflows the parent (capacity 4).

5. Split the internal node of 5 keys by promoting the middle key (25) to the root. The original parent splits into two internal nodes: left = [7, 19], right = [33, 44].

6. The right internal node [33, 44] becomes the parent of the leaf [25, 26]. The smallest key value in that parent is 33.

Therefore, the smallest key value in the parent of the leaf that contains 25 is 33.