Final answer:
The formula to find the total number of nodes at level l in the worst-case B-tree with degree m is (m / 2)^l. This assumes the minimum node occupancy, with the root as the first level. Actual B-trees may vary depending on factors such as node occupancy and tree properties.
Step-by-step explanation:
The general formula that tells us the total number of nodes at level l in the worst-case B-tree with m as the degree and n as the total number of nodes (not keys) is based on the properties of a B-tree.
B-trees are balanced data structures, commonly used in databases and file systems to maintain sorted data. In a worst-case scenario, where we consider minimal occupancy of nodes (except for the root), each node at a level l would contain the minimum number of children, which is m / 2.
To find the number of nodes at any level l, assuming the root is at level 0, we must raise the minimum number of children possible to the power of l. This gives us the formula (m / 2)^l. However, one must understand that this formula is a simplified representation, and actual B-trees may have a higher number of nodes at a given level due to variable node occupancy.
For the total number of nodes n, the relationship with the levels and degree of the tree might require more complex calculations that take into account various factors, including maximum occupancy, actual node counts in practice, and the properties of the specific B-tree in question.