<1>depth and no. of entries

depth max no. of level

the min no. of nodes to reach depth d for a heap
= 1 + 2 + 4 +....+ 2^d-1 + 1
= 2^d

since
the total no. of nodes n
>= the min. no. of nodes to reach depth d

==> n >= 2^d

==> log₂ n >= d

<2> Worst-case Times for tree operations

The worst-case time performance for the
following operations are all O(d) . d : depth of tree

1. adding an entry in a binary search tree,
   heap or a B-tree.

2. deleting an entry in a binary search tree,
   heap or a B-tree.

3. searching for a specific entry in a binary
   search tree or a B-tree.

Note :

1. the smaller the depth is the more the
   efficiency is. That is why heap and
   B-tree are more efficient compared to other.

2. O(d) = O(log₂ n)

3. Logarithmic algorithm are algorithm with
   worse-case time O (log₂ n)

n ==> log₂ n

2n ==> log₂ n + 1