Operation definition:

Rank$$ given a key k$,$ return the number of objects in the data structure with key at most k $.$

Problem $\backslash$#$1$

For a sorted array, propose an $\backslash (\backslash$mathrm$\{$O$\}(\backslash$operatorname$\{$logn$\})\backslash )-$time implementation of the Rank operation, where n is the number of objects in the array.

Problem $\backslash$#$2$

For a binary search tree augmented with subtree sizes, propose an O$($height$)-$time implementation of the Rank operation.