1. An n-‐vertex directed acyclic graph G is compact if there is some way of numbering the vertices
of G with the integers from 0 to n ‐ 1 such that G contains the edge (i ; j) if and only if i < j, for all i;
j in [0; n ‐1]. Give an O(n^2) - time algorithm for detecting if G is compact.
2. Describe a recursive method that counts the number of leaves in a given binary tree.
3. Describe a non‐recursive method that counts the number of leaves in a given binary tree.