(Solved): Consider a 4-ary tree - that is, a tree with branching factor \( k=4 \). The full property for a \( ...

Consider a 4-ary tree - that is, a tree with branching factor \( k=4 \). The full property for a \( k \)-ary tree is satisfied when every node in the tree has exactly 0 or \( k \) children. Answer the questions below. For the first two questions, count the minimum number of nodes, and the maximum number of nodes, that can exist in a 4 -ary tree with height \( h=8 \). For reference, an empty tree has height 0 , and a tree with a single (root) node has height 1. Based on your observations in the first two questions, for the second two questions determine closed-form expressions (in \( k \) and \( h \) ) for the minimum and maximum number of nodes in a \( k \)-ary tree of height \( h \).