Prove or disprove: the number of internal nodes in a complete binary tree of $K$ nodes is $\lfloor K/2 \rfloor$.
I tried using induction:
Base: 1 node $\rightarrow$ $0$ internal nodes
Assumption: let the number of internal nodes in a complete binary tree of $L$ nodes is $\lfloor L/2 \rfloor$
Inductive step: for $L+2$ we have one new internal node and $\lfloor L/2 \rfloor + 1 = \lfloor (L+2)/2 \rfloor $ and we're done.
But for $L+1$ ,as a complete graph can have one leaf,I get confused.
Anyone can help me?