# Exercise 6.3.2

Why do we want the loop index $i$ in line 2 of BUILD-MAX-HEAP to decrease from $\lfloor A.length / 2 \rfloor$ to $1$ rather than increase from $1$ to $\lfloor A.length/2 \rfloor$?

Otherwise we won't be allowed to call MAX-HEAPIFY, since it will fail the condition of having the subtrees be max-heaps. That is, if we start with $1$, there is no guarantee that $A[2]$ and $A[3]$ are roots of max-heaps.