there is T a binary tree, for each z node (not a leaf) we define

NPL(z) (null path length) as the length of the shortest path from the node to the leaf.

we add npl[z] to each node.

binary tree T is called left tree if npl[left[z]]>=npl[right[z]]

the left tree H is called left heap if for every node z

key[parent[z]]<=key[z]

k- represents the priority if the heap

prove that if we build a binary heap as a binary tree (using pointers ,not arrays) then its left heap

??

so we need to show that our binary tree is left

by npl[left[z]]>=npl[right[z]]

and

key[parent[z]]<=key[z] in our tree

in my book a heap is represented by an array and we translate this array into a tree picture

i dont know how to imagine this tree they want me to show about