WARNING! Read the conditions for the problems in this set very carefully! The type of relation and node can change from problem to problem.
For a complete binary tree with nodes labeled as in the figure above, what is the relation[randrel] of the node labeled node? Type in the node number of the relation[randrel], or if one does not exist, then type NONE.
ANS
To find the parent of node R,
calculate \lfloor (R - 1)/2 \rfloor.
If R = 0, then it has no parent.
To find the left child of node R,
calculate 2R + 1.
If 2R + 1 \geq N, then R has no left
child.
To find the right child of node R,
calculate 2R + 2.
If 2R + 2 \geq N, then R has no
right child.
To find the left sibling of node R,
calculate R - 1 if R is even and
not 0.
If R is odd or is 0, then it has no left sibling.
To find the right sibling of node R,
calculate R + 1 if R is odd,
and R + 1 < N.
If these conditions are not met, then R has no
right sibling.