Use the binary search tree below and evaluate how you could remove various nodes.

For each removal, state whether it is a valid removal using one of the two algorithms from the lecture notes and videos.

A removal can either be:

valid: the removal uses one of the two algorithms and creates a binary search tree

invalid: either a$)$ the removal does not use one of the two algorithms or b$)$ the removal results in a tree that is no longer a binary search tree

Assume the tree is as shown in the picture below for each removal. $($In other words, no nodes have been removed yet.$)$

remove $55$ and replace with $57$

remove $55$ and replace with $54$

remove $55$ and replace with $46$

remove $72$ and replace with $74$

remove $70$ and replace with $65$

remove $70$ and replace with $78$

remove $70$ and replace with $71$

remove $49$ and replace with $46$

remove $49$ and replace with $54$

remove $59$ and replace with $62$