T be a binary search tree whose keys are all distinct. Suppose T is created by inserting each key into the growing tree. Let x be a leaf node and y be its parent node. Show that if x is the right child of y, then y.key is the largest key in T smaller than x.key. (Hint: Show that the assumption that there is another node z whose key satisfies y.key < z.key < x.key will lead to a contradiction.)

Let T be a binary search tree whose keys are all distinct. Suppose T is created by inserting each key into the growing tree. Let x be a leaf node and y be its parent node. Show that if x is the right child of y, then y.key is the largest key in T smaller than x.key. (Hint: Show that the assumption that there is another node z whose key satisfies y.key < z.key < x.key will lead to a contradiction.)