12.2-9 Let T be a binary search tree whose keys are distinct, let x be a leaf node, and let y be its parent. Show that y.key is either the smallest key in T larger than x.key or the largest key in T smaller than x.key. TREE-INSERT (T, z) 1 y = NIL 2 x = T.root 3 while x + NIL 4 y = x if z.key < x.key x = x.left else x = x.right 5 6 7 8 z.p= y 9 if y == NIL 10 T.root = z 11 elseif z.key < y.key 12 y.left = z 13 else y.right: = z // tree T was empty

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