"Consider a version of a binary search tree (BST) for sorted maps with integer keys that stores additional information as data members of each node w of the tree to account for the smallest and largest integer keys in the subtree rooted at w. Suppose that we can access this information using w.min, for the smallest integer key, and w.max, for the largest. Algorithm 4 provides the pseudocode for the constructor of a node in a binary tree with the additional information."

[15 pts.] Consider a version of a binary search tree (BST) for sorted maps with integer keys that stores additional information as data members of each node w of the tree to account for the smallest and largest integer keys in the subtree rooted at w. Suppose that we can access this information using w.min, for the smallest integer key, and w.mar, for the largest Algorithm 4 provides the pseudocode for the constructor of a node in a binary tree with the additional nforation Algorithm 4 Node(k,v, left, right, parent) :- new node 2: .key t.k 3: w.vulue 'U 4: 1D.left left 5: w.rightright 6w.parent parent 7: w.mink 8: ..arf.k 9: return w One can adapt the find operation to account for this information and potentially stop the search carly. Algorithm 5 provides the pseudocode for the new implementation of the find function Algorithm 5 find(T, k) l: ti, T.root 2: while wNULL and kw.key do 3: fw.min or k > w.ma.r then return NULL 4: if k w.mar then 6: if kw.key then if w.lefi-NULL then 8: 9: 10: z Node(k, t, NULL, NULL, w) return a 12: 13 else 14: if w.right = NULL then z Node (k, t, NULL, NULL, w) 16: 17: 18: 19: if u,NULL then 20: 21: return w return