6. [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 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 information Algorithm 4 Node(k, v, left, right, parent) 1: w new node 2: w.key 3: w.valuev 4: w.left left w.rightright 6: w.parent parent 8: w.mazk 9: return w One can adapt the find operation to account for this information and potentially stop the search early. Algorithm 5 provides the pseudocode for the new implementation of the find function. Algorithm 5 find(T,k) l: w T.root 2: while wNULL and kw.key do 3: if k w.mar then return NULL 4: if k w.mar then return NULL 4: if k