Show that the longest simple path from a node r in a red-black tree to a descendant black-height k? What is the smallest possible number? 12, 19, 8 into an initially empty red-black tree that result from the successive deletion of the keys in order 8, 12, 19, 31, 38, 41. leaf has length at most twice that of the shortest simple path from node r to a descendant leaf. What is the largest possible number of internal nodes in a red-black tree with Show the red-black trees that result after successively inserting the keys 41, 38, 31 Use the red-black tree resulting from the previous problem. Show the red-black trees