most, three red nodes in a row on any path from an interior node to a leaf in a red-black tree e standard red-black tree where you can have, at most, one red node in a row). Of the answers listed upper bound on the ratio of the longest path from the root to a leaf and the shortest path from the 2. Suppose you allowed, at root to a leaf as the length of the paths tend toward infnity time . Also, will searches and insertions would still take Oflog n) B) mone of the other answers are correct (C) 3, no D) 3, yes (E) 5. yes (F) 4, yes (G) infinity, no (t) 4, no 13. The namber of sode rotations that occur after an insertion into a red-black tree is (C) (n) (D) (logn) (A) (nlogn) 14. Suppose you made n insertions in a row, n >1, into an empty red-black tree. For some orderings of the n values, can an all-black tree resale? Let the red sncle be case 1, the black uncle case 2, and z be the newly inserted red node. (A) yes, because case 2 can color r black (eventually) (D) none of the other answers are correct (B) yes, becasase case 1 can color z black (eventually) (E) no, because the inserted node always remains red (C) no, because cases I and 2 leave behind a red node (F) yes, because the root is colored black at the end 1 Inserting the integers 1, 2, 3, nd 4 nto an empty red-black tree, in the order given, yields how many recolorings in total? Don't forget to color the root black, if need be. Do not count the initial coloring of the inserted node. (A) 0 (B) 5 (F) 7 (G) 2 (H) none of the other answers are correct D) 8 16. Consider inerting the numbers 1, 2, and 3 into an empty red-black tree inall possble ways (e 3, 2, 1 and 2, 1, 3) How many of these orderings cause a double rotation? (B) 6 (C) 2 (G) sone of the other answers are correct H) I 17. Consider a node z with two children a and b, in a red-black tree, Ifaisaleawhat is the most number of descendants b can have? (A) none of the otber answers are correct (B) 3 (C) 4 (D) 6 (F) 5 (G) 2 (H) 7 18. Consider an AVL tree having a root whose left side has 4 nodes. What is the most number of nodes that can appear on the right side? (A) 16 (B) 15 (E) 11 (G) 12 (H) 8 (D) none of the other answers are correct 19. T or F: Comsider a node z with a single child in an AVL troe. It is possible for z's child to be a parent as well