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Suppose you have a B-tree of height h and minimum degree k. What is the largest...
Suppose you have a B-tree of height h and minimum degree k. Suppose every node is halfway to being full (for the sake of simplicity you can assume k is even). How many keys are stored in such a B-tree?
(a) Find the smallest and the largest number of keys that a heap of height h can have. (b) Prove that the height of a heap with n nodes is [log2 n]
2. (10 pts) Let T be a B-tree with a minimum degree (minimum branching factor) of t that holds n keys. Write the most efficient procedure you can to print the keys of T in sorted order. Then analyze the time complexity of your algorithm. Hint: Extend the procedure for inorder traversal of BST.
2. (10 pts) Let T be a B-tree with a minimum degree (minimum branching factor) of t that holds n keys. Write the most efficient procedure you can to print the keys of T in sorted order. Then analyze the time complexity of your algorithm. Hint: Extend the procedure for inorder traversal of BST. 2. (10 pts) Let T be a B-tree with a minimum degree (minimum branching factor) of t that holds n keys. Write the most efficient procedure...
Prove by mathematical induction that а. h log2 for any binary tree with height h and the number of leaves I b. h > log3 ] for any ternary tree with height h and the number of leaves I.
. [25 pts.] Tree node with largest value children. Consider a complete ternary tree where each node apart from the leaves has exactly 3 children and is associated with a numeric key k. a [15 pts.] Write the pseudo-code of a procedure that returns the node whose children have the largest sum of keys, i.e. the score of a node is the sum of its children key values. Note that leaves would not be considered as they do not have...
Select each statement that is true about BTrees of order m, and height h, containing k keys. In the statements below, we use the phrase "expensive data operations" to denote any kind of remote data transfer required by an algorithm, including things like disk seeks and api calls. All running times are considered to be worst case. (a) h = O(logm k) (b) Searching for a key within a node is an expensive data operation. (c) We can use a...
Suppose you have 3 N-bit unsigned integers: a, b, and c. What is the minimum number of bits required to present: (a*b)+c in order not to get an overflow? Explain how you reached your answer.
1. Suppose we start with an empty B-tree and keys arrive in the following order. – 1, 12, 8, 2, 25, 6, 14, 28, 17, 7, 52, 16, 48, 68, 3, 26, 29, 53, 55, 45 – Build a B-tree of order 5 – Hints • 17: insert/split/promote • 68: insert/split/promote • 3: insert/split/promote • 45:insert/split/promote 2. Suppose we insert the keys {1,2,3, …, n} into an empty B-tree with degree 5, how many nodes does the final B-tree have?
You have a binary search tree. Consider a leave l. B is the set of keys in the path p of l including the leave l and the root of the tree. A is the set of keys to the left of the path p. C is the set of keys to the right of the path p. Is the following statement true or false? Given any element a in A; b in B; c in C; a ≤ b...