Homework Answers
a. When an additional record with key value = 37 is inserted into the file.
b. When an additional record with key value = 94 is inserted into the file.
c. When an additional record with key value = 26 is inserted into the file.
d. Delete the key value = 3.
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Question 4. Consider the B+ tree shown below (also shown in one of the lecture slides),...
Consider the B+ tree index shown in Figure 1. Each intermediate node can hold up to...
Consider the B+ tree index shown in Figure 1. Each intermediate node can hold up to five pointers and four key values. Each leaf can hold up to four records, and leaf nodes are doubly linked as usual, although these links are not shown in the figure. Answer the following questions. Show every step of the insertion and explain the process. 34.21-4 ostas 704 94 986 99-100-105 944954964974 LS Figure 1. (1). Insert a record with search key 109 into...
[Index structure: B+ tree and B tree] (b). B+ tree index structure is said to be...
[Index structure: B+ tree and B tree]
(b). B+ tree index structure is said to be an improvement of B
tree index structure. The most important distinction between them
is that data record pointers exist in both internal and leaf nodes
(i.e., blocks) for a B tree whereas only in the leaf nodes for a B+
tree. Explain why this distinction would make B+ tree a more
efficient structure (in terms of index search speed) overall than a
B tree...
Consider the B+ tree shown in the following as an original tree. 73 85 1 2...
Consider the B+ tree shown in the following as an original tree. 73 85 1 2 5 6 8 1 32 39 41 45 52 58 73 91 99 Answer the following questions: 1) (2 marks) There are currently 18 records in this tree. How many additional records could be added to this tree without changing its height (give the maximum possible number)? (3 marks) Show the B+ tree after inserting a data entry with key 3 into the original...
Question 4. (20 point, 10 points each) Consider the B+ tree index of order d 2...
Question 4. (20 point, 10 points each) Consider the B+ tree index of order d 2 shown below. Assume the left order is for and the right order is for If you can borrow from both siblings, choose the right sibling. Answer these question:s Root 50 73 85 8 18324o 256810*18*27 32 39 73 80* 41 45* 52 58 91 99* a) Show the B+ tree after inserting the data entry with key 7 into the original tree. b) Show...
Question 3. (25 points) Consider the B+ tree index shown below. Each intermediate node can hold up to five pointers and four key values. Each leaf can hold up to four records, and leaf nodes are doub...
Question 3. (25 points) Consider the B+ tree index shown below. Each intermediate node can hold up to five pointers and four key values. Each leaf can hold up to four records, and leaf nodes are doubly linked as usual, although these links are not shown in the figure. If you can borrow from or merge with both siblings, choose the right sibling. Answer the following questions 3080 I1 35425065 9098 12 68 69 70 79 98 99 1001105 30...
please step by step Question V (B+ Trees) (16 pts] Consider the following B+ Tree where...
please step by step
Question V (B+ Trees) (16 pts] Consider the following B+ Tree where M=4 and L=5 2000 12|17| 271D I Show the B+ Tree after each one of the following operations (note that all operations are independent, that is, in b perform the operation on the original B+ Tree, not the one obtained after performing the operation in a). a) Delete(29) b) Insert(6), Insert(7), Insert(8) (show only the B+ Tree after all 3 operations)
2. a) Consider the following AVL Tree. 50 / 25 75 10 Insert the following values...
2. a) Consider the following AVL Tree. 50 / 25 75 10 Insert the following values in the given AVL Tree, one after another, and show the resulting tree after each insertion. You must justify your answer by explaining the rotation operation you performed during insertion. 17 40 10 90 5 100 b) Delete the root of the resulting tree in Question 2.a. Show the resulting AVL Tree. Justify your answer by showing every step during deletion.
8. Given the BST below, show the BST that would result after inserting the key of value 180 if sp...
8. Given the BST below, show the BST that would result after inserting the key of value 180 if splaying is performed starting at the node that was inserted. 100 50 150 40 60 200 30 9. A nice property of splay trees is that each of Find, Insert and Delete takes O(logn) time. TrueFalse? 10. The keys of value N, N-1, N-2... 4, 3, 2, 1 are inserted in this order in a splay tree. What is the final...
Num #2 Below, you are given a correct Red-Black tree, in which red nodes are shown...
Num #2
Below, you are given a correct Red-Black tree, in which red nodes are shown as shaded diamonds, while black nodes are shown as empty circles. Give the final tree obtained from inserting the key '8 into this tree, after the insert function correctly restores the Red-Black Tree properties. It is not necessary to show intermediate steps, but if your final answer is wrong, you will get partial credit if earlier steps are correct. 4 (6 3 10
The rules are: • Leaf Split: In case a leaf node needs to be split during...
The rules are:
• Leaf Split: In case a leaf node needs to be split during
insertion and n is even, the left node should get the extra key.
E.g, if n = 2 and we insert a key 4 into a node [1,5], then the
resulting nodes should be [1,4] and [5]. For odd values of n we can
always evenly split the keys between the two nodes. In both cases
the value inserted into the parent is the...
Consider the B+ tree index shown in Figure 1. Each intermediate node can hold up to five pointers and four key values. Each leaf can hold up to four records, and leaf nodes are doubly linked as usual, although these links are not shown in the figure. Answer the following questions. Show every step of the insertion and explain the process. 34.21-4 ostas 704 94 986 99-100-105 944954964974 LS Figure 1. (1). Insert a record with search key 109 into...
[Index structure: B+ tree and B tree]
(b). B+ tree index structure is said to be an improvement of B
tree index structure. The most important distinction between them
is that data record pointers exist in both internal and leaf nodes
(i.e., blocks) for a B tree whereas only in the leaf nodes for a B+
tree. Explain why this distinction would make B+ tree a more
efficient structure (in terms of index search speed) overall than a
B tree...
Consider the B+ tree shown in the following as an original tree. 73 85 1 2 5 6 8 1 32 39 41 45 52 58 73 91 99 Answer the following questions: 1) (2 marks) There are currently 18 records in this tree. How many additional records could be added to this tree without changing its height (give the maximum possible number)? (3 marks) Show the B+ tree after inserting a data entry with key 3 into the original...
Question 4. (20 point, 10 points each) Consider the B+ tree index of order d 2 shown below. Assume the left order is for and the right order is for If you can borrow from both siblings, choose the right sibling. Answer these question:s Root 50 73 85 8 18324o 256810*18*27 32 39 73 80* 41 45* 52 58 91 99* a) Show the B+ tree after inserting the data entry with key 7 into the original tree. b) Show...
Question 3. (25 points) Consider the B+ tree index shown below. Each intermediate node can hold up to five pointers and four key values. Each leaf can hold up to four records, and leaf nodes are doubly linked as usual, although these links are not shown in the figure. If you can borrow from or merge with both siblings, choose the right sibling. Answer the following questions 3080 I1 35425065 9098 12 68 69 70 79 98 99 1001105 30...
please step by step
Question V (B+ Trees) (16 pts] Consider the following B+ Tree where M=4 and L=5 2000 12|17| 271D I Show the B+ Tree after each one of the following operations (note that all operations are independent, that is, in b perform the operation on the original B+ Tree, not the one obtained after performing the operation in a). a) Delete(29) b) Insert(6), Insert(7), Insert(8) (show only the B+ Tree after all 3 operations)
2. a) Consider the following AVL Tree. 50 / 25 75 10 Insert the following values in the given AVL Tree, one after another, and show the resulting tree after each insertion. You must justify your answer by explaining the rotation operation you performed during insertion. 17 40 10 90 5 100 b) Delete the root of the resulting tree in Question 2.a. Show the resulting AVL Tree. Justify your answer by showing every step during deletion.
8. Given the BST below, show the BST that would result after inserting the key of value 180 if splaying is performed starting at the node that was inserted. 100 50 150 40 60 200 30 9. A nice property of splay trees is that each of Find, Insert and Delete takes O(logn) time. TrueFalse? 10. The keys of value N, N-1, N-2... 4, 3, 2, 1 are inserted in this order in a splay tree. What is the final...
Num #2
Below, you are given a correct Red-Black tree, in which red nodes are shown as shaded diamonds, while black nodes are shown as empty circles. Give the final tree obtained from inserting the key '8 into this tree, after the insert function correctly restores the Red-Black Tree properties. It is not necessary to show intermediate steps, but if your final answer is wrong, you will get partial credit if earlier steps are correct. 4 (6 3 10
The rules are:
• Leaf Split: In case a leaf node needs to be split during
insertion and n is even, the left node should get the extra key.
E.g, if n = 2 and we insert a key 4 into a node [1,5], then the
resulting nodes should be [1,4] and [5]. For odd values of n we can
always evenly split the keys between the two nodes. In both cases
the value inserted into the parent is the...
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