Question

(20 points) Calculate the minimum number of nodes (including the root node) that must be fetched to answer the following query: "Get all records with a search key greater than or equal 29 and less than 79". Show the complete steps. 1. 49 29 69 89 1929 39*49 5969 7989 Figure 1 B+ tree

Answer 1

To search keys greater than or equal to 29 and less than 79

• First, we search the root node, there is only one element 49 and the required search key can be both greater than or less than 49, so we move towards left and right subtree. (Nodes fetched=1)
• Then when we move to the left subtree of the root node, the node contains 29 and the required search key can only be greater than 29 so we move to the right subtree of it. (Nodes fetched=2)
• Then when we move to the right subtree of the root node, the node contains 69 and 89 and the required search key can be both greater than or less than 69 and only less than 89, so we move towards the first and the second child of the node. (Nodes fetched=3)
• Now when we move towards right subtree of the node containing 29, the new node is a leaf node, so our search ends there (Nodes fetched =4)
• Now when we move towards the first child of the node containing 69 and 89, it is also a leaf node, so our search ends there. (Nodes fetched=5)
• Now when we move towards the second child of the node containing 69 and 89, it is also a leaf node, so our search ends there. (Nodes fetched=6).
• Finally, our search ends and we found keys- 29, 39, 49, 59, 69 in the B+ Tree

Total nodes fetched=6