# Question: We wish to implement a dictionary by using direct

We wish to implement a dictionary by using direct addressing on a huge array. At the start, the array entries may contain garbage, and initializing the entire array is impractical because of its size. Describe a scheme for implementing a direct-address dictionary on a huge array. Each stored object should use O(1) space; the operations SEARCH, INSERT, and DELETE should take O(1) time each; and the initialization of the data structure should take O(1) time.

## Answer to relevant Questions

Suppose we use a hash function h to hash n distinct keys into an array T of length m, assuming simple uniform hashing, what is the expected number of collisions? More precisely, what is the expected cardinality of {{k, l} : ...Show that if a node in a binary search tree has two children, then its successor has no left child and its predecessor has no right child.Suppose that the black-height of each of the sub trees α, β, γ, δ, ε in Figures 13.5 and 13.6 is k. Label each node in each figure with its black-height to verify that property 5 is preserved by the ...Can the depths of nodes in a red-black tree be efficiently maintained as fields in the nodes of the tree? Show how, or argue why not.The next two parts will prove inequality (2.3).b. State precisely a loop invariant for the for loop in lines 2-4, and prove that this loop invariant holds. Your proof should use the structure of the loop invariant proof ...Post your question