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This homework assignment is about hash tables and optimal binary search trees (OBST's), as discussed in the lectures. You may write explanations and proofs in English, mathematics, or some mixture of the two. You may write procedures in Cormens pseudocode, or in any commonly used programming language. Page numbers refer to the usual Cormen text. 1. Suppose that the array B[O: m1] is used as a hash table. It has n key-value pairs, where n>0. It resolves collisions by chaining. Simple uniform hashing is in effect. In the chained hash tables discussed in the lectures, each bucket in the array was an association list that mapped keys to their values. However, this hash table is different. Each bucket in B is a binary search tree that maps keys to their values. Keys are totally ordered. The binary search trees might not be well-balanced. 1a. (5 points.) In the best case, how many key comparisons are needed to find a key in B? Briefly explain how the best case can occur. This homework assignment is about hash tables and optimal binary search trees (OBST's), as discussed in the lectures. You may write explanations and proofs in English, mathematics, or some mixture of the two. You may write procedures in Cormens pseudocode, or in any commonly used programming language. Page numbers refer to the usual Cormen text. 1. Suppose that the array B[O: m1] is used as a hash table. It has n key-value pairs, where n>0. It resolves collisions by chaining. Simple uniform hashing is in effect. In the chained hash tables discussed in the lectures, each bucket in the array was an association list that mapped keys to their values. However, this hash table is different. Each bucket in B is a binary search tree that maps keys to their values. Keys are totally ordered. The binary search trees might not be well-balanced. 1a. (5 points.) In the best case, how many key comparisons are needed to find a key in B? Briefly explain how the best case can occur