Assume an M entry hash table which needs to store N keys. Use the function Custom Essay

Assume an M entry hash table which needs to store N keys. Use the function Custom Essay

Assume an M entry hash table which needs to store N keys. Use the function h(i) = i mod M.
a- What is the worst-case search time?
b- Would you use this for time critical applications?

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2) Assume a 2D array A with size of n x n. This array only contains 1s and 0s. All the 1s are before all the 0s in each row. Describe an algorithm to count all the 1s in A and that runs in O(nlogn), and not O(n^2).

example A with n = 4 might look like:
1 1 1 0
0 0 0 0
1 0 0 0
1 1 1 1

3) R – 10.1: We defined a BST so that keys equal to a node’s key can be in either the left or right subtree of the node. Suppose we change the definition so that we restrict equal keys to the right subtree. What must a subtree of a binary search tree containing only equal keys look like in this case?

Solution: A subtree of equal keys must be a single chain of right children.

4) A company wants to offer a free CD to its customers. However, it wishes to offer 1 CD per household. Customers of the same household are defined as those that share the same address. Customers are kept in an unsorted linked list, where each element contains a name and an address.
Describe an efficient algorithm, in pseudocode to prune the company’s customers list. Make sure that you are doing better than the naïve, inefficient O(N^2) method that compares every possible pair of records.

5) You are given a set of n real numbers and another real number x. Describe an O(nlogn) time algorithm that determines whether or not there exists 2 elements in S whose sum is exactly x.