Hash Tables - Sets - Tradeoffs Computers can store and process vast amounts of data. Formal data structures enable a programmer to mentally structure large amounts of data into conceptually manageable relationships. Sometimes we use data structures to allow us to do more:

We have seen how dynamic arrays enable arrays to grow while still achieving constant-time amortized performance.

This problem concerns extending dynamic arrays to let them both grow and shrink on demand. Consider an underflow strategy that cuts the array size in half whenever the array falls below half full. Give an example sequence of insertions and deletions where this strategy gives a bad amortized cost.

Then, give a better underflow strategy than that suggested above, one that achieves constant amortized cost per deletion. All nodes store data, two child pointers, and a parent pointer. The data field requires four bytes and each pointer requires four bytes.

Only leaf nodes store data; internal nodes store two child pointers. The data field requires four bytes and each pointer requires two bytes. Which operations have to be modified to support this? Design a data structure to support the following operations: Give an algorithm to concatenate two binary search trees into one binary search tree.

The best-fit heuristic for bin packing is as follows. Consider the objects in the order in which they are given.

For each object, place it into the partially filled bin with the smallest amount of extra room after the object is inserted.

If no such bin exists, start a new bin. Repeat the above using the worst-fit heuristic, where we put the next object in the partially filled bin with the largest amount of extra room after the object is inserted.

Design an algorithm to perform any sequence of the following operations: There are no insertions or deletions; the only change is to the values of the numbers. Extend the data structure of the previous problem to support insertions and deletions. Each element now has both a key and a value.

An element is accessed by its key. The addition operation is applied to the values, but the elements are accessed by its key.

The Partial-sum operation is different. This means the arrays are full of random garbage to begin with, so you must be very careful.

Implement versions of several different dictionary data structures, such as linked lists, binary trees, balanced binary search trees, and hash tables. Conduct experiments to assess the relative performance of these data structures in a simple application that reads a large text file and reports exactly one instance of each word that appears within it.

Write a brief report with your conclusions.Write an algorithm for printing a singly linked list in reverse, using only constant extra space. This instruction implies that you cannot use recursion but you may assume that your algorithm is a list member function.

A linked list is a sequential access data structure, where each element can be accesed only in particular order. A typical illustration of sequential access is a roll of paper or tape - all prior material must be unrolled in order to get to data you want.

Mar 03, · Please help me in writing the code for reversing a doubly linked list using recursion in C benjaminpohle.com: Resolved.

In its most simplest form, a singly linked list is a linked list where each node is an object that stores a reference to an element and a reference, called next, to another node. Note that a node is defined in terms of itself, which is called self-referential structure.

The linked list data structure is designed to be efficient for insertion or removal of elements from any position in the list. However other operations such as getting the last element or finding an element that stores specific data requires scanning most or all the elements in the list.

Doubly Linked List: Different from a singly linked list, a doubly linked list allows us to go in both directions -- forward and reverse. Such lists allow for a great variety of quick update operations, including insertion and removal at both ends, and in the middle.

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