An Overview Algorithms And Data Structures Computer Science Essay

An Overview Algorithms And Data Structures Computer Science Essay Algorithms consist of a set of rules to execute calculations by hand or machine. It can also be defined as an abstraction consisting a program executed on a machine (Drozdek 2004). This program will follow operations carried out in sequence on data organized in data structures. These data structures are generally categorized into: Linear data structures examples which are arrays, matrices, hashed array trees and linked list among others. The tree data structures which include binary tree, binary search tree, B- trees, heaps e.t.c. Hashes which consist of the commonly used hash table Graph Graph: This is an abstract data structure which implements the graph oriented concepts. The graph will consist of arcs or edges as (x, y) of nodes or vertices. The edges may assume some value or numeric attribute such as cost length or capacity. Some of the operations of the graph structure G would include: Adjacent (x, y) an operation testing whether for the existence of an edge between x and y. Set_ node, value (G x, a) an operation setting the value associated with node x to a Add (G x, y) an operation that adds to the graph an arc from x and y if it is not existent. Graph algorithms are implemented within computer science to find the paths between two nodes like the depth or breadth first search or the shortest path (Sedgewick 2001 p 253). This is implemented by the Dijkstras algorithm. The Floyd Warshall algorithm is used to derive the shortest path between nodes. Linked lists These are linear data structures consisting of a data sequence linked by a reference. Linked lists provide implementation for stacks, queues, skip lists and hash tables. Linked lists are preferred over arrays because the lists may be ordered differently from how they are stored in memory. These lists will therefore allow the removal or insertion of nodes at any point. Each component or record has a node containing an address to the next node called the pointer or next link. The remainder of the fields are known as the payload, cargo, data or information. The list has first node as the head and the last node as the tail. A linked list may be circularly linked where the last node references the first node in the same list or linear where the link field is open. B -Tree This is a tree data structure that stores sorted data and allows searches, deletions, insertions and sequential access. The operations in the B- Tree are normally optimized for bulky data systems. The B -Tree has variants of design. However the B -Tree stores keys in the internal nodes. However this does not normally reflect at the leaves. The general variations are B+ Tree and B* Tree (Comer 129). The searching process is similar for the B- Tree and the binary search tree. It commences at the root and a traversal is executed from top to bottom. The search points at the child pointer with values between the search values. The insertion starts at the leaf node which if containing fewer than legally acceptable elements qualify for an addition, otherwise the node is evenly split into two nodes. A median is chosen in determining the left or right hand placements with values greater than the median going to the right node. The median here acts as the separation value. The deletion process assumes two popular strategies. Either the element located is deleted followed by a restructuring of the tree. Alternatively a scan may be performed followed by a restructuring of the tree after the candidate node to be delete has been identified. Hashes This is a data structure employing the hash function mapping to identity keys. The function transforms the key as an index of an array. The function then maps every key possibility to a unique slot index. Using well dimensioned hash tables every look up is independent of the population in the array. The hash table efficiency is utilized in database indexing, implementation of sets and cache and associative arrays. A simple array is central to the hash table algorithm. This algorithm derives an index from the elements key. This index is then used to store the elements in the array. The hash function f represents the implementation of the calculation. Hash tables implement various types of memory tables. The keys are used in this case for persistent data structures and disk based database indices. Greedy Algorithms. These algorithms work by making most promising decisions at the onset whatever the outcome would be is not taken into consideration at that moment. These algorithms are considered straight forward, simple and short sighted (Chartrand 1984). The upside or advantage to these greedy algorithms is that they are easy to invent and implement and will prove efficient. Their disadvantage is that they are not able problems optimally because of their greedy approach. Greedy algorithms are applied when we try to solve optimization problems. A typical implementation of these algorithms is the making change problem whereby we are required to give change using minimum number of notes or coins. We commence by giving the largest denomination first. Informally the greedy algorithm for this problem would follow the steps below: Begin without anything At each stage and without passing a given amount Consider the largest addition to the set. A formal algorithm of the implementation of the making change problem can be written as here below: MkChange C à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ {100, 25, 10, 5, 1} // C is a constant set of different coinage denominations Sol à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ {X} // Represents the solution set Sumà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ 0 which is the sum of items in {X} WHILE Sum. Not = n L =Largest of C such that Sum +L IF no such item THEN RETURN No item SUM à ¢Ã¢â‚¬  Ã‚  Sum+L RETURN S. An approach by the greedy algorithm to ensure optimization is the maintaining of two sets one for chosen items and the other for rejected items. Based on the two sets the algorithm will carry out four functions. Function one checks whether the chosen set of items can provide a solution. Function two checks for flexibility of the set. The selection function identifies the candidates. The objective function gives a solution. The greedy algorithm applies for the shortest path. The Dijkstras algorithm aims at determining the length of the shortest path. This path runs from S the source to other nodes. Typically Dijkstras algorithm maintains two sets of nodes S and C. S in this case consists of already selected nodes whereas C will consist of the rest of the nodes within the graph (Papadimitrious Steiglitz 1998). At the initialization of the algorithm our set X has only S. After execution {X} includes all the nodes of the graph. During every step in the algorithm a node in C that is closest to S is chosen. The remainder nodes that dont belong to S will result in a disconnected graph. The diagrams below illustrate the Dijkstra algorithm Considering the graph G = (V, E). Each node of the graph has an infinite cost apart from the source node with 0 costs (Design and Analysis of Computer Algorithms 2010) Source: Design and Analysis of Computer Algorithms 2010 Initialize d[S] to zero and choose the node closest to S. Add to S while relaxing all other nodes adjacent to S. Update every node. The diagram here below illustrates this process: Source: Design and Analysis of Computer Algorithms 2010 Choose the closest node X and relax adjacent nodes while updating u, v and y as indicated in the diagram below. Source: Next we consider y as closest and add to S and relax V as indicated in the diagram below Source: Design and Analysis of Computer Algorithms 2010 Consider u and adjust v as a neighbor as indicated in the diagram here below. Source: Design and Analysis of Computer Algorithms 2010 Finally add V and the predecessor list now defines the shortest path from S which was the source node. The diagram below illustrates the resulting shortest path Source: Design and Analysis of Computer Algorithms 2010 Spanning trees Typically graphs will have a number of paths between nodes. Spanning tree graphs consist of all the nodes with a path between any two nodes. A graph consists of different spanning trees. A disconnected graph will represent a spanning forest. A breadth first spanning tree results after a breadth first search on this graph. The depth first spanning tree results after a depth first search on the spanning tree. Spanning tree applications among others includes the travelling salesman problem here below: Problem: Considering an undirected graph G= (V, E) having a non negative integer cost associated with every edge and representing a certain distance. We can derive a tour of the graph G with the minimum cost. The salesman may start from city 1 and go on to the six cities (1 6) and return back to city 1. The first approach would run in the following manner from city: 1 to 4 to 2 to 5 to 6 to 3 to 1 resulting in a total of 62 kilometers. The diagram below shows this approach. Adding the edge weights we have 15+10+8+15+9+5 = 62 Source: Design and Analysis of Computer Algorithms 2010 The other alternative approach which is the most optimal would run in the following man from city: 1 to 2 to 5 to 4 to 6 to 3 to 1 resulting in a total of 48 kilometers. The diagram below shows this approach. Adding the edge weights we have 10+8+8+8+9+5= 48 Kilometers Source: Design and Analysis of Computer Algorithms 2010 Other applications using the panning tree approach are like the airlines route determination, designing of computer networks, the laying of oil pipelines to connect refineries and road link constructions between cities. (Goodrich Tamassia 2010; Sedgewick 2002). A typical minimum spanning tree application based on the spanning tree application MST(minimum spanning tree) cost can be used o determine the points of connection of some cable for example the fiber optic being laid along a certain path. The edges with a larger weight which corresponds to more cost would be those that require more attention and resources to lay the cable. An appropriate result would be derived from the graph with the minimum cost. Prims Algorithm. The approach for this algorithm is that it proceeds from an arbitrary root node at every stage. A new edge being added to the tree at every step. The addition process terminates when all the nodes in the graph have been achieved. This algorithm concentrates on the shortest edge. Therefore the time lapse for the algorithm will depend on how the edge is searched. The straight forward search method identifies the smallest edge by searching adjacently a list of all nodes in the graph. Every search as an iteration has a cost time O (m). Total cost time to run a complete search is O (mn). The Prim algorithm (basic) takes the following steps: Initialize the tree to consist of a start node WHILE not all nodes in the tree Loop Examine all nodes in the graph with one end point in the tree Find the shortest edge adding it to the tree End. After each step or iteration a partially completed spanning tree holding a maximum number of shortest edges is created as A and B will consist of the remaining nodes. The loop looks for the shortest edge between A and B. Kruskals Algorithm. This is an algorithm that computes the minimum spanning tree (MST). This is done by building a generic algorithm into a forest. Kruskals algorithm will consider every edge and is ordered based on the increasing weight. Consider an edge (u, v) that connecting two different trees. It follows that (u, v) will be added to the set of edges in the generic algorithm. The resultant is a single tree from two trees connected by (u, v). The algorithm can be outlined as follows: Commence with an empty set E selecting at each stage the shortest edge not yet chosen or discarded regardless of its location on the graph MST KRUSKAL (G, w) A à ¢Ã¢â‚¬  Ã‚ { } // the set containing the edges of the MST for every node n in V[G] do make_set (n) sort edge of E by decreasing weights w for each edge (u, n) in E do if FIND_SET (u) not equal FIND_SET (n) then A=A U {(U, N)} UNION (u, n) Return A The algorithm above makes use of disjoint set data structures. Kruskals algorithm can also be implemented with the priority queue data structure. The resulting algorithm is shown below: MST KRUSKAL (G) for each node n in V[G] do define S(n) à ¢Ã¢â‚¬  Ã‚ { n} initialize the queue Q consisting of all the edges of the graph G. Weights are not used as key here A à ¢Ã¢â‚¬  Ã‚ { } // This set will contain the edges of the generic algorithm(MST) WHILE A has v-1 edges do n à Ã¢â‚¬Å¾ S(n) and u à Ã¢â‚¬Å¾ S(u) IF S (n)! = S (u) Then add edge (u, n) to A S(n) U S(u) Return A The Binary Search Tree. A binary tree is one where every internal node X will store an element. Generally the elements in the left sub tree of X are less than or equal to X whereas those on the right sub tree are equal or greater than X. This represents the binary search tree property. The binary search tree height amounts to the number of links between the root and the deepest node (Skeinna 2008). The implementation of the binary search tree is such as a linked data structure where each node is an object with a total of three pointer fields namely left, right and Parent. These points to nodes corresponding to the left, right children and the parent. A NIL in any of these fields indicates no parent or child. The root node contains NIL in the Parent field. Dynamic programming algorithms These typically explores ways of optimization sequence based decisions in determining solutions. The algorithms employed avoid full enumeration of partial decisions that having a sub optimal contribution to the final solution. They instead concentrate only on optimal contributors (Aho Hopcrost 1983). The optimal solution is derived from a polynomial number of decision steps. At other times it is necessary for the algorithm to be fully implemented, however in most cases only the optimal solution is considered. Dynamic programming algorithms use of duplication and every sub solution is stored for later referencing. These solutions to the sub problems are held in a table. The total sub problems are then worked out using the bottom up technique. The steps in this bottom up technique will include the following: Begin by addressing the smallest sub problem Combine and sum up their solution increasing the scope and size UNTIL arriving at the solution of the original problem Dynamic programming relies on the principle of optimality. This principle alludes to the fact that present in an optimal decision or choice sequences are sub sequences that must be optimal as well. Warshall Algorithm. The WFI algorithm as it is also known is a graph analysis algorithm used to determine the shortest path in a weighted graph (Chartrand 1984). A comparison carried out will cover all possible paths between nodes of the graph. Consider graph G with nodes V as 1 to N. Let sPath(i, j, k) be the function that will return the shortest path between I and j while using the nodes 1 to k, demonstrates a recursive formula that results as shown here below sPath(i, j, k) = min{shortestPath(I, j, k-1),shortestPath(i, j, k -1)+shortestPath(k, j, k-1)} shortestPath(i, j, 0) = edgeCost(i, j) This forms the heart of the WFI algorithm. The shortest path is first computed as shortestPath(i, j, k) for all (i, j) pairs of k where k = 1 to n. The Floyd Warshall algorithm iteratively determine paths lengths between nodes (i, j) over i=j. The initial path is considered as zero, the algorithm provides the path lengths between the nodes. Conclusion Data structures and their associated algorithms are fundamental even today in providing the means for data storage and manipulation (Sage 2006). Core and complex computer processing involving memory management functions for operating systems, the database management systems cache implementation rely on data structures and their associated algorithms to execute efficiently and effectively. It is therefore becomes necessary that an adequate study of these data structures and algorithms is carefully studied and understood by system programmers to ensure the design of efficient and effective software.

Animation and transition Effects

According to what is mentioned in the fundamentals of the system, the user requirements, the slides must consist of some animation effects pictures and words. The system must also include transition effects where one slide changes to another. On the first slide or homepage however, there will be no animation or transition effects, because most of the information is displayed on the Main Page and if for example each contaminant of the Contents is seen appearing, disappearing, dissolving e.t.c, then the user is most likely to get confused. The other disadvantage of including animations and transition effects on the homepage is that they take some time of carry out the effect, and even though the timings can be changed, it is almost certain that it will take the reader more than 5 seconds to learn how to use the system. However, the reader may still get confused when navigating throughout the other slides seeing many different transition effects taking place. So there will only be two transition effects used which are Checker box across and Checker box down. The user will have the choice of clicking on a selected category from the Contents, if he does not do this within a generous period of 2 minutes then the transition effect will automatically take place and the slide will change to the next slide. This will be useful because people who just wish to look at the system and don't want to use it, or foreigners, they can see the cool effects and different slides which will be very eye catching and attract the users attention. Breakdown of final solution into sub-tasks Even though the final design was considered best possible from a range of people, there was still room for implementation, which additionally helped, achieves a professional looking eye catching, attractive system. What to do to implement the final design and how to do it can be put into a step-by-step list, and each can be put into sub-tasks The first task: Create the homepage slide (the first slide that the user will see when using the system) The Title the Amp Oval will be done in the specified font but the letter ‘O' in ‘Oval' in the cricket ball shape will be achieved by copying the text into Microsoft Paint, then selecting or free-form selecting the letter ‘O' and adding colour using colour applying facilities and further manipulating the ‘O' into a Cricket Ball. The second task: Obtaining the grass effect: The grass effect in the background will be obtained by saving a picture of grass from the internet. Only one square chunk of the grass will need to be copied and pasted in Microsoft Paint so that the contrast and colour can be altered to make it have the effect of a background. This will then be copied and pasted several times in the presentation to fill the appropriate areas. The third task: Creating navigation buttons: In Microsoft PowerPoint there is already a making-life easy option of inserting action buttons under the slide show menu. This also contains the facilities for decisions to be made of what slide to hyperlink to by pressing the button. If the button need be altered then by clicking the button, a menu will open up ‘Format auto shape' where the colour of the button, and various other things can be done to the action button. The fourth task: Adding maps and images: The Site map locating the Amp Oval will be scanned directly out of an A-Z on the appropriate page. It will be saved as a .jpeg file and opened up in Microsoft Paint, where the size can be changed to fit it in the available area, and an arrow and an ‘X' can be marked to show where exactly on the map it is. The stadium side view image will be imported from the internet onto the system. This will be saved as well as a larger image, which is the result of stretching the original image. The t-shirt will be opened in Paint and parts of it will be changed using the select option. The fifth task: Adding animation and transitional effects to each slide: Each slide will contain similar animation and transition effects to add more interest and get the users attention. The final task: Testing to see if the system works: Ultimately the most important task is to check if the system works, if it doesn't work as required then the errors can be corrected. If this final task is not carried out, then there is no idea if the system will meet the User requirements. Test Plan It can not be emphasized enough how important it is to carry out a test plan to confirm and re-confirm that the design contains everything mentioned in the user requirements, any additional, and implementations are to be considered after the design has been implemented. It is very important to know that no errors are to be discovered in the system. Therefore, a test plan has been assembled together and thought of with great precision to make sure that the system is to the highest of standards.

Request for funding of a community development project Essay

We at the Ottawa Foundation, Toledo Ohio would like to apply for the annual grant for financing a short term project of upgrading the community park located at the heart of the city. We are primarily a nonprofit catholic organization with strength of 50 active volunteers and we work in collaboration with local businesses and other volunteer organization such as Habitat for humanity , University of Toledo social service group etc. Our primary objective is to drive community development programs using the help of local community members and local neighborhoods. Though we are well funded by local business groups, the current economic slowdown has compelled us to search for alternative funding sources to fuel our projects. As Collins Foundation exists to improve and give greater expression to the religious, educational, cultural, and scientific endeavors in the state to assist in improving the quality of life in the state we thought that there could be no better organization that could understand and support our objectives towards the final goal of community development. So we would like to submit a detailed proposal of our plans and cost analysis to your organization for approval of a grant amount of approximately 7000 USD. We would appreciate your prompt response and would be highly obliged if we are supported in this endeavor. Thanking you, Regards, Christy Grandowics, CEO- Ottawa Foundation, Toledo, Ohio The Ottawa Foundation is a nonprofit catholic community which unites 20 civic organization, businesses and institutions to improve the areas in and around Toledo, Ohio. The major achievements accomplished in the past years include upgrade of Play pens at various local government day care centers, such as Apple tree Foundation run by University of Toledo, Sunshine at Toledo Children’s hospital. We are under the Tax Exemption Act#22 , Toledo Taxation Policy. The current project’s objective is primarily to upgrade the Wildwood metro park located at the south east part of the city. The trail starts from University of Toledo Campus and continues for about 30 miles to the crossing of Central and Reynolds. The service area includes 28 neighborhoods, with a total population of over 35,000. The neighborhoods include both multi- and single-family housing. Wild wood Park has seen extensive use by youth and adult sports leagues, trail advocates, dog trainers and general community park users. The proposed project will improve access and durability of the park, enhance patron safety, upgrade critical facilities such as children’s playground and shelter, and provide a buffer to the adjacent neighborhood. It also serves as a natural habitat for deer, rabbits and various seasonal birds and smaller animals. The park also includes different varieties of wood which are donated annually to â€Å"Small Homes & Shelter† a foundation serving the North West Ohio by providing shelters for homeless during the winter months. This project would involve the redevelopment and renovation of 5 acres of the existing 30-acre David Douglas Park in central Vancouver. Renovations will include the re-alignment of the main entry drive and expansion of parking facilities, re-alignment of trail segments, and installation of new play equipment, picnic shelter, vegetative screening, invisible dog fencing and support facilities such as night patrol for enhanced security measures. Though Ottawa Foundation is a nonprofit organization and is being supported by various flourishing local businessmen, and the state government the current economic recession has led to cost cutting of funds and so we would need some financial help urgently to fuel this project. As Wildwood Metro Park has maximum footfall during the months of April-October we would like to start the renovation during the months of October till mid December before the onset of heavy snowfall. Currently we are looking for nonprofit construction firms and student bodies like â€Å"Habitat for Humanity† to get the construction work done at a minimum cost to us. The blue print for this project is currently being looked upon by Dr Jim Weiss who serves as a faculty in the civil engineering department of University of Toledo and had served in various firms prior to his appointment as a faculty member and is experienced in transportation and construction engineering. He has his team of five graduate students who have agreed to volunteer for this current project development.

Dancing from Past to Present Nation, Culture, Identities Free Essay Example, 1250 words

According to the research findings, it can, therefore, be said that salsa is a modern Latin style of dance that emerged in mid the 1960s. It is derived from Cuban rhythms. It was discovered by the civil rights movements that were in existence in the 1960 s. The discovery explains why Latin America embraced the dance style within a period of a decade. Its international influence was a result of influence from various historical events and social conditions. The events are such as the Puerto Rican Dilemma, Cuban revolution, Black Pride Movements, urban migration, civil rights movements, and the need for the replacement of the hegemony of Anglo rock. Salsa has attracted many people from across the world because of its music and a lovely dance style. The oppression of the Latinos was one of the ideas for the invention of the dance style. It gave rise to modern movements that became accustomed to the Latinos. They practiced it on weekends, after work, in dance halls, and as the liberatio n of the mind and body. Most of the salsa s lyrics were about the struggles of the unfortunate and the problems encountered in life. We will write a custom essay sample on Dancing from Past to Present Nation, Culture, Identities or any topic specifically for you Only $17.96 $11.86/page Many people fail to comprehend what the dance means while watching it performed. Dance, as well as music, has potential symbols of identity of various ethnic groups in the world. People mistake dance as a form of entertainment whereas much can be learned concerning the cultures of the dancers.