Sorting and Searching Techniques.
INTRODUCTION
Sorting is the process of rearranging the given objects in some specific order. It is done so as to serve the purpose of searching. Objects (data) stored everywhere like in libraries, hospitals, warehouses, institutes and in different databases have to be searched and retrieved. So for the data to be retrieved easily and in more of an understandable form it is important for that data to be sorted.
There are many sorting techniques of which three are what we are going to discuss.
Shell Sort.
Bucket Sort.
Radix Sort.
WORKING
Shell Sort
This sorting algorithm essentially uses insertion sort to breakdown the problem. It breaks the problem into smaller pieces.
Table 1: Index
0 1 2 3 4 5 6 7 8 9
Table 2: Array
40 80 35 75 60 57 34 90 70 45
There is this gap value in shell sort that starts out as being:
Gap Value = (length of the array/2)
= 10/2 = 5
Now we are going to select sub arrays using the gap value. From index 0 and after the gap of 5 from this index we will be at index 5 and if we go again after the gap of 5 we will be at index 10 as there is no index no 10 we have two indexes 0 and 5 so we will have a sub array [40, 57] and similarly now we will start with index no 1 and repeat the process. In the end will have sub arrays [40, 57], [34, 80], [35, 90], [75, 70] and [60, 45].
Now we will have to use insertion sort on every sub array and if they are not sorted we will swap them in their indices.
40 34 35 70 45 57 80 90 75 60
Now we will take gap value further simplify it so we can have smaller gap values. So we will take previous gap value and divide it by 2.
Gap Value = 5/2 = 2.5 = 2
Now using this gap value we will have sub arrays [40...
... middle of paper ...
...algorithm is:
O(kn)
Where k = no. of digits in the longest in put number and n = no. of inputs.
PROS & CONS
Shell Sort
Pros:
It is efficient when the array list is medium sized.
It is better complexity than that of insertion sort.
Relatively simple to implement.
Cons:
It poses some very difficult mathematical problems many of which have not been solved yet.
It is not known that which choice of increments the best results.
It is somewhat a complex sorting algorithm.
Bucket Sort
Pros:
It is good for a rough sort.
It’s fast.
It is easy to implement.
Cons:
Does not sort in place.
Radix Sort
Pros:
It does not perform comparisons on individual items.
It’s fast.
It is easy to implement.
Cons:
Not a good choice for floating point numbers.
Not good for arbitrary strings.
Does not sort in place.
2) Analyze the graph that compares the Segment Sequence numbers of the three scenarios. Why does the Drop_NoFast scenario have the slowest growth in sequence numbers?
x 3, 4 x 4 x 4, 5 x 5 x 5, 6 x 6 x 6, 7 x 7 x 7, 8 x 8 x 8, 9 x 9 x 9)
The contemporary world is full of marvels. Technological advances have enabled mankind to fly in the heavens, instantaneously communicate with distant relatives thousands of miles away, construct buildings that are able to withstand many natural disasters, cure deadly diseases, and even travel to and study areas beyond the confines of planet Earth. While there are many factors that contributed to man’s ability to overcome what many once thought were impossible feats, it is the study of engineering that has enabled one to study the elements and leverage all that they have to offer. Mathematics lies at the heart of all science, including engineering. Without progressions in mathematical concepts, engineering principles and applications would not have advanced as quickly as they have throughout history.
Let us see now how this algorithm works. The algorithms randomly creates solutions. Each one of these solutions has a fitness value based on some criteria. Those solutions of a specific problem are also called Phenotype, while the encoding of each solution is called Genotype. We refer on Representation as the procedure of establish the mapping between genotypes and phenotypes. Representation is used as in two different ways. As mentioned before, representation establish the mapping between the genotype and the phenotype. This means that representation could encode ore decode the candidate solutions.
1. Put the two sorted subsequences to be merged, denoted by S1 and S2 on stacks of the same name. Assume that the sorting is in ascending order; hence, each stack has its minimum values at the top of the stack.
Throughout the history of chemistry, one of the most basic things used to solve problems is a formula. Formulas are so fundamental in chemistry, and in other fields, that they were used before the periodic table was arranged and well before the elements we know now were discovered. Formulas have proven to be very useful and have drastically increased the speed at which problems can be solved. For example, Lavoisier, a natural philosopher, had much difficulty in making quantitative predictions to prove that in any reaction the mass of the reactants has to equal the mass of products. He was unable to calculate the number of pounds of salt needed to make a hundred pounds of soda. For this reason, thousands of numerical relationships needed to
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...s E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Algorithms, Second Edition. MIT Press and McGraw-Hill, 2001. ISBN 0-262-03293-7. Section 7.1:Quicksort, pp.145–149.
...as if its one of the secrets to the building blocks of the universe, there may be more ideas or concepts gained through and newer, even better possibilities of philosophy and mathematics can unfold from it.
The next step is to choose the criteria that we are going to take into consideration. In my opinion, the most important criteria are the following (their order does not indicate their importance):
i.e., Height of stage i = (3/2) * Height of stage i+1. Then sequence of stage heights are 2,3,4,6,9,13...
There are a lot of searching algorithms, from which Linear Search Algorithm is one of the simple and easy algorithm, but it also have complexity, which we discuss here,
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However, between 1850 and 1900 there were great advances in mathematics and physics that began to rekindle the interest (Osborne, 45). Many of these new advances involved complex calculations and formulas that were very time consuming for human calculation.