Hill sorting algorithm example explanation
The following is an example of the Hill sorting algorithm: Suppose we have an array to be sorted: [49, 38, 65, 97, 76, 13, 27, 49*]. 1. First, choose an initial increment, such as d1 = 5. - According to this increment, the array was divided into several sub-sequences. - Subsequence 1:49, 04 (Assuming there is a 04 element in the original array to demonstrate the complete process). - Subsequence 2:38, 49. - Subsequence 3:65, 13. - Subsequence 4:97, 27. - Subsequence 5:76, 49* - Then, he directly inserted and sorted each subsequence. For example, in subsequence 1, 49 and 04 were compared. Since 49 > 04, their positions were swapped, resulting in 04, 49. He did the same for the other sub-sequences. After this sort, the array becomes: 13, 27, 49*, 55, 04, 49, 38, 65, 97, 76 (Here, let's assume that there are 55 elements in the original array to demonstrate the complete process). 2. Then, reduce the increment, for example, d = 3. - Regroup the sub-sequences: - Subsequence 1:13, 55, 49. - Subsequence 2:27, 04, 38. - Subsequence 3:49*, 65, 76. - Subsequence 4:55, 97. - The sequence was directly inserted into the sequence. Using subsequence 1 as an example, if 13 was compared with 55, 13<55 would not swap, and if 55 was compared with 49, 55 > 49 would swap their positions, resulting in 13, 49, and 55. After doing similar operations on the other sub-sequences, the array becomes: 13, 04, 49*, 38, 27, 49, 55, 65, 97, 76. 3. Finally, when increment d = 1. - At this moment, the entire array was a sub-sequence, and they would directly insert and sort it again. Starting from the second element, 04 was compared with 13, 04<13, and their positions were swapped. Then, they were compared and swapped in turn until the entire array was in order. Finally, they obtained: 04, 13, 27, 38, 49*, 49, 55, 65, 76, 97. The basic idea of Hill's sorting was to first cut the entire sequence of elements to be sorted into several sub-sequences and then directly insert them. Then, the increment was reduced in order before sorting. When the elements in the entire sequence were basically in order (the increment was small enough), then all the elements were directly inserted and sorted. Because the direct insert sort was very efficient when the elements were basically in order (close to the best situation), Hill's sort had a greater advantage in time efficiency.
Hill's sorting example
以下是一个希尔排序的例子： 假设有数组{8,9,1,7,2,3,5,4,6,0}。 1. 首先确定增量序列，这里采用常见的以数组长度的一半为初始增量，然后每次减半。初始增量为$10/2 = 5$。 - 第一轮排序（增量为5）： - 将数组分为5组，分别为{8,3}，{9,5}，{1,4}，{7,6}，{2,0}。 - 对每组进行直接插入排序（这里以交换法为例），例如对于{8,3}这一组，因为8 > 3，所以交换得到{3,8}。同理对其他组进行操作，第一轮排序后的数组变为{3,5,1,6,0,9,8,4,7,2}。 - 第二轮排序（增量为$5/2 = 2$）： - 将数组分为2组，分别为{3,1,0,8,7}和{5,6,9,4,2}。 - 对每组进行直接插入排序，如对于{3,1,0,8,7}这一组，先比较3和1，因为3 > 1，交换得{1,3,0,8,7}，再比较3和0，交换得{1,0,3,8,7}等操作。第二轮排序后的数组变为{1,0,3,4,2,5,8,6,7,9}。 - 第三轮排序（增量为$2/2 = 1$）： - 此时整个数组为一组，进行直接插入排序，最终得到有序数组{0,1,2,3,4,5,6,7,8,9}。
How to write the reflection summary of the big class mathematics algorithm sorting teaching
The following is an example of a reflection summary on the teaching of large classes of mathematical equations: ** I. Achievement of teaching objectives ** 1. ** Knowledge and Skills ** - In the teaching of sorting calculations, the first thing to consider was whether the children had mastered the sorting of calculations according to specific rules (such as from small to big, from big to small, or according to the order of the results of the calculations, etc.). For example, for simple addition formulas such as 1 + 1, 2+1, 3 + 1, etc., observe whether the child can understand the increasing relationship of numbers and correctly sort them. If most of the children could accurately arrange the calculations according to the requirements, it meant that this knowledge had achieved a certain effect. However, if some children had difficulties, it might be because there were problems in comparing the size of numbers or calculating the results of the formulas. They needed to strengthen the practice of basic number calculation and size comparison in the subsequent teaching. 2. ** In terms of process and method ** - In the teaching process, attention should be paid to whether the children learned to use certain methods to sort the calculations. For example, he could calculate the results of each algorithm before sorting them, or he could directly observe the rules of the numbers in the algorithm to sort them. If children relied more on the calculation results to sort, then in the teaching, children could be guided to further explore the rules of the numbers in the calculation, such as the first addend increasing by 1, the second addend changing the rules of the calculation results, etc., to cultivate children's logical thinking ability. At the same time, it was necessary to examine the child's operational ability in the sorting process, such as whether he could arrange the calculation cards correctly. This involved the child's fine hand movements and spatial perception. 3. ** Emotional attitude ** - Observe the interest and participation of the children in the calculation sequence activity. If the child showed initiative and was willing to participate in the sorting game or operation activities, it meant that the design of the teaching activities was more successful in attracting the attention of the child. For example, by setting up interesting situations (such as digital baby queuing, etc.), it could stimulate the curiosity and enthusiasm of children. However, if the child shows boredom or is not focused, the teaching method may need to be adjusted, adding more interesting elements or using different teaching aids to increase the child's enthusiasm. ** 2. Teaching content ** 1. ** Difficulty Level of the content ** - For the children in the upper class, the content of the algorithm sorting needed to be grasped well. If the calculation was too simple, such as a simple addition of numbers within 1 - 5, it might not be able to meet the learning needs of young children and effectively improve their mathematical ability. On the other hand, if the calculations were too complicated, involving large numbers or complex symbols, the child might lose interest in learning because it was difficult to understand. For example, when introducing carry addition or subtract sorting, it was necessary to gradually advance according to the child's actual ability to accept it. First, start with the simple non-carry addition sorting, let the child establish the concept and method of sorting, and then gradually increase the difficulty. 2. ** The content is systematic and coherent ** - The teaching content of the algorithm sorting should be systematic, from simple to complex, from a single rule to multiple rules. For example, they would first sort the numbers according to their size, then sort them according to the results of the calculation, and finally sort them according to some law of the numbers in the calculation (such as the law of arithmetic difference). In the teaching process, it was necessary to ensure the continuity between each link so that the child could naturally transition to the next stage of learning. If there was a lack of cohesiveness in the organization of the teaching content, the child might feel confused and unable to effectively grasp the method of sorting the equations. ** 3. Teaching Method ** 1. ** Teaching Method ** - When explaining the rules of the algorithm sequence, the teaching method was necessary. However, he had to pay attention to the way he taught and the language he used. For the older children, the language should be concise and vivid. For example, when explaining the order of the results from the smallest to the largest, one could say,"We have to line up the small results in front and the big results behind, just like how we line up small animals according to their height." If the teaching was too boring and abstract, it might be difficult for the child to understand the rules of sorting. 2. ** Effect of the Manipulation Method ** - The operation method was very important in the teaching of arithmetic sorting. By letting the children operate the calculation cards to sort, they could deepen their understanding of the concept of sorting. However, he had to pay attention to the guidance during the operation. For example, when providing calculation cards for children to sort, whether or not they were given enough hints and guidance. If the child made more mistakes during the operation, it might be because the explanation before the operation was not clear enough, or the design of the operation material (calculation card) was not reasonable enough, such as the size of the calculation was not clear, the shape of the card was not conducive to the child's operation, etc. 3. ** Integration of gaming methods ** - The game method could make teaching more interesting. For example, they could design a game called "Arithmetic Sequencing Relaying Race". The children would be divided into small groups, and the children in each group would complete the task of sorting an algorithm in turn. However, he had to pay attention to the fairness and balance of competition in the game. If the competition in the game was too intense, some children might feel pressured and affect their learning. If the game was not challenging, the children might feel bored. ** 4. Teaching Resources ** 1. ** Use of Teaching Aids ** - Arithmetic cards were commonly used in the teaching of arithmetic sorting. He had to check whether the design of the calculation card was reasonable, such as whether the font size and color of the numbers were easy for children to recognize, and whether the material of the card was durable. Other than the calculation cards, other teaching materials could also be used, such as digital blocks. Children could use the digital blocks to express the calculations and sort them. If the type of teaching aid was single, it might not be able to meet the needs of children with different learning styles. 2. ** The assistance of multi-media resources ** - In today's teaching, multi-media resources can be used as an effective auxiliary tool. For example, an animation could be made to demonstrate the process of sorting the algorithm, so that children could understand the sorting rules more intuitively. However, it was important to pay attention to whether the content of the multi-media resources was in line with the cognitive level of young children and whether the rhythm of the animation was moderate. If the animation is played too fast or the content is too complicated, the child may not be able to keep up with the rhythm and benefit from it. ** 5. Modification measures ** 1. ** Modifications for targets that have not been achieved ** - If some of the children have not mastered the knowledge and skills of the algorithm sorting, they can provide additional practice materials for these children after class, such as specially designed algorithm sorting exercise books, for individual tutoring. At the same time, in the follow-up teaching, he added some revision sessions on comparing the size of numbers and simple calculations to lay a more solid foundation for the algorithm sorting. 2. ** Upgrade teaching content ** - According to the actual learning situation of the children, adjust the difficulty of the teaching content. If the overall level of the children was high, they could add some complicated calculations or a combination of multiple rules to the content. If the children's ability to accept was weak, they could slow down the teaching progress and explain the basic content in more detail and practice more. 3. ** To improve teaching methods ** - In terms of teaching method, he further optimized the language expression and used more vivid and interesting metaphor to explain the sorting rules. In terms of operation methods, the materials were checked and optimized in advance, and the inspection and individual guidance were strengthened during the operation. As for the game method, the rules and difficulty of the game were adjusted according to the feedback of the children to make the game more attractive and educational. 4. ** Rich teaching resources ** - There were many types of teaching materials. In addition to the calculation cards and the number blocks, they could also make some self-made teaching materials. For example, they could write the calculation on a small card and then string it up so that the child could hang it on the wall in order. In terms of multi-media resources, more targeted animations or videos could be produced according to the learning situation of the children. For example, special explanation animations could be made for the types of sorting that were prone to errors. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
An example of a vernacular explanation of genes
Genes were like a small manual in the body, containing all kinds of instructions for the body's cells to work. For example, a person's appearance, height, and other external characteristics seemed to grow according to the instructions in the gene manual. For example, some people had large eyes, which might be due to the instructions in their genes to make their eyes grow bigger. For example, some diseases were also related to genes. For example, some people in Africa had sickle cell leukemia, which was caused by a certain gene. Some people's allergy and immunity were also related to genes. For example, allergic rhinoceros, asthma, and ankylosing vertebra might be inherited from their family genes. Identical twins had almost identical genes, just like two very similar things made from the same small manual. Therefore, they looked very similar. Even fingerprints were very difficult to distinguish. For example, the twins in the Malaysia case looked too similar. The police could not tell who was driving the drug. In the end, they could only be acquitted. "Life Like a White Birch" is equally exciting. Everyone is welcome to click and read it!
High school mathematics error problem book sorting example
To give an example, mathematics is an explanation, mathematics is an example of rigorous thinking. Give examples, give a brief explanation of your experience.
Mathematics was an abstract form of thinking that used symbols and formulas to describe and study concepts such as quantity, structure, change, and space. Mathematics could be regarded as a rigorous science. Its derivation and proof required rigorous logic and precise calculations. A classic mathematical example was the Eulerian formula:e^x = cosx + sin(x). This formula was widely praised in the mathematics community because it revealed the existence of the power index e of natural numbers and converted angles and radians into a simpler representation. The proof of this formula required strict logic and precise calculations, and it had to follow strict mathematical rules and axioms. The rigor and abstractness of mathematics made it a discipline widely used in science, engineering, economics, finance, and other fields. Mathematics had a wide range of applications, including physics, chemistry, biology, economics, finance, computer science, and so on. The rigorous thinking and methods of mathematics could allow people to better understand and solve various complex problems and promote the development of science and technology.
sorting
Sorting was an important step in logistics. It was the job of sorting and placing materials according to different rules. In the logistics and storage center, the sorting process usually worked like this. First, the first-level transit station at the destination needed to be unpacked, and then the items would be sent to the second-level transit station. Then, after the items arrived at the Level 2 transit station, they needed to be allocated to the station. The complement staff determined the station according to the address and filled in the corresponding code. Finally, the sorting staff would sort the items according to the code and place them on the corresponding station vehicles. The purpose of sorting was to take the goods out of the shelves or stacks according to the order requirements, and to sort them according to different customers or distribution routes for loading. Intelligent sorting was a development trend of sorting. It used automated equipment to classify and sort items, improving the efficiency and quality of sorting.
Fruit sorting
Fruit sorting was the process of sorting and grading fruits according to certain standards. At present, fruit sorting technology mainly consisted of mechanical sorting technology based on size and intelligent sorting technology based on machine vision. The sorting technology based on size was mainly mechanical sorting. It was sorted by drum sieve and roller belt sorters. It had the advantages of fast sorting speed and high work efficiency, but it was easy to destroy the external quality of the fruit, and there was a deviation in the sorting results of irregularly shaped fruits. The intelligent sorting technology based on machine vision used a binoculars camera, an infrared sensor, and an improved algorithm to achieve efficient and intelligent sorting of fruits through a combination of software and hardware. This technology could accurately detect the appearance, sugar content, moisture content, and other indicators of the fruit, and use the flexible robotic arm to accurately grab the high-quality fruit to reduce the damage to the fruit. In addition, spectrum-based technology and automatic sorting technology were also applied in the field of fruit sorting. In recent years, the emergence of AI fruit sorters has further improved the efficiency and accuracy of sorting, and can grade the quality of fruits according to multiple dimensions. In general, fruit sorting technology was developing in the direction of intelligence and efficiency.
vegetable sorting
The vegetable sorting work was the process of sorting, grading, sorting, and packaging the vegetables picked from the farmland according to certain rules. This work process included harvesting and picking, cleaning and removing impurities, sorting and sorting, inspection and quality control, weighing, packaging and tagging, product inspection and other steps. The vegetable sorter needed to divide the vegetables into different categories according to the requirements of the variety, size, appearance, quality, and maturity of the vegetables, and carry out quality testing to ensure that they met the product quality standards. They also needed to weigh, package, and label the product to ensure that the information was accurate. The job of sorting vegetables required attention to detail, quality control and sorting skills, as well as good health, teamwork, and communication skills.
vegetable recognition algorithm
Distance measurement algorithm
The following is an algorithm for measuring distance with fingers (using the thumb as an example): Raise your right arm horizontally, make a fist with your right hand, and raise your thumb. Using his right eye (left eye closed), he overlapped the left side of his thumb with the target in a straight line. If the right arm and thumb were still, he would close his right eye and observe the left side of the thumb with his left eye. He would find that the boundary was a distance away from the right side of the target. He estimated the distance and multiplied it by 10. The result was the approximate distance to the target. This method required a certain amount of experience, and there were some objective things that could provide some reference. For example, the size of the house and the distance between the houses were generally about 10 meters, or the distance between the utility poles was 50 meters, the town utility poles were 100 meters, and the high-voltage power was 200 meters. He still needed to practice more to be able to use it skillfully, and the measurement error would be smaller. The other way was to place your thumb in front of you (with your arm fully extended) and close one eye. Hover your thumb over an object of known size (such as a car). In the case of not moving the thumb, close the open eye and open the other eye to estimate the distance that the thumb has "moved" relative to the object you are looking at. For example, the length of a car is known to be about 4.5 meters. If the thumb moves half of the length of the car (about 2.25 meters), multiply the result by 10 to obtain the approximate distance between the car and you (in this case, about 22.5 meters). <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>