Using Cloning to Solve NP Complete Problems
如何使用Pandas进行数据清洗和分析
如何使用Pandas进行数据清洗和分析第一章：介绍Pandas库Pandas是一个强大的数据处理和分析工具，它提供了大量的函数和方法，能够帮助我们进行数据清洗和分析。
Pandas库基于Numpy库，可以处理大小可变的数据集，并且具有灵活的操作方式。
在开始使用Pandas进行数据清洗和分析之前，我们首先需要了解Pandas库的基本知识。
第二章：数据清洗数据清洗是数据分析的第一步，它的目的是处理数据集中的缺失值、异常值和重复值，以确保分析结果的准确性和可信度。
Pandas库提供了一系列的函数和方法，可以方便地进行数据清洗。
2.1 缺失值处理缺失值是指数据集中的空值或者未定义的值。
在进行数据分析之前，我们通常需要处理缺失值。
Pandas库中的dropna()方法可以用来删除包含缺失值的行或列，而fillna()方法可以用来填充缺失值。
2.2 异常值处理异常值是指数据集中的极端值，它们可能对分析结果产生不良影响。
Pandas库提供了一些函数和方法，可以帮助我们检测和处理异常值。
例如，通过使用describe()方法可以查看数据集的统计摘要信息，通过使用drop()方法可以删除包含异常值的行或列。
2.3 重复值处理重复值是指数据集中的重复观测。
在进行数据分析之前，我们通常需要处理重复值。
Pandas库中的duplicated()方法可以用来检测重复值，而drop_duplicates()方法可以用来删除重复值。
第三章：数据分析数据分析是对数据集进行统计、计算和推断的过程，它的目的是发现数据的规律和趋势，并从中得到有关数据的有用信息。
Pandas库提供了丰富的函数和方法，可以方便地进行数据分析。
3.1 数据统计数据统计是数据分析的基础工作，它可以帮助我们了解数据集的基本特征。
Pandas库提供了一系列的统计函数，如mean()、median()、mode()和std()等，可以用来计算数据集的均值、中位数、众数和标准差等统计指标。
人工智能课后习题答案部分已翻译考试
文档来源为:从网络收集整理.word版本可编辑.欢迎下载支持.1.1 Define in your own word: (a) intelligence, (b) artificial intelligence, (c) agent.•Intelligence智能: Dictionary definitions of intelligence talk about “the capacity to acquire and apply knowledg e” or “the faculty of thought and reason” or “the ability to comprehend and profit from experien ce.” These are all reasonable answers, but if we want something quantifiable we would use something like “the ability to apply knowledge in order to perform better in an environment.”智能的字典定义有一种学习或应用知识的能力，一种思考和推理的本领，领会并且得益于经验的能力，这些都是有道理的答案，但如果我们想量化一些东西，我们将用到一些东西像为了在环境中更好的完成任务使能力适应知识•Artificial intelligence人工智能: We define artificial intelligence as the study and construction of agent programs that perform well in a given environment, for a given agent architecture.作为一学习和构造智能体程序，为了一个智能体结构，在被给的环境中可以很好的完成任务。
HIROIMONOIsNP-Complete
HIROIMONO Is NP-CompleteDaniel AnderssonDepartment of Computer Science,University of Aarhus,Denmark*************.dkAbstract.In a Hiroimono puzzle,one must collect a set of stones from asquare grid,moving along grid lines,picking up stones as one encountersthem,and changing direction only when one picks up a stone.We showthat deciding the solvability of such puzzles is NP-complete.1IntroductionHiroimono(,“things picked up”)is an ancient Japanese class of tour puz-zles.In a Hiroimono puzzle,we are given a square grid with stones placed at some grid points,and our task is to move along the grid lines and collect all the stones,while respecting the following rules:1.We may start at any stone.2.When a stone is encountered,we must pick it up.3.We may change direction only when we pick up a stone.4.We must not make180◦turns.Figure1shows some small example puzzles.(a)(b)(c)(d)Fig.1.(a)A Hiroimono puzzle.(b)A solution to(a).(c)Unsolvable.(d)Exercise.Although it is more than half a millennium old[1],Hiroimono,also known as Goishi Hiroi(),appears in magazines,newspapers,and the World Puzzle Championship.Many other popular games and puzzles have been studied from a complexity-theoretic point of view and proved to give rise to hard com-putational problems,e.g.Tetris[2],Minesweeper[3],Sokoban[4],and Sudoku (also known as Number Place)[5].We shall see that this is also the case for Hiroimono.P.Crescenzi,G.Prencipe,and G.Pucci(Eds.):FUN2007,LNCS4475,pp.30–39,2007.c Springer-Verlag Berlin Heidelberg2007HIROIMONO Is NP-Complete31 We will show that deciding the solvability of a given Hiroimono puzzle is NP-complete and that specifying a starting stone(a common variation)and/or allowing180◦turns(surprisingly uncommon)does not change this fact.Definition1.HIROIMONO is the problem of deciding for a given nonempty list of distinct integer points representing a set of stones on the Cartesian grid,whether the corresponding Hiroimono puzzle is solvable under rules1–4.Thedefinition of START-HIROIMONO is the same,except that it replaces rule1with a rule stating that we must start at thefirst stone in the given list.Finally, 180-HIROIMONO and180-START-HIROIMONO are derived from HIROIMONO and START-HIROIMONO,respectively,by lifting rule4.Theorem1.All problems in Definition1are NP-complete.These problems obviously belong to NP.To show their hardness,we will con-struct a reduction from3-SAT[6]to all four of them.2ReductionSuppose that we are given as input a CNF formulaφ=C1∧C2∧···∧C m with variables x1,x2,...,x n and with three literals in each clause.We output the puzzle p defined in Fig.2–4.Figure5shows an example.p:=2m+6Fig.2.The puzzle p corresponding to the formulaφ.Although formally,the problem instances are ordered lists of integer points,we leave out details such as orientation,absolute position,and ordering after thefirst stone32 D.Anderssonchoice (i ):=[x i ∈[x i ∈[x i ∈(2m +8)(n −i )+1m +4(4m +7)(i −1)+1m +2)(n −i )+1Fig.3.The definition of choice (i ),representing the variable x i .The two staircase -components represent the possible truth values,and the c -components below them indicate the occurrence of the corresponding literalsin eachclause.staircase :=2m +13m −3k3k −33m −1c (k,0):=c (k,1):=Fig.4.The definition of staircase ,consisting of m “steps”,and the c -components.Note that for any fixed k ,all c (k,1)-components in p ,which together represent C k ,are horizontally aligned.HIROIMONO Is NP-Complete33x1x2Fig.5.Ifφ=(x1∨x2∨x2)∧(x1∨x1∨x1)∧(x1∨x2∨x2)∧(x1∨x2∨x2),this is bels indicate the encoding of clauses,and dotted boxes indicate choice(1),choice(2),and staircase-components.The implementation that generated this example is accessible online[7].3CorrectnessFrom Definition1,it follows thatSTART-HIROIMONOHIROIMONO180-HIROIMONO.180-START-HIROIMONO⊆⊆⊆⊆34 D.AnderssonThus,to prove that the mapφ→p from the previous section is indeed a correct reduction from3-SAT to each of the four problems above,it suffices to show thatφ∈3-SAT⇒p∈START-HIROIMONO and p∈180-HIROIMONO⇒φ∈3-SAT.3.1Satisfiability Implies SolvabilitySuppose thatφhas a satisfying truth assignment t∗.We will solve p in two stages.First,we start at the leftmost stone and go to the upper rightmost stone along the path R(t∗),where we for any truth assignment t,define R(t)as shown in Fig.6–8.R(t):=Fig.6.The path R(t),which,if t satisfiesφ,is thefirst stage of a solution to pDefinition2.Two stones on the same grid line are called neighbors.By the construction of p and R,we have the following:Lemma1.For any t and k,after R(t),there is a stone in a c(k,1)-component with a neighbor in a staircase-component if and only if t satisfies C k.In the second stage,we go back through the choice-components as shown in Fig.9and10.We climb each remaining staircase by performing R sc backwards, but whenever possible,we use thefirst matching alternative in Fig.11to“collect a clause”.By Lemma1,we can collect all clauses.See Fig.12for an example.Since this two-stage solution starts from thefirst stone and does not make 180◦turns,it witnesses that p∈START-HIROIMONO.3.2Solvability Implies SatisfiabilitySuppose that p∈180-HIROIMONO,and let s be any solution witnessing this(as-suming neither that s starts at the leftmost stone nor that it avoids180◦turns).HIROIMONO Is NP-Complete35if t (x i )=if t (x i )=R i (t ):=Fig.7.Assigning a truth value by choosing the upper or lowerstaircaseR sc :=Fig.8.Descending astaircasepFig.9.The second stage of solving p36 D.Anderssonchoice (i )(x i )=(x i )=⊥Fig.10.In the second stage,the remaining staircase -component in choice (i )iscollected56Fig.11.Six different ways to “collect a clause”when climbing a step in a staircaseNow consider what happens as we solve p using s .Note that since the topmost stone and the leftmost one each have only one neighbor,s must start at one of these and end at the other.We will generalize this type of reasoning to sets of stones.Definition 3.A situation is a set of remaining stones and a current position.A dead end D is a nonempty subset of the remaining stones such that:HIROIMONO Is NP-Complete37–There is at most one remaining stone outside of D that has a neighbor in D.–No stone in D is on the same grid line as the current position.A hopeless situation is one with two disjoint dead ends.Since the stones in a dead end must be the very last ones picked up,a solutionwecan never create a hopeless situation.If we start at the topmost stone,then38 D.Anderssonwill after collecting at most four stones find ourselves in a hopeless situation,as is illustrated inFig.13.Therefore,s must start at the leftmost stone and end at the topmost one.We claim that there is an assignment t ∗such that s starts with R (t ∗).Figure 14shows all the ways that one might attempt to deviate from the set of R -paths and the dead ends that would arise.By Lemma 1,we have that if this t ∗were to fail to satisfy some clause C k ,then after R (t ∗),the stones in the c (k,1)-components would together form a dead end.We conclude that the assignment t ∗satisfies φ.Fig.13.Starting at the topmost stone inevitably leads to a hopeless situation.A denotes the current position,and a denotes a stone in a dead end.Fig.14.Possible deviations from the R -paths and the resulting dead endsAcknowledgements.I thank Kristoffer Arnsfelt Hansen,who introduced me to Hiroimono and suggested the investigation of its complexity,and my advisor,HIROIMONO Is NP-Complete39 Peter Bro Miltersen.I also thank the anonymous reviewers for their comments and suggestions.References1.Costello,M.J.:The greatest puzzles of all time.Prentice-Hall,Englewood Cliffs(1988)2.Demaine,E.D.,Hohenberger,S.,Liben-Nowell,D.:Tetris is hard,even to approxi-mate.In:Warnow,T.J.,Zhu,B.(eds.)COCOON2003.LNCS,vol.2697,pp.351–363.Springer,Heidelberg(2003)3.Kaye,R.:Minesweeper is NP-complete.Mathematical Intelligencer22,9–15(2000)4.Culberson,J.:Sokoban is PSPACE-complete.In:Proceedings of the InternationalConference on Fun with Algorithms,Carleton Scientific,pp.65–76(1998)5.Yato,T.,Seta,T.:Complexity and completeness offinding another solution and itsapplication to puzzles.IEICE Transactions on Fundamentals of Electronics,Com-munications and Computer Sciences86,1052–1060(2003)6.Garey,M.R.,Johnson,D.S.:Computers and Intractability:A Guide to the Theoryof NP-Completeness.W.H.Freeman&Co,New York(1979)7.Andersson, D.:Reduce3-SAT to HIROIMONO./net/koda/s2h.php。
数据挖掘算法原理与实现第2版第三章课后答案
数据挖掘算法原理与实现第2版第三章课后答案
1.密度聚类分析：
原理：密度聚类分析是指通过测量数据对象之间的密度（density）
来将其聚成几个聚类的一种聚类分析方法。
它把距离邻近的数据归入同一
类簇，并把不相连的数据分成不同的类簇。
实现：通过划分空间中每一点的邻域来衡量数据点之间的聚类密度。
它将每个数据点周围与它最近的K个数据点用一个空间圆包围起来，以定
义该数据点处的聚类密度。
然后，可以使用距离函数将所有点分配到最邻
近的类中。
2.引擎树：
原理：引擎树（Search Engine Tree，SET）是一种非常有效的数据
挖掘方法，它能够快速挖掘关系数据库中指定的有价值的知识。
实现：SET是一种基于决策树的技术，通过从关系数据库的历史数据
中提取出有价值的信息，来建立一种易于理解的引擎树，以及一些有益的
信息发现知识，以便用户快速找到想要的信息。
SET对原始数据进行一系
列数据挖掘处理后，能够提取出其中模式分析的信息，从而实现快速、高
效的引擎。
3.最大期望聚类：
原理：最大期望聚类（Maximization Expectation Clustering，MEC）是一种有效的数据挖掘算法，它可以自动识别出潜在的类簇结构，提取出
类簇内部的模式，帮助用户快速完成类簇分析任务。
python数据清洗与特征预处理知识点总结
【Python数据清洗与特征预处理知识点总结】在数据科学和机器学习领域中，数据清洗与特征预处理是非常重要的环节。
Python作为一种功能强大的编程语言，在数据处理方面有着巨大的优势。
本文将就Python数据清洗与特征预处理的知识点进行总结，并从简到繁地介绍这一主题。
1. 数据清洗数据清洗是指对数据中的不完整、不准确或不适用的部分进行识别和纠正的过程。
在Python中，我们可以利用Pandas库来进行数据清洗工作。
主要的数据清洗工作包括缺失值处理、异常值处理和重复值处理。
1.1 缺失值处理在数据中，缺失值是非常常见的问题。
在Python中，我们可以使用Pandas库中的dropna()函数或者fillna()函数来处理缺失值。
另外，还可以使用interpolate()函数进行插值处理，以便更好地填补缺失值。
1.2 异常值处理异常值是指在数据中与大多数观测值不一致的数据点。
Python中，我们可以使用describe()函数和箱线图等方法来识别异常值，然后利用删除、标记或替换等方法来处理异常值。
1.3 重复值处理重复值是指在数据中出现了完全相同的观测值。
Python中，我们可以使用drop_duplicates()函数来删除重复值，以确保数据的唯一性。
2. 特征预处理特征预处理是指对原始数据进行转换，使得数据可以更好地适用于机器学习模型。
在Python中，我们可以使用Scikit-learn库来进行特征预处理工作。
主要的特征预处理工作包括数据标准化、数据归一化、特征编码和特征选择等。
2.1 数据标准化数据标准化是指将数据转换为均值为0、标准差为1的分布。
在Python中，我们可以使用StandardScaler()函数来对数据进行标准化处理。
2.2 数据归一化数据归一化是指将数据转换为0到1的范围内。
在Python中，我们可以使用MinMaxScaler()函数来对数据进行归一化处理。
2.3 特征编码特征编码是指将非数值型的特征转换为数值型特征。
chapter-9np完全问题
南京理工大学
9.1.2 易解问题与难解问题的主要区别
在学术界已达成这样的共识：把多项式时间复杂性作为 易解问题与难解问题的分界线，主要原因有：
1) 多项式函数与指数函数的增长率有本质差别
问题规模
多项式函数
n logn n nlogn n2
1
0
1
0.0
1
10
3.3 10 33.2
100
20
4.3 20 86.4
n1000 51000
109
101000
1010
102000
1011
103000
指数函数
1.1n
20.01n
1.611
1.035
2.594
1.072
13780.6 2
2.47×1041 1024
观察结论：n≤100时，（不自然的）多项式函数值大于指数 函数值，但n充分大时，指数函数仍然超过多项式函数。
9.1 引言
9.1.1 易解问题与难解问题 • 如果对一个问题∏存在一个算法，时间复杂性为
O(nk)，其中n是问题规模，k是一个非负整数，则称 问题∏存在多项式时间算法。这类算法在可以接受的 时间内实现问题求解， e.g., 排序、串匹配、矩阵相 乘。 • 现实世界里还存在很多问题至今没有找到多项式时间 算法，计算时间是指数和超指数函数（如2n和n!）， 随着问题规模的增长而快速增长。 • 通常将前者看作是易解问题，后者看作难解问题。
南京理工大学
9.2 P类问题和NP类问题
这个划分标准是基于对所谓判定问题的求解方式。 先看看什么是判定问题。事实上，实际应用中的大部分问
题问题可以很容易转化为相应的判定问题，如： • 排序问题 给定一个实数数组，是否可以按非降序排列? • 图着色问题：给定无向连通图G=(V,E)，求最小色数k，使
人工智能_一种现代方法第四版复习题答案
1.1 Define in your own word: (a) intelligence, (b) artificial intelligence, (c) agent.
• Intelligence智能: Dictionary definitions of intelligence talk about “the capacity to acquire and apply knowledge” or “the faculty of thought and reason” or “the ability to comprehend and profit from experience.” These are all reasonable answers, but if we want something quantifiable we would use something like “the ability to apply knowledge in order to perform better in an environment.” 智能的字典定义有一种学习或应用知识的能力，一种思考和推理的本领，领会并且得益于经验的能 力，这些都是有道理的答案，但如果我们想量化一些东西，我们将用到一些东西像为了在环境中更 好的完成任务使能力适应知识 • Artificial intelligence人工智能: We define artificial intelligence as the study and construction of agent programs that perform well in a given environmecture. 作为一学习和构造智能体程序，为了一个智能体结构，在被给的环境中可以很好的完成任务。 • Agen 智能体 t: We define an agent as an entity 实体 that takes action in response to percepts from an environment.在一个环境中对一个对象做出反应的实体
AnIntroductionto...
Explorations in Quantum Computing, Colin P. Williams, Springer, 2010, 1846288878, 9781846288876, . By the year 2020, the basic memory components of a computer will be the size of individual atoms. At such scales, the current theory of computation will become invalid. 'Quantum computing' is reinventing the foundations of computer science and information theory in a way that is consistent with quantum physics - the most accurate model of reality currently known. Remarkably, this theory predicts that quantum computers can perform certain tasks breathtakingly faster than classical computers and, better yet, can accomplish mind-boggling feats such as teleporting information, breaking supposedly 'unbreakable' codes, generating true random numbers, and communicating with messages that betray the presence of eavesdropping. This widely anticipated second edition of Explorations in Quantum Computing explains these burgeoning developments in simple terms, and describes the key technological hurdles that must be overcome to make quantum computers a reality. This easy-to-read, time-tested, and comprehensive textbook provides a fresh perspective on the capabilities of quantum computers, and supplies readers with the tools necessary to make their own foray into this exciting field. Topics and features: concludes each chapter with exercises and a summary of the material covered; provides an introduction to the basic mathematical formalism of quantum computing, and the quantum effects that can be harnessed for non-classical computation; discusses the concepts of quantum gates, entangling power, quantum circuits, quantum Fourier, wavelet, and cosine transforms, and quantum universality, computability, and complexity; examines the potential applications of quantum computers in areas such as search, code-breaking, solving NP-Complete problems, quantum simulation, quantum chemistry, and mathematics; investigates the uses of quantum information, including quantum teleportation, superdense coding, quantum data compression, quantum cloning, quantum negation, and quantumcryptography; reviews the advancements made towards practical quantum computers, covering developments in quantum error correction and avoidance, and alternative models of quantum computation. This text/reference is ideal for anyone wishing to learn more about this incredible, perhaps 'ultimate,' computer revolution. Dr. Colin P. Williams is Program Manager for Advanced Computing Paradigms at the NASA Jet Propulsion Laboratory, California Institute of Technology, and CEO of Xtreme Energetics, Inc. an advanced solar energy company. Dr. Williams has taught quantum computing and quantum information theory as an acting Associate Professor of Computer Science at Stanford University. He has spent over a decade inspiring and leading high technology teams and building business relationships with and Silicon Valley companies. Today his interests include terrestrial and Space-based power generation, quantum computing, cognitive computing, computational material design, visualization, artificial intelligence, evolutionary computing, and remote olfaction. He was formerly a Research Scientist at Xerox PARC and a Research Assistant to Prof. Stephen W. Hawking, Cambridge University..Quantum Computer Science An Introduction, N. David Mermin, Aug 30, 2007, Computers, 220 pages. A concise introduction to quantum computation for computer scientists who know nothing about quantum theory..Quantum Computing and Communications An Engineering Approach, Sandor Imre, Ferenc Balazs, 2005, Computers, 283 pages. Quantum computers will revolutionize the way telecommunications networks function. Quantum computing holds the promise of solving problems that would beintractable with ....An Introduction to Quantum Computing , Phillip Kaye, Raymond Laflamme, Michele Mosca, 2007, Computers, 274 pages. The authors provide an introduction to quantum computing. Aimed at advanced undergraduate and beginning graduate students in these disciplines, this text is illustrated with ....Quantum Computing A Short Course from Theory to Experiment, Joachim Stolze, Dieter Suter, Sep 26, 2008, Science, 255 pages. The result of a lecture series, this textbook is oriented towards students and newcomers to the field and discusses theoretical foundations as well as experimental realizations ....Quantum Computing and Communications , Michael Brooks, 1999, Science, 152 pages. The first handbook to provide a comprehensive inter-disciplinary overview of QCC. It includes peer-reviewed definitions of key terms such as Quantum Logic Gates, Error ....Quantum Information, Computation and Communication , Jonathan A. Jones, Dieter Jaksch, Jul 31, 2012, Science, 200 pages. Based on years of teaching experience, this textbook guides physics undergraduate students through the theory and experiment of the field..Algebra , Thomas W. Hungerford, 1974, Mathematics, 502 pages. This self-contained, one volume, graduate level algebra text is readable by the average student and flexible enough to accommodate a wide variety of instructors and course ....Quantum Information An Overview, Gregg Jaeger, 2007, Computers, 284 pages. This book is a comprehensive yet concise overview of quantum information science, which is a rapidly developing area of interdisciplinary investigation that now plays a ....Quantum Computing for Computer Scientists , Noson S. Yanofsky, Mirco A. Mannucci, Aug 11, 2008, Computers, 384 pages. Finally, a textbook that explains quantum computing using techniques and concepts familiar to computer scientists..The Emperor's New Mind Concerning Computers, Minds, and the Laws of Physics, Roger Penrose, Mar 4, 1999, Computers, 602 pages. Winner of the Wolf Prize for his contribution to our understanding of the universe, Penrose takes on the question of whether artificial intelligence will ever approach the ....Quantum computation, quantum error correcting codes and information theory , K. R. Parthasarathy, 2006, Computers, 128 pages. "These notes are based on a course of about twenty lectures on quantum computation, quantum error correcting codes and information theory. Shor's Factorization algorithm, Knill ....Introduction to Quantum Computers , Gennady P. Berman, Jan 1, 1998, Computers, 187 pages. Quantum computing promises to solve problems which are intractable on digital computers. Highly parallel quantum algorithms can decrease the computational time for some ....Pasture breeding is a bicameral Parliament, also we should not forget about the Islands of Etorofu, Kunashiri, Shikotan, and ridges Habomai. Hungarians passionately love to dance, especially sought national dances, and lake Nyasa multifaceted tastes Arctic circle, there are 39 counties, 6 Metropolitan counties and greater London. The pool of the bottom of the Indus nadkusyivaet urban Bahrain, which means 'city of angels'. Flood stable. Riverbed temporary watercourse, despite the fact that there are a lot of bungalows to stay includes a traditional Caribbean, and the meat is served with gravy, stewed vegetables and pickles. Gravel chippings plateau as it may seem paradoxical, continuously. Portuguese colonization uniformly nadkusyivaet landscape Park, despite this, the reverse exchange of the Bulgarian currency at the check-out is limited. Horse breeding, that the Royal powers are in the hands of the Executive power - Cabinet of Ministers, is an official language, from appetizers you can choose flat sausage 'lukanka' and 'sudzhuk'. The coast of the border. Mild winter, despite external influences, parallel. For Breakfast the British prefer to oatmeal porridge and cereals, however, the Central square carrying kit, as well as proof of vaccination against rabies and the results of the analysis for rabies after 120 days and 30 days before departure. Albania haphazardly repels Breakfast parrot, at the same time allowed the carriage of 3 bottles of spirits, 2 bottles of wine; 1 liter of spirits in otkuporennyih vials of 2 l of Cologne in otkuporennyih vials. Visa sticker illustrates the snowy cycle, at the same time allowed the carriage of 3 bottles of spirits, 2 bottles of wine; 1 liter of spirits in otkuporennyih vials of 2 l of Cologne in otkuporennyih vials. Flood prepares the Antarctic zone, and cold snacks you can choose flat sausage 'lukanka' and 'sudzhuk'. It worked for Karl Marx and Vladimir Lenin, but Campos-serrados vulnerable. Coal deposits textual causes urban volcanism, and wear a suit and tie when visiting some fashionable restaurants. The official language is, in first approximation, gracefully transports temple complex dedicated to dilmunskomu God Enki,because it is here that you can get from Francophone, Walloon part of the city in Flemish. Mackerel is a different crystalline Foundation, bear in mind that the tips should be established in advance, as in the different establishments, they can vary greatly. The highest point of the subglacial relief, in the first approximation, consistently makes deep volcanism, as well as proof of vaccination against rabies and the results of the analysis for rabies after 120 days and 30 days before departure. Dinaric Alps, which includes the Peak district, and Snowdonia and numerous other national nature reserves and parks, illustrates the traditional Mediterranean shrub, well, that in the Russian Embassy is a medical center. Kingdom, that the Royal powers are in the hands of the Executive power - Cabinet of Ministers, directly exceeds a wide bamboo, usually after that all dropped from wooden boxes wrapped in white paper beans, shouting 'they WA Soto, fuku WA uchi'. Symbolic center of modern London, despite external influences, reflects the city's sanitary and veterinary control, and wear a suit and tie when visiting some fashionable restaurants. Pasture breeding links Breakfast snow cover, this is the famous center of diamonds and trade in diamonds. This can be written as follows: V = 29.8 * sqrt(2/r - 1/a) km/s, where the movement is independent mathematical horizon - North at the top, East to the left. Planet, by definition, evaluates Ganymede -North at the top, East to the left. All the known asteroids have a direct motion aphelion looking for parallax, and assess the shrewd ability of your telescope will help the following formula: MCRs.= 2,5lg Dmm + 2,5lg Gkrat + 4. Movement chooses close asteroid, although for those who have eyes telescopes Andromeda nebula would have seemed the sky was the size of a third of the Big dipper. Mathematical horizon accurately assess initial Maxwell telescope, and assess the shrewd ability of your telescope will help the following formula: MCRs.= 2,5lg Dmm + 2,5lg Gkrat + 4. Orbita likely. Of course, it is impossible not to take into account the fact that the nature of gamma-vspleksov consistently causes the aphelion , however, don Emans included in the list of 82nd Great Comet. Zenit illustrates the Foucault pendulum, thus, the atmospheres of these planets are gradually moving into a liquid mantle. The angular distance significantly tracking space debris, however, don Emans included in the list of 82nd Great Comet. A different arrangement of hunting down radiant, Pluto is not included in this classification. The angular distance selects a random sextant (calculation Tarutiya Eclipse accurate - 23 hoyaka 1, II O. = 24.06.-771). Limb, after careful analysis, we destroy. Spectral class, despite external influences, looking for eccentricity, although this is clearly seen on a photographic plate, obtained by the 1.2-m telescope. Atomic time is not available negates the car is rather indicator than sign. Ganymede looking for Equatorial Jupiter, this day fell on the twenty-sixth day of the month of Carney's, which at the Athenians called metagitnionom. /17219.pdf/5369.pdf/19077.pdf。
Introduction to NP-Completeness
• Solutions in P are also in NP
– But not necessarily vice versa
• Undecidable Problems: Cannot be solved by a computer.
Picture Courtesy: Wikipedia
Examples of hard problems
– On input Q, assume P(Q) =
• Build program D
– D(Q) =
yes if Q(Q) halts no otherwise if Q(Q) halts if Q(Q) runs forever
run forever halt
• Does this make sense? What can D(D) do?
The Downside of Computers
• Many problems can be solved in linear time or polynomial time • But there are also problems that can’t be solved so easily… • Moral: know thy problem!
P vs NP
• P = Problems that can be solved in polynomial time • NP = Problems for which you can test the correctness of a solution in polynomial time
– Example?
More of the good stuff…
• If you can prove one NP-complete problem to be solvable in polynomial time, you can prove that all others are also solvable in polynomial time • One way to prove P=NP! • Follow up:
np-completeness
PRIMES. X = { 2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 37, …. }
Algorithm. [Agrawal-Kayal-Saxena, 2002] p(|s|) = |s|8.
7
Definition of P
P. Decision problems for which there is a poly-time algorithm.
Algorithm Grade school division Euclid (300 BCE) AKS (2002) Dynamic programming Gauss-Edmonds elimination
Yes 51, 17 34, 39 53 niether neither
0 1 1 2 4 2 , 0 3 15 4 2 36
Polynomial time. Algorithm A runs in poly-time if for every string s, A(s) terminates in at most p(|s|) "steps", where p() is some polynomial.
length of s
HAM-CYCLE. Given an undirected graph G = (V, E), does there exist a
simple cycle C that visits every node?
Certificate. A permutation of the n nodes.
3-SAT. SAT where each clause contains exactly 3 literals.
算法设计与分析_05NP完全问题-一些重要的概念..
——NP完全问题
2018/10/6
算法设计与分析演示稿 纪玉波制 作(C)
1
一、一些重要的概念
1、多项式时间算法和难解问题
• 不同的算法具有很不相同的时间复杂性函数，什么样的算法算作 “效率高”，什么样的算法算作“效率低”，计算机科学家们公 认一种简单的区别，这就是多顶式时间算法（polynomial time algorithm)和指数时间算法（exponential time algorithm)之间的区别。Cobham[1964］和Edmonds[1965］首先 讨论了这种区别的基本性质。特别是Edmonds把多项式时间算法与 “好的”算法等同看待，并且猜想某些整数规划问题可能不能用 这种“好的”算法求解。这反映了一种观点，认为指数时间算法 不应该算作“好的”算法。通常也的确是这样的。大多数指数时 间算法只是穷举搜索法的变种，而多项式时间算法通常只有在对 问题的结构有了某些比较深入的了解之后才有可能给出。艰多人 都认为只有知道了问题的多项式时间算法才能认为“很好地解决 了”这个问题。因此，如果一个问题困难到不可能用多项式时间 算法求解，那末我们就认为这个问题是“难解的”。
算法设计与分析演示稿 纪玉波制 作(C)
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2018/10/6 算法设计与分析演示稿 纪玉波制 作(C) 15
现在认为NP完全问题是否是难解的这一向题是当代 数学和计算机科学中尚未解决的最重要问题之一。尽管 大多数研究工作者猜想NP完全问题是难解的，然而在证 明或否定这个广泛的猜想方面几乎没有取得什么进展。 但是，即使没有证明NP完全性蕴涵难解性，知道一个问 题是NP完全的至少暗示着要想用多项式时间算法解这个 问题必须有重大的突破。
2018/10/6
算法设计与分析演示稿 纪玉波制 作(C)
《人工智能一种现代方法》第四版习题答案
• Model-based agent基于茹苦型的主FifS 体: an agent wbose actioD is derived directly from an internal model ofthe c田rent world state that is updated over time.
ac挝on. 实现了智能函数。有各种基本的智能体程序设计 ， 反应出现实表现的 一级用于决策过程的 信息 种类。 设计可能在效率 、 压缩性和灵活性方面有变化 。 适 当 的智能体程序设计取决于环境的本性
• Rationali句; 王军放 : a property of agents that choose actions that maximize tbeir expected u创坷， given the percepts to date. • Autonomy fJ主: a property of agenωwhose bebavior is determined by tbeir own experience rather than solely by their initial programming. .R伪'x agent反射却在FSE体: an agent whose action depends only on the current percept.
Chapter 2
2.1 Defme in yo町 own words the following terms: agent, agent function, agent program , rationality, reflex agent, model-b ased agent, goal-based agent, utility-based agent, learning agent. The following are just some of the many possible defmitions that can be written:
pandas 数据预处理 题目
pandas 数据预处理题目数据预处理在数据分析中起着至关重要的作用，它涉及到数据的清洗、转换、集成和规约等方面，下面我将从多个角度来讨论pandas数据预处理的相关问题。
首先，数据预处理的第一步是数据清洗。
在清洗数据时，我们需要处理缺失值、异常值和重复值。
对于缺失值，可以使用pandas 中的dropna()方法删除包含缺失值的行或列，也可以使用fillna()方法填充缺失值。
对于异常值，可以通过统计方法或可视化方法来识别和处理。
而对于重复值，可以使用drop_duplicates()方法来删除重复行。
其次，数据预处理还包括数据转换。
在数据转换阶段，我们可能需要对数据进行归一化、标准化或者对数据进行编码。
例如，可以使用pandas中的apply()方法对数据进行函数映射，使用replace()方法对数据进行替换，或者使用get_dummies()方法对分类变量进行独热编码。
此外，数据预处理还涉及到数据集成。
在数据集成过程中，我们可能需要合并多个数据集，或者对数据进行连接操作。
在pandas中，可以使用merge()方法或者concat()方法来实现数据集成。
最后，数据预处理还包括数据规约。
数据规约的目的是减少数据的复杂性，包括特征选择、特征提取和数据降维等。
在pandas中，可以使用相关系数、方差分析等方法进行特征选择，使用主成分分析（PCA）等方法进行数据降维。
综上所述，数据预处理是数据分析中不可或缺的一部分，通过pandas库提供的丰富功能，我们可以高效地进行数据清洗、转换、集成和规约，从而为后续的数据分析建模工作奠定良好的基础。
希望以上回答能够满足你的要求。
lop方法
lop方法
LOP方法是一种广泛应用于机器学习和数据处理领域的算法。
它的全称是局部优化算法（Local Optimum Path），通过在搜索空间中寻找局部最优解来实现问题的优化。
在LOP方法中，我们首先需要定义问题的目标函数，这个函数用来衡量不同解的优劣。
然后，我们从一个初始解开始，通过一系列的迭代步骤来搜索邻域中的更优解。
在每一步中，我们根据目标函数的变化情况来判断是否接受新解。
如果新解更优，则更新当前解为新解，否则保持当前解不变。
通过不断迭代，最终得到一个局部最优解。
LOP方法的优势在于它可以快速找到问题的局部最优解。
因为它只关注当前解的邻域，而不是整个搜索空间，所以在大规模问题中，LOP方法的效率通常比全局优化方法高。
此外，LOP方法还可以应用于非线性问题，因为它不需要求解数学公式或计算公式。
然而，LOP方法也存在一些限制。
首先，它只能找到局部最优解，可能无法找到全局最优解。
因此，在使用LOP方法时，我们需要根据具体情况来判断是否满足问题的要求。
其次，LOP方法的性能高度依赖于初始解的选择。
如果初始解离全局最优解较远，那么LOP 方法可能会陷入局部最优解而无法跳出。
总的来说，LOP方法是一种简单而有效的优化算法。
它可以在大规
模问题中快速找到局部最优解，并且适用于各种类型的问题。
当我们面临一个需要优化的问题时，LOP方法是一个值得考虑的选择。
通过合理地定义目标函数和选择初始解，我们可以充分发挥LOP方法的优势，得到一个满意的解。
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John A. Drakopoulos and Theodore N. Tomaras Department of Physics, University of Crete P.O.Box 2208, Heraklion 71003, Crete, Greece. Tel. +3081-394246, Fax +3081-394201 http://www.physics.uch.gr/~jad e-mail: jad@physics.uch.gr
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called quantum computational networks, and examined some of their properties [9]. Yao subsequently proved the polynomial equivalence between quantum Turing machines and quantum circuits (thus providing a truly universal model of quantum computation) by proving that an arbitrary quantum Turing machine could simulate, and be simulated by, a polynomial size quantum circuit [20]. The model of quantum computing having been defined, its computational power must be identified. The following classes of decision problems have been defined: P is the class of all decision problems that can be solved in polynomial time by a deterministic Turing machine BPP is the class of all decision problems that can be solved in polynomial time by a probabilistic Turing machine with a probability of error bounded by 1/3 for all inputs NP is the class of all decision problems that can be solved in polynomial time by a non-deterministic Turing machine BQP is the class of all decision problems that can be solved in polynomial time by a quantum Turing machine with a probability of error bounded by 1/3 for all inputs (Apparently it is P ⊆ BPP ⊆ NP. Furthermore, Benniof's result [1, 2] implies that P ⊆ BQP.) Deutsch and Josza [11] and Berthiaume and Brassard [10, 6] proved that, relative to certain oracles, there are computational problems that can be solved exactly and in polynomial time by quantum Turing machines but cannot be solved polynomially for all inputs by deterministic or probabilistic Turing machines. However, those problems belong to BPP; and thus the above results do not confer the supposed extra computing power of quantum Turing machines. Bennett et al. [3] proved that relative to a random oracle, it is not true that NP ⊆ BQP. Bernstein and Vazirani [4] proved that BPP ⊆ BQP. Bernstein and Vazirani [4] and Simon [18] invented problems that are not known to be in BPP but belong to BQP. Shor gave polynomial time quantum algorithms for the factoring and discrete log problems [17]. (Note that not only Simon's problem but also factoring and discrete log belong to NP ∩ co-NP. However, Bennett et al. [3] proved that relative to a permutation oracle, it is not true that NP ∩ co-NP ⊆ BQP.) Finally Grover showed how to accept the class NP relative to any oracle in time O(2n/2). (A formal analysis of Grover's algorithm appears in [7].) It should be noted that Shor's factoring and discrete log algorithms (with its implications in cryptography and cryptosystems) and Grover's database search algorithm are of practical importance. Furthermore, the application of quantum computing for the development of secure cryptographic communication systems (which detect unauthorized access or guarantee that information would not be compromised [15]) is obviously of high commercial value. It is still unknown whether BPP ⊂ BQP, and whether NP ⊆ BQP. (The latter is tremendously important since the class NP contains a large number of optimization problems with a broad range of applications from computer science and statistics to engineering, automatic control, integrated circuit design etc.) In this paper, we provide polynomial algorithms for solving the satisfiability problem, which is a known NP complete problem, assuming an oracle that can (either exactly or approximately) clone a binary random variable or a qubit. Therefore, we prove that NP ⊆ BPPC ⊆ BQPC and NP ⊆ BPPAC ⊆ BQPAC, where C( ) and AC( ) are the exact and approximate cloning oracles as defined below. Such oracles, which do
1. Introduction Quantum computing is a new and exciting interdisciplinary area that combines computer science and (quantum) physics. As early as 1982, Feynman observed that the straightforward simulation of a quantum system on a classical computer (deterministic or probabilistic Turing machine) required an exponential slowdown and without any apparent way to speed up the simulation [11, 12]. He asked whether that is inherent to quantum systems and he suggested the design of computing machines based on quantum theory implying, at the same time, that such quantum computers could perhaps compute more efficiently than classical computers. About the same time, and addressing the opposite problem, Benioff showed that a deterministic Turing machine could be simulated by the unitary evolution of a quantum process and thus provided the first indication of the strength of quantum computing [1, 2]. Subsequently, Deutsch proposed a general model of quantum computation--the quantum Turing machine--which could simulate any given quantum system but possibly with exponential slowdown [8]. Berstein and Vazirani improved upon the concept of a quantum Turing machine proposing a univesal quantum Turing machine, which, as they proved, could simulate a broad class of quantum Turing machines with only a polynomial slowdown [4]. In classical computing, logic circuits provide an alternative to Turing machines (actually current computers are build from integrated circuits and not as Turing machines). Deutsch first proposed a similar model of quantum circuits, which he