LETTER Genetically-Designed Time Delay Neural Networks for Multiple-interval Urban Freeway

上海大学《人工智能》网络课课后习题答案1.1育才新工科-人工智能简介1【判断题】《人工智能》课程为理工类通选课,本课程给予学生的主要是思想而不是知识。

对1。

2图灵是谁？1【单选题】图灵曾协助军方破解（)的著名密码系统Enigma。

A、英国B、美国C、德国D、日本2【判断题】电影《模仿游戏》是纪念图灵诞生90周年而拍摄的电影。

X3【判断题】图灵使用博弈论的方法破解了Enigma。

对1.3为什么图灵很灵？1【单选题】1937年,图灵在发表的论文(）中,首次提出图灵机的概念。

A、《左右周期性的等价》B、《论可计算数及其在判定问题中的应用》C、《可计算性与λ可定义性》D、《论高斯误差函数》2【单选题】1950年,图灵在他的论文（）中,提出了关于机器思维的问题。

A、《论数字计算在决断难题中的应用》B、《论可计算数及其在判定问题中的应用》C、《可计算性与λ可定义性》D、《计算和智能》3【判断题】存在一种人类认为的可计算系统与图灵计算不等价。

X4【判断题】图灵测试是指测试者与被测试者(一个人和一台机器）隔开的情况下，通过一些装置(如键盘)向被测试者随意提问。

如果测试者不能确定出被测试者是人还是机器,那么这台机器就通过了测试，并被认为具有人类智能。

对1.4为什么图灵不灵？1【单选题】以下叙述不正确的是(）。

A、图灵测试混淆了智能和人类的关系B、机器智能的机制必须与人类智能相同C、机器智能可以完全在特定的领域中超越人类智能D、机器智能可以有人类智能的创造力2【单选题】在政府报告中，（)的报告使用“机器智能”这个词汇。

A、中国B、英国C、德国D、美国3【多选题】机器智能可以有自己的“人格”体现主要表现在（）。

A、模型间的对抗—智能进化的方式B、机器智能的协作-机器智能的社会组织C、机器智能是社会的实际生产者D、机器智能可以有人类智能的创造力4【判断题】图灵测试存在的潜台词是机器智能的极限可以超越人的智能,机器智能可以不与人的智能可比拟。

LetterIntermittent Control for Fixed-Time Synchronization ofCoupled NetworksYongbao Wu, Ziyuan Sun, Guangtao Ran, and Lei XueDear Editor,This letter deals with fixed-time synchronization (Fd-TS) of com-plex networks (CNs) under aperiodically intermittent control (AIC) for the first time. The average control rate and a new Lyapunov func-tion are proposed to overcome the difficulty of dealing with fixed-time stability/synchronization of CNs for AIC. Based on the Lya-punov and graph-theoretical methods, a Fd-TS criterion of CNs is given. Moreover, the method of this letter is also applicable to the study of finite-time synchronization of CNs for AIC. Finally, the the-oretical results are applied to study the Fd-TS of oscillator systems, and simulation results are given to verify the effectiveness of the results.Recently, the dynamics of CNs have attracted extensive attention due to their wide applications in real-world networks. As one of the most important collective behaviors of CNs, synchronization has received considerable interest in many fields [1]. It should be noted that the most existing results about the synchronization of CNs stud-ied asymptotic synchronization and exponential synchronization [2], and they are often classified into infinite-time synchronization. In many practical problems, achieving synchronization within a finite time is more desirable and useful. Therefore, finite-time synchroniza-tion (Fe-TS) has been investigated by many researchers. In contrast with infinite-time synchronization, Fe-TS has been reported to pos-sess faster convergence and better performance against uncertainties and disturbances.Nevertheless, a significant limitation of Fe-TS is that the settling time depends on the initial values. In many practical systems, the ini-tial values may be difficult to obtain in advance. Fortunately, this problem was overcome by Polyakov [3] through introducing the con-cept of fixed-time stability and presenting fundamental results on fixed-time stability. Inspired by Polyakov’s novel fixed-time stabil-ity theory, there are some follow-up works about fixed-time stability for various CNs [4]–[6]. Compared to Fe-TS, the settling time of Fd-TS is determined by the designed controller parameters, which do not rely on the initial values and can be estimated in advance. Further-more, many practical systems such as microgrid systems and space-craft dynamics usually desire to achieve fixed-time convergence. Consequently, it is meaningful and necessary to further explore the Fd-TS of CNs both in theory and methods.In general, it is difficult to realize self-synchronization for CNs due to the complexity of node dynamics and topologies. Therefore, many kinds of control techniques have been employed to achieve the syn-chronization of CNs in [7]. Different from the continuous control schemes, the discontinuous control methods such as intermittent con-trol (IC) [2], [8], and impulsive control have been extensively stud-ied because they can reduce control cost as well as the number of information exchanges. It is known that IC can be divided into peri-odically IC (PIC), and AIC [2], and AIC takes PIC as a special case; thus, it is more general to consider AIC. For AIC, scholars mainly considered asymptotic synchronization [2], exponential synchroniza-tion [9], and Fe-TS. However, there are few results focusing on the Fd-TS for CNs by AIC. The existing theory to study asymptotic syn-chronization, exponential synchronization, and Fe-TS cannot be directly extended to Fd-TS. Moreover, the Fd-TS theoretical frame-work based on AIC is not established. Therefore, it is urgently neces-sary to develop a new theory and methods to investigate the Fd-FS of CNs via AIC, which motivates this work. The main contributions of this letter are as follows.sup i{ζi+1−µi}≤con1 sup i{ζi+1−ζi}≤con2con1con2ζiµiϑηi=(µi−ζi)/ (ζi+1−ζi)ϑ≥liminf i→∞{ηi}1) Unlike the existing literature dealing with finite-time stability/synchronization for IC, in this letter, we establish a theoreti-cal framework of fixed-time stability/synchronization for AIC for the first time. 2) Compared with the existing literature [4], an auxiliary function is introduced to consider the Fd-TS of CNs under IC, which allows the control function in the rest intervals of IC to be zero. In the existing literature [4], the control function in the rest intervals of IC is not zero, which may be regarded as a switching control rather than an IC in a general sense. Thus, the control strategy proposed in this letter is more general. 3) In [2], [9], some scholars mainly con-sidered the asymptotic synchronization or exponential synchroniza-tion for AIC. Moreover, the existing literature have certain restric-tions on the control intervals, such as ,, where and are positive constants. For parameters and , see Fig. 1. This letter uses the average con-trol rate in (5), not the infimum of the control rate, which is easy to satisfy the condition of the theorem because of . In addition, the idea of using the aver-age control rate in this letter also can apply to the study of finite-time stability/synchronization for AIC, which is more general.x k(t)=(x k1(t),x k2(t),...,x km(t))αkh:R m×R m→R m f k:R m×R+→R mb kh≥0b kk=0k∈Nwhere and ; coupled function ; and is coupling weight and for all .System (1) is considered as a master system, and we consider theCorresponding author: Yongbao Wu.Citation: Y. B. Wu, Z. Y. Sun, G. T. Ran, and L. Xue, “Intermittent control for fixed-time synchronization of coupled networks,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 6, pp. 1488–1490, Jun. 2023.Y. B. Wu and L. Xue are with the School of Automation, Southeast University, Nanjing 210096, China (e-mail:Z. Y. Sun is with the Department of Applied Mathematics, University of G. T. Ran is with the Department of Control Science and Engineering, Harbin Institute of Technology, Harbin 150001, China (e-mail: ranguangtao@ ).Color versions of one or more of the figures in this paper are available online at .Digital Object Identifier 10.1109/JAS.2023.123363ζiζi+1μi+1μi+2ζi+2ζi+3μi……Fig. 1. Schematic diagram of AIC. Blue and yellow areas represent control and rest intervals, respectively.1488 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 10, NO. 6, JUNE 2023z k (t )∈R m u k (t )in which and is an AIC strategy.y k (t )=z k (t )−x k (t )Let be error vector. Based on systems (1) andf k (x k k k (z k k (x k kh (x k k h h )=in which and sign(y k )=diag(sign(y k 1),sign(y k 2),...,sign(y km ))N ={0,1,2,...}[ζi ,µi )[µi ,ζi +1)ζ0=0[y k ]p =(|y k 1|p ,|y k 2|p ,...,|y km |p )T ;ϱs>0(s =1,2,3)q >10<p <1where and ; and stand for the i th control interval and rest interval, respectively; , , , and .f k αkh βk >0φkh >0Assumption 1: Functions and satisfy the Lipschitz condi-tions with Lipschitz constants and , respectively.ϑ∈(0,1)Definition 1 [8]: For AIC strategy (4), there are and con 12[t 2,t 1)ϑT ϑin which stands for the total control interval length on , represents the average control rate, and is called the elasticity number.T (y (0))>0lim t →T (y (0))y (t )=0y (t )≡0t ≥T (y (0))y (t )=(y T 1(t ),y T 2(t ),...,y T n (t ))T T (y (0))y (0)T ∗>0y(0)Definition 2: The master system (1) and slave system (2) are said to achieve Fe-TS, if there is a settling time such that and for , where . The time is called the settling time of syn-chronization, which is dependent of . Especially, if there is a fixed time which is independent of , then systems (1) and (2) achieve the Fd-TS.Analysis of Fd-TS: This section gives two lemmas to study the Fd-TS under AIC (4). Then, a Fd-TS criterion of CNs is given.a 12∗∗in which , , , and Then, whenϑProof: See Section II in the Supplementary material.■iin which , , and If there existsˆa11exp {(1−q )˘εT ϑϑwhere , and are defined in Definition 1.Proof: See Section III in the Supplementary material.■Now, a main result is state as follows.(G ,A )A =(b kh φkh )n ×n ˘ε>0Theorem 1: If the digraph with is stronglyconnected, and there exists satisfying the following inequali-a 33k 44k 3k 1k )−4∑n h =1b kh φkh >0a 4k =2βk +4∑n h =1b kh φkh T ∗in which , , , and , then systems (1)and (2) achieve the Fd-TS, and settling time satisfiesˆa 1=a 1exp {(1−q )˘εT ϑ}a 2=2σmin ϱ2a 1=2σmin ϱ3(mn )1−q2σ1min =min k ∈N {c 1−p2k }σ2min =min k ∈N {c 1−q 2k }c k >0with , , ,, , and can be found in [10].Proof: See Section IV in the Supplementary material.■ϑRemark 1: Theorem 1 requires two inequalities in (8) to be true.We can get that if the average control rate is greater, the condi-tions are easier to meet when other parameters are fixed, which shows that the design of IC has an essential impact on the Fd-TS of CNs.U (t )=exp {Θ(t )}Ψ(t )Θ(t )t ∈[µi ,ζi +1),Remark 2: In the proof of Lemma 2, we use an auxiliary function , where function is defined in Section III-1of the Supplementary material. Moreover, when we can U(t )≤−(˘εϑ−a 4)U (t )[µi ,ζi +1)which enables to be established in the rest intervals . Similar ideas were discussed in semilinear sys-tems [8]. This letter uses the technique to overcome the difficulty of studying Fd-TS of CNs under AIC.sup i {ζi +1−µi }=con 1sup i {ζi +1−ζi }=con 2con 1con 2ηi =(µi −ζi )/(ζi +1−ζi )ϑ≥inf i ∈N {ηi }Remark 3: In Lemma 2, we give a synchronization criterion to achieve the Fd-TS of the systems under AIC for the first time. In the existing results [2], [9], some scholars mainly considered the asymp-totic synchronization or exponential synchronization for IC. More-over, the existing results have certain restrictions on the control and rest intervals, such as , ,where and are positive constants. In this letter, we use the average control rate instead of the infimum of the control rate , which is easier to satisfy the conditions of the theorem because of . In addition, the idea of using an average control rate in this letter also applies to the study of Fe-TS, which is more general. However, as far as we know, no author has considered the general case for Fe-TS under AIC by using the technique of this letter.T ∗ϑT ϑa 1a 2T ∗ϑT ∗Remark 4: We give an important differential inequality (7) in Lemma 2, which can deal with Fd-TS of CNs for AIC. Moreover, the fixed time depends on the average control rate and elasticity number . In addition, we find that the larger parameters and in (7), the smaller the fixed time . And when the average control rate is greater, the settling time will be smaller.Remark 5: Recently, some scholars have considered the Fd-TS for CNs under AIC [4]. For the IC, this letter allows the control function in the rest intervals of the IC to be zero. In the existing results [4], the control function in the rest intervals of IC is not zero, which may be regarded as a switching control. In addition, the average control rate of AIC is considered, which provides less conservative results.Application and numerical simulations: See Section IV in the Supplementary material.Conclusions: We considered the Fd-TS of CNs under AIC. The average control rate and a new Lyapunov function were proposed to overcome the difficulty of dealing with fixed-time stability/synchro-nization of CNs for AIC. Meanwhile, a Fd-TS criterion of CNs was given. Finally, we applied the theoretical results to study the Fd-TS of oscillator systems, and simulation results were given to verify the effectiveness of the results. Considering the influence of the delay factor, the Fd-TS of delayed CNs under AIC will be studied in the future.Acknowledgments: This work was supported in part by the Natu-ral Science Foundation of Jiangsu Province of China (BK20220811,BK20202006); the National Natural Science Foundation of China (62203114, 62273094); the Fundamental Research Funds for the Central Universities, and the “Zhishan” Scholars Programs of South-WU et al .: INTERMITTENT CONTROL FOR FD-TS OF CNS 1489east University; China Postdoctoral Science Foundation (2022M 710684); and Excellent Postdoctoral Foundation of Jiangsu Provinceof China (2022ZB116).Supplementary material: The supplementary material of this let-ter can be found in links https:///est/d3296793221015/pdf.ReferencesF. Dörfler and F. Bullo, “Synchronization in complex networks of phaseoscillators: A survey,” Automatica , vol. 50, no. 6, pp. 1539–1564, 2014.[1]X. Liu and T. Chen, “Synchronization of complex networks viaaperiodically intermittent pinning control,” IEEE Trans. Automatic Control , vol. 60, no. 12, pp. 3316–3321, 2015.[2]A. Polyakov, “Nonlinear feedback design for fixed-time stabilization oflinear control systems,” IEEE Trans. Automatic Control , vol. 57, no. 8,pp. 2106–2110, 2011.[3]Q. Gan, F. Xiao, and H. Sheng, “Fixed-time outer synchronization ofhybrid-coupled delayed complex networks via periodically semi-intermittent control,” J. Franklin Institute , vol. 356, no. 12, pp. 6656–6677, 2019.[4]J. Liu, Y. Wu, M. Sun, and C. Sun, “Fixed-time cooperative tracking fordelayed disturbed multi-agent systems under dynamic event-triggered control,” IEEE/CAA J. Autom. Sinica , vol. 9, no. 5, pp. 930–933, 2022.[5]Z. Zuo, B. Tian, M. Defoort, and Z. Ding, “Fixed-time consensustracking for multiagent systems with high-order integrator dynamics,”IEEE Trans. Autom. Control , vol. 63, no. 2, pp. 563–570, 2018.[6]W. Yu, P. DeLellis, G. Chen, M. Di Bernardo, and J. Kurths,“Distributed adaptive control of synchronization in complex networks,”IEEE Trans. Autom. Control , vol. 57, no. 8, pp. 2153–2158, 2012.[7]Y. Guo, M. Duan, and P. Wang, “Input-to-state stabilization ofsemilinear systems via aperiodically intermittent event-triggered control,” IEEE Trans. Control Network Syst., vol. 9, no. 2, pp. 731–741, 2022.[8]Y. Wu, S. Zhuang, and W. Li, “Periodically intermittent discreteobservation control for synchronization of the general stochastic complex network,” Automatica , vol. 110, p. 108591, 2019.[9]M. Y. Li and Z. Shuai, “Global-stability problem for coupled systems ofdifferential equations on networks,” J. Differential Equations , vol. 248,no. 1, pp. 1–20, 2010.[10] 1490IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 10, NO. 6, JUNE 2023。

1000 A+B Problem 送分题1001 Exponentiation 高精度1003 Hangover 送分题1004 Financial Management 送分题1005 I Think I Need a Houseboat 几何1006 Biorhythms 送分题1007 DNA Sorting 送分题1008 Maya Calendar 日期处理1010 STAMPS 搜索＋DP1011 Sticks 搜索1012 Joseph 模拟/数学方法1014 Dividing 数论/DP?/组合数学->母函数?1015 Jury Compromise DP1016 Numbers That Count 送分题1017 Packets 贪心1018 Communication System 贪心1019 Number Sequence 送分题1020 Anniversary Cake 搜索1023 The Fun Number System 数论1025 Department 模拟1026 Cipher 组合数学1027 The Same Game 模拟1028 Web Navigation 送分题1031 Fence 计算几何1034 The dog task 计算几何1037 A decorative fence DP/组合数学1039 Pipe 几何1042 Gone Fishing 贪心/DP1045 Bode Plot 送分题(用物理知识)1046 Color Me Less 送分题1047 Round and Round We Go 高精度1048 Follow My Logic 模拟1049 Microprocessor Simulation 模拟1050 To the Max DP1053 Set Me 送分题1054 The Troublesome Frog 搜索1060 Modular multiplication of polynomials 高精度1061 青蛙的约会数论1062 昂贵的聘礼DP1064 Cable master DP/二分查找1065 Wooden Sticks DP1067 取石子游戏博弈论1068 Parencodings 送分题1069 The Bermuda Triangle 搜索1070 Deformed Wheel 几何1071 Illusive Chase 送分题1072 Puzzle Out 搜索1073 The Willy Memorial Program 模拟1074 Parallel Expectations DP1075 University Entrance Examination 模拟1080 Human Gene Functions DP->LCS变形1082 Calendar Game 博弈论1084 Square Destroyer 搜索？1085 Triangle War 博弈论1086 Unscrambling Images 模拟?1087 A Plug for UNIX 图论->最大流1088 滑雪DFS/DP1090 Chain ->格雷码和二进制码的转换1091 跳蚤数论1092 Farmland 几何1093 Formatting Text DP1094 Sorting It All Out 图论->拓扑排序1095 Trees Made to Order 组合数学1096 Space Station Shielding 送分题1097 Roads Scholar 图论1098 Robots 模拟1099 Square Ice 送分题1100 Dreisam Equations 搜索1101 The Game 搜索->BFS1102 LC-Display 送分题1103 Maze 模拟1104 Robbery 递推1106 Transmitters 几何1107 W's Cipher 送分题1110 Double Vision 搜索1111 Image Perimeters 搜索1112 Team Them Up! DP1113 Wall 计算几何->convex hull1119 Start Up the Startup 送分题1120 A New Growth Industry 模拟1122 FDNY to the Rescue! 图论->Dijkstra 1125 Stockbroker Grapevine 图论->Dijkstra 1128 Frame Stacking 搜索1129 Channel Allocation 搜索（图的最大独立集）1131 Octal Fractions 高精度1135 Domino Effect 图论->Dijkstra1137 The New Villa 搜索->BFS1141 Brackets Sequence DP1142 Smith Numbers 搜索1143 Number Game 博弈论1147 Binary codes 构造1148 Utopia Divided 构造1149 PIGS 图论->网络流1151 Atlantis 计算几何->同等安置矩形的并的面积->离散化1152 An Easy Problem! 数论1157 LITTLE SHOP OF FLOWERS DP1158 TRAFFIC LIGHTS 图论->Dijkstra变形1159 Palindrome DP->LCS1160 Post Office DP1161 Walls 图论1162 Building with Blocks 搜索1163 The Triangle DP1170 Shopping Offers DP1177 Picture 计算几何->同等安置矩形的并的周长->线段树1179 Polygon DP1180 Batch Scheduling DP1182 食物链数据结构->并查集1183 反正切函数的应用搜索1184 聪明的打字员搜索1185 炮兵阵地DP->数据压缩1187 陨石的秘密DP（BalkanOI99 Par的拓展）1189 钉子和小球递推?1190 生日蛋糕搜索/DP1191 棋盘分割DP1192 最优连通子集图论->无负权回路的有向图的最长路->BellmanFord 1193 内存分配模拟1194 HIDDEN CODES 搜索+DP1197 Depot 数据结构->Young T ableau1201 Intervals 贪心/图论->最长路->差分约束系统1202 Family 高精度1209 Calendar 日期处理1217 FOUR QUARTERS 递推1218 THE DRUNK JAILER 送分题1233 Street Crossing 搜索->BFS1245 Programmer, Rank Thyself 送分题1247 Magnificent Meatballs 送分题1248 Safecracker 搜索1250 T anning Salon 送分题1251 Jungle Roads 图论->最小生成树1271 Nice Milk 计算几何1273 Drainage Ditches 图论->最大流1274 The Perfect Stall 图论->二分图的最大匹配1275 Cashier Employment 图论->差分约束系统->无负权回路的有向图的最长路->Bellman-Ford1280 Game 递推1281 MANAGER 模拟1286 Necklace of Beads 组合数学->Polya定理1288 Sly Number 数论->解模线性方程组1293 Duty Free Shop DP1298 The Hardest Problem Ever 送分题1316 Self Numbers 递推同Humble Number一样1322 Chocolate 递推/组合数学1323 Game Prediction 贪心1324 Holedox Moving BFS+压缩储存1325 Machine Schedule 图论->二分图的最大匹配1326 Mileage Bank 送分题1327 Moving Object Recognition 模拟?1328 Radar Installation 贪心（差分约束系统的特例）1338 Ugly Numbers 递推(有O(n)算法)1364 King 图论->无负权回路的有向图的最长路->BellmanFord1370 Gossiping (数论->模线性方程有无解的判断)+(图论->DFS)2184 Cow Exhibition DP2190 ISBN 送分题2191 Mersenne Composite Numbers 数论2192 Zipper DP->LCS变形2193 Lenny's Lucky Lotto Lists DP2194 Stacking Cylinders 几何2195 Going Home 图论->二分图的最大权匹配2196 Specialized Four-Digit Numbers 送分题2197 Jill's Tour Paths 图论->2199 Rate of Return 高精度2200 A Card Trick 模拟2210 Metric Time 日期处理2239 Selecting Courses 图论->二分图的最大匹配2243 Knight Moves 搜索->BFS2247 Humble Numbers 递推(最优O(n)算法)2253 Frogger 图论->Dijkstra变形(和1295是一样的)2254 Globetrotter 几何2261 France '98 递推2275 Flipping Pancake 构造2284 That Nice Euler Circuit 计算几何2289 Jamie's Contact Groups 图论->网络流?2291 Rotten Ropes 送分题2292 Optimal Keypad DP2299 Ultra-QuickSort 排序->归并排序2304 Combination Lock 送分题2309 BST 送分题2311 Cutting Game 博弈论2312 Battle City 搜索->BFS2314 POJ language 模拟2315 Football Game 几何2346 Lucky tickets 组合数学2351 Time Zones 时间处理2379 ACM Rank T able 模拟+排序2381 Random Gap 数论2385 Apple Catching DP(像NOI98“免费馅饼”)2388 Who's in the Middle 送分题(排序)2390 Bank Interest 送分题2395 Out of Hay 图论->Dijkstra变形2400 Supervisor, Supervisee 图论->二分图的最大权匹配?2403 Hay Points 送分题2409 Let it Bead 组合数学->Polya定理2416 Return of the Jedi 图论->2417 Discrete Logging 数论2418 Hardwood Species 二分查找2419 Forests 枚举2421 Constructing Roads 图论->最小生成树2423 The Parallel Challenge Ballgame 几何2424 Flo's Restaurant 数据结构->堆2425 A Chess Game 博弈论2426 Remainder BFS2430 Lazy Cows DP->数据压缩1375 Intervals 几何1379 Run Away 计算几何->1380 Equipment Box 几何1383 Labyrinth 图论->树的最长路1394 Railroad 图论->Dijkstra1395 Cog-Wheels 数学->解正系数的线性方程组1408 Fishnet 几何1411 Calling Extraterrestrial Intelligence Again 送分题1430 Binary Stirling Numbers 日期处理1431 Calendar of Maya 模拟1432 Decoding Morse Sequences DP1434 Fill the Cisterns! 计算几何->离散化/1445 Random number 数据结构->碓1447 Ambiguous Dates 日期处理1450 Gridland 图论(本来TSP问题是NP难的，但这个图比较特殊，由现成的构造方法)1458 Common Subsequence DP->LCS1459 Power Network 图论->最大流1462 Random Walk 模拟+解线性方程组1463 Strategic game 贪心1466 Girls and Boys 图论->n/a1469 COURSES 贪心1475 Pushing Boxes DP1476 Always On the Run 搜索->BFS1480 Optimal Programs 搜索->BFS1481 The Die Is Cast 送分题1482 It's not a Bug, It's a Feature! 搜索->BFS1483 Going in Circles on Alpha Centauri 模拟1484 Blowing Fuses 送分题1485 Fast Food DP(似乎就是ioi2000的postoffice)1486 Sorting Slides 图论->拓扑排序1505 Copying Books DP+二分查找1510 Hares and Foxes 数论1512 Keeps Going and Going and ... 模拟1513 Scheduling Lectures DP1514 Metal Cutting 几何1515 Street Directions 图论->把一个无向连通图改造成为有向强连通图1517 u Calculate e 送分题1518 Problem Bee 几何1519 Digital Roots 送分题(位数可能很大)1520 Scramble Sort 排序1547 Clay Bully 送分题1555 Polynomial Showdown 送分题(非常阴险)1563 The Snail 送分题1601 Pizza Anyone? 搜索1604 Just the Facts 送分题1605 Horse Shoe Scoring 几何1606 Jugs 数论/搜索1631 Bridging signals DP+二分查找1632 Vase collection 图论->最大完全图1633 Gladiators DP1634 Who's the boss? 排序1635 Subway tree systems 图论->不同表示法的二叉树判同1637 Sightseeing tour 图论->欧拉回路1638 A number game 博弈论1639 Picnic Planning 图论->1641 Rational Approximation 数论1646 Double Trouble 高精度1654 Area 几何1657 Distance on Chessboard 送分题1658 Eva's Problem 送分题1660 Princess FroG 构造1661 Help Jimmy DP1663 Number Steps 送分题1664 放苹果组合数学->递推1677 Girls' Day 送分题1688 Dolphin Pool 计算几何1690 (Your)((Term)((Project))) 送分题1691 Painting A Board 搜索/DP1692 Crossed Matchings DP1693 Counting Rectangles 几何1694 An Old Stone Game 博弈论?1695 Magazine Delivery 图论->1712 Flying Stars DP1713 Divide et unita 搜索1714 The Cave 搜索/DP1717 Dominoes DP1718 River Crossing DP1719 Shooting Contest 贪心1729 Jack and Jill 图论->1730 Perfect Pth Powers 数论1732 Phone numbers DP1734 Sightseeing trip 图论->Euler回路1738 An old Stone Game 博弈论?1741 Tree 博弈论?1745 Divisibility DP1751 Highways 图论->1752 Advertisement 贪心/图论->差分约束系统1753 Flip Game 搜索->BFS1755 Triathlon 计算几何?1770 Special Experiment 树形DP1771 Elevator Stopping Plan DP1772 New Go Game 构造?1773 Outernet 模拟1774 Fold Paper Strips 几何1775 Sum of Factorials 送分题1776 T ask Sequences DP1777 Vivian's Problem 数论1870 Bee Breeding 送分题1871 Bullet Hole 几何1872 A Dicey Problem BFS1873 The Fortified Forest 几何+回溯1874 Trade on Verweggistan DP1875 Robot 几何1876 The Letter Carrier's Rounds 模拟1877 Flooded! 数据结构->堆1879 Tempus et mobilius Time and motion 模拟+组合数学->Polya定理1882 Stamps 搜索+DP1883 Theseus and the Minotaur 模拟1887 Testing the CATCHER DP1889 Package Pricing DP1893 Monitoring Wheelchair Patients 模拟+几何1915 Knight Moves 搜索->BFS1916 Rat Attack 数据结构->?1936 All in All DP?1946 Cow Cycling DP1947 Rebuilding Roads 二分1985 Cow Marathon 图论->有向无环图的最长路1995 Raising Modulo Numbers 数论->大数的幂求余2049 Finding Nemo 图论->最短路2050 Searching the Web 模拟(需要高效实现)2051 Argus 送分题(最好用堆，不用也可以过)2054 Color a Tree 贪心2061 Pseudo-random Numbers 数论2080 Calendar 日期处理2082 Terrible Sets 分治/2083 Fractal 递归2084 Game of Connections 递推(不必高精度)2105 IP Address 送分题2115 C Looooops 数论->解模线性方程2136 Vertical Histogram 送分题2165 Gunman 计算几何2179 Inlay Cutters 枚举2181 Jumping Cows 递推2182 Lost Cows ->线段树/＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝1370 Gossiping (数论->模线性方程有无解的判断)+(图论->DFS)1090 Chain ->格雷码和二进制码的转换2182 Lost Cows ->线段树/2426 Remainder BFS1872 A Dicey Problem BFS1324 Holedox Moving BFS+压缩储存1088 滑雪DFS/DP1015 Jury Compromise DP1050 To the Max DP1062 昂贵的聘礼DP1065 Wooden Sticks DP1074 Parallel Expectations DP1093 Formatting Text DP1112 Team Them Up! DP1141 Brackets Sequence DP1157 LITTLE SHOP OF FLOWERS DP1160 Post Office DP1163 The Triangle DP1170 Shopping Offers DP1179 Polygon DP1180 Batch Scheduling DP1191 棋盘分割DP1293 Duty Free Shop DP2184 Cow Exhibition DP2193 Lenny's Lucky Lotto Lists DP2292 Optimal Keypad DP1432 Decoding Morse Sequences DP1475 Pushing Boxes DP1513 Scheduling Lectures DP1633 Gladiators DP1661 Help Jimmy DP1692 Crossed Matchings DP1712 Flying Stars DP1717 Dominoes DP1718 River Crossing DP1732 Phone numbers DP1745 Divisibility DP1771 Elevator Stopping Plan DP1776 T ask Sequences DP1874 Trade on Verweggistan DP1887 Testing the CATCHER DP1889 Package Pricing DP1946 Cow Cycling DP1187 陨石的秘密DP（BalkanOI99 Par的拓展）1485 Fast Food DP(似乎就是ioi2000的postoffice) 2385 Apple Catching DP(像NOI98“免费馅饼”) 1064 Cable master DP/二分查找1037 A decorative fence DP/组合数学1936 All in All DP?1505 Copying Books DP+二分查找1631 Bridging signals DP+二分查找1159 Palindrome DP->LCS1458 Common Subsequence DP->LCS1080 Human Gene Functions DP->LCS变形2192 Zipper DP->LCS变形1185 炮兵阵地DP->数据压缩2430 Lazy Cows DP->数据压缩1067 取石子游戏博弈论1082 Calendar Game 博弈论1085 Triangle War 博弈论1143 Number Game 博弈论2311 Cutting Game 博弈论2425 A Chess Game 博弈论1638 A number game 博弈论1694 An Old Stone Game 博弈论?1738 An old Stone Game 博弈论?1741 Tree 博弈论?2083 Fractal 递归1104 Robbery 递推1217 FOUR QUARTERS 递推1280 Game 递推2261 France '98 递推2181 Jumping Cows 递推1316 Self Numbers 递推同Humble Number一样2084 Game of Connections 递推(不必高精度) 1338 Ugly Numbers 递推(有O(n)算法)2247 Humble Numbers 递推(最优O(n)算法)1322 Chocolate 递推/组合数学1189 钉子和小球递推?1947 Rebuilding Roads 二分2418 Hardwood Species 二分查找2082 Terrible Sets 分治/1001 Exponentiation 高精度1047 Round and Round We Go 高精度1060 Modular multiplication of polynomials 高精度1131 Octal Fractions 高精度1202 Family 高精度2199 Rate of Return 高精度1646 Double Trouble 高精度1147 Binary codes 构造1148 Utopia Divided 构造2275 Flipping Pancake 构造1660 Princess FroG 构造1772 New Go Game 构造?1005 I Think I Need a Houseboat 几何1039 Pipe 几何1070 Deformed Wheel 几何1092 Farmland 几何1106 Transmitters 几何2194 Stacking Cylinders 几何2254 Globetrotter 几何2315 Football Game 几何2423 The Parallel Challenge Ballgame 几何1375 Intervals 几何1380 Equipment Box 几何1408 Fishnet 几何1514 Metal Cutting 几何1518 Problem Bee 几何1605 Horse Shoe Scoring 几何1654 Area 几何1693 Counting Rectangles 几何1774 Fold Paper Strips 几何1871 Bullet Hole 几何1875 Robot 几何1873 The Fortified Forest 几何+回溯1031 Fence 计算几何1034 The dog task 计算几何1271 Nice Milk 计算几何2284 That Nice Euler Circuit 计算几何1688 Dolphin Pool 计算几何2165 Gunman 计算几何1755 Triathlon 计算几何?1379 Run Away 计算几何->1113 Wall 计算几何->convex hull1434 Fill the Cisterns! 计算几何->离散化/1151 Atlantis 计算几何->同等安置矩形的并的面积->离散化1177 Picture 计算几何->同等安置矩形的并的周长->线段树2419 Forests 枚举2179 Inlay Cutters 枚举1025 Department 模拟1027 The Same Game 模拟1048 Follow My Logic 模拟1049 Microprocessor Simulation 模拟1073 The Willy Memorial Program 模拟1075 University Entrance Examination 模拟1098 Robots 模拟1103 Maze 模拟1120 A New Growth Industry 模拟1193 内存分配模拟1281 MANAGER 模拟2200 A Card Trick 模拟2314 POJ language 模拟1431 Calendar of Maya 模拟1483 Going in Circles on Alpha Centauri 模拟1512 Keeps Going and Going and ... 模拟1773 Outernet 模拟1876 The Letter Carrier's Rounds 模拟1883 Theseus and the Minotaur 模拟2050 Searching the Web 模拟(需要高效实现)1012 Joseph 模拟/数学方法1086 Unscrambling Images 模拟?1327 Moving Object Recognition 模拟?1893 Monitoring Wheelchair Patients 模拟+几何1462 Random Walk 模拟+解线性方程组2379 ACM Rank T able 模拟+排序1879 Tempus et mobilius Time and motion 模拟+组合数学->Polya定理1520 Scramble Sort 排序1634 Who's the boss? 排序2299 Ultra-QuickSort 排序->归并排序1008 Maya Calendar 日期处理1209 Calendar 日期处理2210 Metric Time 日期处理1430 Binary Stirling Numbers 日期处理1447 Ambiguous Dates 日期处理2080 Calendar 日期处理2351 Time Zones 时间处理1770 Special Experiment 树形DP1916 Rat Attack 数据结构->?1197 Depot 数据结构->Young T ableau1182 食物链数据结构->并查集2424 Flo's Restaurant 数据结构->堆1877 Flooded! 数据结构->堆1445 Random number 数据结构->碓1023 The Fun Number System 数论1061 青蛙的约会数论1091 跳蚤数论1152 An Easy Problem! 数论2191 Mersenne Composite Numbers 数论2381 Random Gap 数论2417 Discrete Logging 数论1510 Hares and Foxes 数论1641 Rational Approximation 数论1730 Perfect Pth Powers 数论1777 Vivian's Problem 数论2061 Pseudo-random Numbers 数论1014 Dividing 数论/DP?/组合数学->母函数?1606 Jugs 数论/搜索1995 Raising Modulo Numbers 数论->大数的幂求余2115 C Looooops 数论->解模线性方程1288 Sly Number 数论->解模线性方程组1395 Cog-Wheels 数学->解正系数的线性方程组1000 A+B Problem 送分题1003 Hangover 送分题1004 Financial Management 送分题1006 Biorhythms 送分题1007 DNA Sorting 送分题1016 Numbers That Count 送分题1019 Number Sequence 送分题1028 Web Navigation 送分题1046 Color Me Less 送分题1053 Set Me 送分题1068 Parencodings 送分题1071 Illusive Chase 送分题1096 Space Station Shielding 送分题1099 Square Ice 送分题1102 LC-Display 送分题1107 W's Cipher 送分题1119 Start Up the Startup 送分题1218 THE DRUNK JAILER 送分题1245 Programmer, Rank Thyself 送分题1247 Magnificent Meatballs 送分题1250 T anning Salon 送分题1298 The Hardest Problem Ever 送分题1326 Mileage Bank 送分题2190 ISBN 送分题2196 Specialized Four-Digit Numbers 送分题2291 Rotten Ropes 送分题2304 Combination Lock 送分题2309 BST 送分题2390 Bank Interest 送分题2403 Hay Points 送分题1411 Calling Extraterrestrial Intelligence Again 送分题1481 The Die Is Cast 送分题1484 Blowing Fuses 送分题1517 u Calculate e 送分题1547 Clay Bully 送分题1563 The Snail 送分题1604 Just the Facts 送分题1657 Distance on Chessboard 送分题1658 Eva's Problem 送分题1663 Number Steps 送分题1677 Girls' Day 送分题1690 (Your)((Term)((Project))) 送分题1775 Sum of Factorials 送分题1870 Bee Breeding 送分题2105 IP Address 送分题2136 Vertical Histogram 送分题1555 Polynomial Showdown 送分题(非常阴险) 2388 Who's in the Middle 送分题(排序)1519 Digital Roots 送分题(位数可能很大)1045 Bode Plot 送分题(用物理知识)2051 Argus 送分题(最好用堆，不用也可以过) 1011 Sticks 搜索1020 Anniversary Cake 搜索1054 The Troublesome Frog 搜索1069 The Bermuda Triangle 搜索1072 Puzzle Out 搜索1100 Dreisam Equations 搜索1110 Double Vision 搜索1111 Image Perimeters 搜索1128 Frame Stacking 搜索1142 Smith Numbers 搜索1162 Building with Blocks 搜索1183 反正切函数的应用搜索1184 聪明的打字员搜索1248 Safecracker 搜索1601 Pizza Anyone? 搜索1713 Divide et unita 搜索1129 Channel Allocation 搜索（图的最大独立集）1190 生日蛋糕搜索/DP1691 Painting A Board 搜索/DP1714 The Cave 搜索/DP1084 Square Destroyer 搜索？1010 STAMPS 搜索＋DP1194 HIDDEN CODES 搜索+DP1882 Stamps 搜索+DP1101 The Game 搜索->BFS1137 The New Villa 搜索->BFS1233 Street Crossing 搜索->BFS2243 Knight Moves 搜索->BFS2312 Battle City 搜索->BFS1476 Always On the Run 搜索->BFS1480 Optimal Programs 搜索->BFS1482 It's not a Bug, It's a Feature! 搜索->BFS 1753 Flip Game 搜索->BFS1915 Knight Moves 搜索->BFS1017 Packets 贪心1018 Communication System 贪心1323 Game Prediction 贪心1463 Strategic game 贪心1469 COURSES 贪心1719 Shooting Contest 贪心2054 Color a Tree 贪心1328 Radar Installation 贪心（差分约束系统的特例）1042 Gone Fishing 贪心/DP1752 Advertisement 贪心/图论->差分约束系统1201 Intervals 贪心/图论->最长路->差分约束系统1097 Roads Scholar 图论1161 Walls 图论1450 Gridland 图论(本来TSP问题是NP难的，但这个图比较特殊，由现成的构造方法)2197 Jill's Tour Paths 图论->2416 Return of the Jedi 图论->1639 Picnic Planning 图论->1695 Magazine Delivery 图论->1729 Jack and Jill 图论->1751 Highways 图论->1122 FDNY to the Rescue! 图论->Dijkstra1125 Stockbroker Grapevine 图论->Dijkstra1135 Domino Effect 图论->Dijkstra1394 Railroad 图论->Dijkstra1158 TRAFFIC LIGHTS 图论->Dijkstra变形2395 Out of Hay 图论->Dijkstra变形2253 Frogger 图论->Dijkstra变形(和1295是一样的)1734 Sightseeing trip 图论->Euler回路1466 Girls and Boys 图论->n/a1515 Street Directions 图论->把一个无向连通图改造成为有向强连通图1635 Subway tree systems 图论->不同表示法的二叉树判同1275 Cashier Employment 图论->差分约束系统->无负权回路的有向图的最长路->Bellman-Ford1274 The Perfect Stall 图论->二分图的最大匹配1325 Machine Schedule 图论->二分图的最大匹配2239 Selecting Courses 图论->二分图的最大匹配2195 Going Home 图论->二分图的最大权匹配2400 Supervisor, Supervisee 图论->二分图的最大权匹配?1637 Sightseeing tour 图论->欧拉回路1383 Labyrinth 图论->树的最长路1094 Sorting It All Out 图论->拓扑排序1486 Sorting Slides 图论->拓扑排序1149 PIGS 图论->网络流2289 Jamie's Contact Groups 图论->网络流?1192 最优连通子集图论->无负权回路的有向图的最长路->BellmanFord 1364 King 图论->无负权回路的有向图的最长路->BellmanFord1985 Cow Marathon 图论->有向无环图的最长路1087 A Plug for UNIX 图论->最大流1273 Drainage Ditches 图论->最大流1459 Power Network 图论->最大流1632 Vase collection 图论->最大完全图2049 Finding Nemo 图论->最短路1251 Jungle Roads 图论->最小生成树2421 Constructing Roads 图论->最小生成树1026 Cipher 组合数学1095 Trees Made to Order 组合数学2346 Lucky tickets 组合数学1286 Necklace of Beads 组合数学->Polya定理2409 Let it Bead 组合数学->Polya定理1664 放苹果组合数学->递推。

一、单选(共计50分,每题2.5分)1、卷积神经网络的激活函数是（）。

A. 阶跃函数B. S型函数C. ReLU函数D. 线性函数错误:【C】2、BP神经网络的激活函数是（）。

A. 阶跃函数B. S型函数C. ReLU函数D. 线性函数错误:【B】3、如果八数码问题的启发式函数定义为当前格局与目标格局位置不符的数码数目，请问以下当前状态的启发式函数值（）A. 3B. 4C. 4D. 6错误:【A】4、以下第一个被提出的神经元数学模型是（）。

A. M-P模型B. BP模型C. Hopfield模型D. CNN模型错误:【A】5、刘明的母亲是教师，用谓词逻辑可以表示为Teacher（mother（Liuming））这里mother（Liuming）是（）。

A. 常量B. 变元C. 函数D. 一元谓词错误:【C】6、轮盘选择方法中，适应度函数与选择概率的关系是（）。

A. 正比例相关B. 负比例相关C. 指数相关D. 不相关错误:【A】7、已知CF1(H)=-0.5 CF2(H)=0.3,请问结论H不确定性的合成CF1,,2(H)=?（）。

A. -0.2B. -0.15C. -0.8D. -0.29错误:【D】8、MYCIN系统中使用不确定推理，规则E→H由专家指定其可信度CF（H，E），若E不支持结论H为真，那么可以得到以下结论？（）。

A. CF（H，E）=0B. CF（H，E）>0C. CF（H，E）<0D. CF（H，E）=-1错误:【C】9、李明的父亲是教师，用谓词逻辑可以表示为Teacher（father（Liming））这里father（Liming）是（）。

A. 常量B. 变元C. 函数D. 一元谓词错误:【C】10、在遗传算法中，将所有妨碍适应度值高的个体产生，从而影响遗传算法正常工作的问题统称为（）。

A. 优化问题B. 迭代问题C. 功能问题D. 欺骗问题错误:【D】11、在当前人工智能领域主要使用的程序设计语言是（）。

LSTM神经网络在时间序列预测中的优化与改进时间序列预测是一项重要的任务，它在许多领域中都具有广泛的应用，如金融预测、天气预测、股票市场分析等。

LSTM（Long Short-Term Memory）神经网络是一种特殊的循环神经网络（RNN），它在处理时间序列数据时具有优秀的性能。

然而，LSTM网络也存在一些问题和局限性。

本文将探讨LSTM神经网络在时间序列预测中的优化与改进方法，以提高其性能和应用范围。

首先，我们将讨论LSTM网络中存在的问题。

传统的LSTM模型往往只考虑当前时刻的输入和前一个时刻的隐藏状态，而忽略了更早时刻的信息。

这种局限性使得传统LSTM模型无法充分捕捉到长期依赖关系。

为了解决这个问题，研究人员提出了多层LSTM模型和堆叠式LSTM 模型。

多层LSTM模型通过堆叠多个隐藏层来增加模型深度，从而提高了对长期依赖关系建模能力。

堆叠式LSTM模型则通过将多个独立训练的LSTM模型串联起来，进一步增加了模型的表达能力。

其次，我们将介绍一些LSTM网络的优化方法。

LSTM网络中的参数通常是通过反向传播算法进行训练的。

然而，传统的反向传播算法在处理长序列数据时容易出现梯度消失或梯度爆炸问题。

为了解决这个问题，研究人员提出了一些优化方法，如梯度裁剪、权重正则化和自适应学习率调整。

梯度裁剪通过限制参数更新的范围来避免梯度爆炸问题。

权重正则化则通过在损失函数中加入正则项来避免过拟合问题。

自适应学习率调整方法可以根据参数更新情况自动调整学习率，以提高训练效果。

此外，我们还将介绍一些改进的LSTM模型和技术。

为了进一步提高LSTM网络在时间序列预测中的性能，研究人员提出了一些改进模型和技术。

其中之一是双向LSTM（BLSTM）模型，在BLSTM中，输入序列可以从两个方向进行处理，并且每个时刻都可以访问到过去和未来时刻的信息，从而提高了模型的表达能力。

另一个改进是注意力机制，注意力机制可以根据输入的重要性动态地调整模型的注意力，从而更好地捕捉序列中的关键信息。