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IE 332 Homework
创建日期：2024-04-16 18:13:48
标签： IE 332
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IE 332 - Homework #1 Due: Sept 29th, 11:59pm EST Read Carefully. Important! As outlined in the course syllabus this homework is worth 9% of your final grade. The maximum attainable mark on this homework is 165. As was also outlined in the syllabus, there is a zero tolerance policy for any form of academic misconduct. The assignment can be done individually or in pairs. You must upload your homework on time for it to be graded. No late assignments will be accepted. Only the last uploaded version of your assignment will be graded. NOTE: You should aim to submit no later than 30 minutes before the deadline, as there could be last minute network traffic that would cause your assignment to be late, resulting in a grade of zero. You must use the provided LATEX template on Brightspace to submit your assignment. No exceptions. Page i of i IE 332 Homework #1 Due: Sept 29 2021 1. This question is meant to reinforce your understanding of how a CPU executes program code by focusing on the low-level instructions it executes, versus higher-level instructions you would use in a programming language such as R. You will use the hypothetical assembly language outlined below in Table 1, in addition to 10 registers referred to by $r0, . . . ,$r15, and system RAM as needed. instruction meaning example add reg1, reg2, reg3 reg1 = reg2 + reg3 add $r0, $r1, $r2 sub reg1, reg2, reg3 reg1 = reg2− reg3 sub $r0, $r1, $r2 div reg1, reg2, reg3 reg1 = reg2/reg3 div $r0, $r1, $r2 divi reg1, reg2, reg3 reg1 = reg2/reg3, truncates fractional values divi $r0, $r1, $r2 mul reg1, reg2, reg3 reg1 = reg2 ∗ reg3 mul $r0, $r1, $r2 muli reg1, reg2, x reg1 = reg2 ∗ x, where x is some integer mul $r0, $r1, 4 addi reg1, reg2, x reg1 = reg2 + x, where x is some integer addi $r0, $r1, 5 subi reg1, reg2, x reg1 = reg2− x, where x is some integer subi $r0, $r1, 5 divr reg1, reg2, x reg1 = reg2/x, where x is real, truncates result divr $r0, $r1, 2 mod reg1, reg2, reg3 reg1 = reg2 mod reg3 mod $r0, $r1, $r2 mov reg1, reg2 reg1 = reg2 mov $r0, $r1 label: create a reference label in the code main: name: .type, value create .type variable in RAM where name = value var1: .word 5 lw reg, RAM_source move word from RAM to a register lw $r4, var1 sw reg, RAM_source move word from register to RAM sw $r4, var1 la reg, RAM_source move address of RAM to a register la $r4, var1 sa reg, RAM_source move address in register to RAM sa $r4,var1 b label jump to a label in the program b main beq reg1,reg2,label jump to label if reg1 = reg2 beq $r0,$r1,main blt reg1,reg2,label jump to label if reg1 < reg2 blt $r0,$r1,main bgt reg1,reg2,label jump to label if reg1 > reg2 bgt $r0,$r1,main bqe reg1,reg2,label jump to label if reg1 ≥ reg2 bqe $r0,$r1,main ble reg1,reg2,label jump to label if reg1 ≤ reg2 ble $r0,$r1,main bne reg1,reg2,label jump to label if reg1 ̸= reg2 bne $r0,$r1,main print reg print contents of register to screen print $r0 prints reg print string pointed to in register to screen prints $r0 read reg get keyboard input (after ENTER pressed); store in reg read $r0 .wordspace size allocates mory of size integers, all initialized to zero arr: .wordspace 10 done end of program Table 1: Hypothetical assembly language *NOTE: for lw if RAM_source is an integer instead of a memory address, or reg1 and/or reg2 in beq, blt, bgt, bge,ble, bne, then it will be automatically interpreted as such. For instance, lw $r1, 4, will be an equivalent instruction to setting $r1=4. Also, potential variable types include .word (for integers or floats), .bit (for bits), .asciiz (for strings/character arrays - noting that each character has an associated bit pattern and can be interpreted as an integer as well). Furthermore, a sequence of comma separated integers is accepted as valid input, allowing you to create integer arrays, e.g., arr: .asciiz 10,13,12. Arrays are indexed from 1, and accessing a value from an array is done by referring to the RAM_source as array_name[index] (e.g., if loading an array value, use lw $r1, A[1] where A is the array name). The size of the array is stored at position 0, (e.g. A[0]). Ex. computing the first n Fibonacci numbers (Fn = Fn−1 + Fn−2 for n > 0, F1 = 1 and F2 = 1): string1: .asciiz “The result is: ” value: .word 0 main: read $r9 ble $r9, 0, end lw $r0, value addi $r0, $r0, 1 beq $r9, 1, end mov $r2, $r0 mov $r1, $r2 lw $r8, 1 loop: add $r0, $r1, $r2 mov $r2, $r1 mov $r1, $r0 addi $r8, $r8, 1 beq $r9, $r8, end b loop end: sw $r0, value la $r7, string1 prints $r7 print $r0 done (a) (20 points) Translate the following C program into assembly instructions without adding personal insight or design modifications - translate it in a way that a compiler would. When submitting your results show a table with two columns: (1) the original C program, (2) your assembly code. You can increase the page margins or reduce font size to 10pt to improve readability, if needed. You do not have to create assembly code for printf (replace directly with assembly instruction). Do NOT debug the C code. HINTS: (1) start your translation from main(), not line 1. (2) consider negation of conditional statements. 1 double findOddEven ( in t arr [ ] , s i z e_t arr_len ){ 2 i n t odds [ arr_len / 2 ] ; i n t evens [ arr_len / 2 ] ; // Odd and Even numbers 3 i n t counterOdd = 0 , counterEven = 0 ; 4 f o r ( in t i = 0 ; i < arr_len ; i++ ){ 5 i f ( arr [ i ] % 2 == 0){ 6 evens [ counterEven ] = arr [ i ] ; counterEven += 1; 7 } e l s e { 8 odds [ counterOdd ] = arr [ i ] ; counterOdd += 1; 9 } 10 } 11 p r i n t f ( ”The odd array = ” ) ; 12 f o r ( in t i = 0 ; i < counterOdd ; i++ ){ p r i n t f ( ”%d\t ” , odds [ i ] ) ; } 13 p r i n t f ( ”The even array = ” ) ; 14 f o r ( in t i = 0 ; i < counterEven ; i++ ){ p r i n t f ( ”%d\t ” , evens [ i ] ) ; } 15 16 return counterOdd/CounterEven ; 17 } 18 i n t main ( ) { 19 i n t arr [ ] = {1 , 2 , 3 , 4 , 5 , 6} ; 20 i n t arr_len = s i z e o f ( arr ) / s i z e o f ( arr [ 0 ] ) ; 21 double d = findOddEven ( arr , arr_len ) ; 22 d = d + 2 ∗ d 23 p r i n t f ( ”%d” ,d) ; 24 return 0 ; 25 } IE 332 Homework #1 Page 2 of 10 (b) (4 points) Provide pseudocode for the given C program. Be mindful of the balance between too little and too much detail. That is focus on conveying the idea of what is being done, not necessarily how it is done in C! (c) (4 points) Convert the given C code to equivalent but fewest lines of R code to print the same result. Use existing R function(s) or you will lose points. Do not line-by-line convert the C code! You should need no more than 7 lines of R code. (d) Suppose that the C algorithm is re-executed for an arr[] of odd length. i. (5 points) Alter the C code, if needed, to accommodate this change and yield accurate output. If not needed, argue why. ii. (5 points) Re-translate the C code from (i), if any changes to it were made. If no changes are required argue why. iii. (5 points) Provide a tight bound for the worst-case runtime and space complexity of the original C code. Briefly, but sufficiently, justify your answers. IE 332 Homework #1 Page 3 of 10 2. Divide and conquer. After every snow at Purdue, n Purdue staff members apply salt to k campus sidewalks. Suppose we have a sorted (in increasing order) array T = [t1, t2, . . . , tk] where ti is the amount of time needed to apply salt to sidewalk i, i = 1, . . . , k, and that each staff member can only salt sidewalks that are of consecutive numbers (e.g., sidewalks 1, 2 and 3, but not 1 and 3). Also, each sidewalk can be salted by only one staff member. Purdue is seeking a solution to salt all the sidewalks such that the maximum time any staff member is outside salting is minimized, and have assigned you to solve the problem for them. After much thought you have decided to apply the below-sketched modification to the iterative binary search algorithm (it may help to draw a picture to visualize the process using an example T): 1. if the number of sidewalks is less than the number of staff members then the problem is trivially solved as the largest value in T ; otherwise, it is not trivial and you need find the minimum value in [0,∑i ti]. 2. The remainder of the algorithm is very similar to that in lecture 9 slide 25, noting instead of testing if x < A[m] or not, you will be testing whether there is an allocation of k sidewalks among n members of staff using the isFeasible(T, n, x) function provided in part (b). 

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MOEC0021 STA 106 ENGG 1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A PHIL2617 PHYS3116 MIE250 BCPM0008 ECN 620 QBUS6830 ECSE-415 ECON5102 MGMT20005 MAT 653 ECO 480 COMP 5/600 CSSE 5600 ME 571 7CCMMS61 CS 550 COMP2865 MATH3075 STATS 506 QTM 220 ISYS2120 FIT5106 STAT 153 MKTG3112 ECON2102 ELE2018 COMP3031 MSIN0010 SCC461 MATH237 CS246 CSC3065 CSE 101 ICTWEB411 COMP9313 ECOS 2025 FN620 MATH11111 MATH 3018 KE1068 FINA 6112 C++ MISM 6202 MSIN0105 CSC8631 MECO6935 COMP4121 ACCT2011 DPBS1150 EEL 3701C F19PL OPM 661 CSE 310 CS918 BIOL30001 ACCT3563 BANK3600 MET CS622 MATH367 ACCT5907 Continuing COMP5048 COMP61021 CS3334 GSOE9210 CSCI-570 COMP 5322 HW 2 ALY-6020 IEOR 4706 DATA 200 EBUS504 CGE12412 COMP4108 7SSMM800 ECMM171P MATE50002 CS225 RS 6003 BH2274 ELEC3111 MAT6669 ECON-UA 227 PHIL 1012 7SSMM603 TB028A P6 ECS708 CSC 427 CS6476 CSE 250A A1A2 ITS61504 EECS 376 model HW6 UV0010 ECON 6074 MG4F7 CMP-7030Y INFO3008 BFIP013 ECON 5068 MATH6002 CS3483 PSTAT 131 C31FM CSOR W4246 AAEC 5307 DATA ELEC362 COMSM0047 ECN6006 MA20224 BST351 MATH 323 MATH323 AA2021 COMP3811 COMP2013 IB9X60 INVP001 EMATM0051 COMP220 BLAW1002 E20 TCP8001 ECON61001 EART40005 ECONM1022 MATH 365 MATH 367 ELEC6218 COMP 5812M EDUC 5061M ELEC ENG 1101 equation MATH6174 ST334 C4 EC9570 A33648 EBUS603 ECON47815 stata WFMS0001 PEM102 INF6060 ionically ELECTRICAL MATH 375 MMW 12 MKTG860 ECON60401 ALY6010 SOST20131 Introduction COM3524 MME2 GGR305 JNB 538 EECS101 COMM5030 IEOR E4601 2B CSC336 EN2315 LAW 432 CSC263 MATH2001 OLET1143 CSCB63 SIT772 COMM1170 STAT 441 MS930 INFT3050 GLBH0030 Stat 120B MAST10007 MGEC61 Machine GGR 252H1S ECON7030 Financial Marketing MGMT30019 ECON5120 SDSC 8009 CSC165H1S DSCI 551 3081W ACM41000 ECA 5304 MATH 1064 ECSE444 DATA 604 COMP7105 MIE1615 ECON4004 ENV200H1S EC481 MKT 306 EC1B1 MATH08051 ALY6140 CS260C CSE30 MSIN0226 CS4103 CSC3064 AM16 COMP11212 CSE4101 PSTAT 174 Math 380W CNT 5106C STAT 310 FIN2028 CS5014 STAT 425 COMP 4102A ELEC2140 MANF9544 QRM 9 QRM 8 ECON 457 COMPSCI 4091 MATH 523 DNSC-4211 PEAS 6000 MSIN0180 COMP2119 A2A HT 2022 IB93F0 MAS316/414 ACCT2522 MSIN0181 ATMS 201 COMP3425 MATH7861 SOLA2060 MA 325 7CCEMCTH ECON 432 INFT2051 SOLA 2060 ECOS2002 Stats141XP BIOA02H3 S2022 MA4601 K5 COMP5329 EG 284 IB3A70 WECO1020 COMP3027 Energy ACS61011 MAST20026 STAT 533 MATA31 ENVS257 BEM2031 EC 486 COMP0172 CS3214 EECE5644 IB2B20 COSC2536 COSC1147 COMP6214 5CCM242A COMP0130 AMME2000 MTMG50: EG238 ACF6006 QBUS2810 COSC2391 ECON7560 MATH377 STA305 CS 486 COMP1117B EL648 ELEC3909 ECON 241 COMP 4901W BUSI4428 ENEN20002 ENGN4524 ELEC3115 CSC 413 PSYC 100B ECON1002 MATH256 ANSC20005 MTHS2008 MATH40082 COSC 2406 FIT3174 STA 238 CMT202 Differential Equations MTHM017 GARCH 101 MATH2069 CSC336S ACSC12 ETF2121 CEME 2001 DB B474F ARHT1001 EECS 3311 3220 STATS 786 CS 484 COMP20008 MATH4091 ECE 455 CSCI 204 BUS B200F BA 875 BU5562 COSC 1147 X11 GEOG 101 IMM250F CSE 584A MATH38172 LAB 4 ELEC5882M FINS5523 EE 430 COMP 465 6CCS3PRE 7CCSMNSE FINANCE ACMB02H3 ENGG2112 ELEC5616 SCM B371 CHEM3120 CS22 ECMT2130 MAST30011 ADSPBF706 CENG0013 ACCOUNTING BUSS1040 CHEM 181 MAT136H1 GY 6183 COMP3170 AGRI90089 PHYSICS 1002 ECON10003 IEOR E4004 ACS61012 MATH 40550 MKTG2113 TELE4653 ENSC1004 ECE 232E MK726 MTRX2700 SHEET 3 CSCA08 COMP30027 Math 2XX3 statistic MMAN3200 BISM7213 ECMM109 ECON 2022 FNCE 20005 GR5067 CSCB09 ME 3017 CS 5100 PHYS 2903 COMS 4771 COMP222 COMP 1046 CSC148H1 ISYS2038 FINS2615 OT5206 COMP2048 A6 MECH5770M MA826/20 CMPT 726 STA457 INFS6071 INFS588 integral ECON 216 IRDR 0017 MA323 PA 15213 PSYC2001 ENV222 Statistics ACCT5930 ACCT12 LAND2121 ME 5405 COMM1180 TELE3113 A7 ECE 568 ACCT2019 INFS1200 ENGG1340 CS 1400 ASST3 FINM7409 SWEN30006 INFO2222 FIN20150 SOSS1000 CSSE7231 FINS5513 COMS3200 CECN 702 ECON4060H MN3515 HW2 PSYA02H3 ECON 2112 COMP90051 CS 1652 MA30059 AF1605 MKTG7501 ECO-6003B COM4521 CTM ECON3350 COMP 3804 ELEC9762 BISM 7255 ST22 MATH20014 MNE3122 COMP343 MATH5165 ELE7029 ENGR30002 SEEM3500 ECON7350 RISK5002 FINM7405 COMP90059 MOS 3320B STAT 431 BISM7221 MATH3014 MTH783P EBA 35302 ACS133 BUS2206 IE5600 ECOS 3997 EDST2003 FIN 534 Elec4430 MATS3001 MGT6047 FINS5514 MIS602 ATS1279 ECMM445 2F CS262 EFIMM0097 FINM2002 ECMT3150 FINC5090 WACC1000 MECH4620 ECOS 2002 SEESGS79 STAT COMP3007 BUSB200F ACST8040 CAES9920 STAT0020 INFR11205 PHYS2111 FINM7402 STAT 428 SOFT3202 ME220 ACC-ACF2100 EC9410 CSE 120 COMP90042 SEE5211 ECON0048 BUSN2036 MKT2010 3SMFE4 EFIMM0117 ECON3034 MTH5120 EFIMM0120 X0 W19186 MATH 034 COMP2100 COMS4104 CS1210 MENG10005 ACCT 5906 ECMT1020 MGTS7607 MATH3090 CIV4100 CSYS5020 ELE2019 PHS4200 ACS6124 MSIN0225 PHAS0061 6CCS3BIM FINM7403 COMP8410 PY406 COMP2620 CS226 SDEV2004 COMP6080 BFF1001 HR410 MCEN30017 AMS3328 ML3 ELE8059 FINC3017 ACAD001 FTEC2101 ES480 3D ELECTENG 734 MTH731U MATH-UA 251 CSCI-UA 9473 A2 MSDM5058 FIT5047 COM6012 1FIN B386F MPHY202P ACCT6003 ECE 6913 HMB312H1 AC1025 MTH6105 Math6168 FINM 3003 CS24320 PHYS2134 ACCT3011 MECH1400 COMP30024 ENGGEN 121 COMP3721 MCD2080 ECON 7002 MAS439 COMP6216 ECON2011 M23367 CSC597 COMP6247 BRIEF QBUS6180 EENG22000 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