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CSC 373 Dynamic Programming
创建日期：2024-06-27 17:14:12
标签： CSC 373
Dynamic Programming

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CSC 373 Dynamic Programming


Required filename for MarkUs submission: a2.pdf

Remember to write the full name and MarkUs username of every group member (up to three) prominently on your submission.

Please read and understand the policy on Collaboration given on the Course Information Sheet. Then, to protect yourself, list on the front of your submission every source of information you used to complete this homework (other than your own lecture and tutorial notes). For example, indicate clearly the name of every student from another group with whom you had discussions, the title and sections of every textbook you consulted (including the course textbook), the source of every web document you used (including documents from the course webpage), etc.

For each question, please write up detailed answers carefully. Make sure that you use notation and terminology correctly, and that you explain and justify what you are doing. Marks will be deducted for incorrect or ambiguous use of notation and terminology, and for making incorrect, unjustified, ambiguous, or vague claims in your solutions.

For every problem, give a Dynamic Programming solution, following the steps outlined in class. Don’t forget to justify that your recurrence relation is correct based on the recursive structure of the problem, and to analyze the time complexity of your final algorithm.

1. Riding a bicycle in Toronto

Suppose the streets in some section of Toronto are modelled as a simple grid, and you want to travel from the lower-left corner (coordinate (0,0)) to the upper-right corner (coordinate (m,n)). Further, to simplify the problem, suppose that every street is one-way so you can only travel right or up (never left and never down).

But riding a bicycle in Toronto is dangerous! So every street segment has a probability that riding on that segment will result in an accident. Let p i,j be the probability that riding right from coordinate (i − 1,j) to (i,j) results in an accident, and q i,j be the probability that riding up from coordinate (i,j − 1) to (i,j) results in an accident. As usual, all probabilities are real numbers in the interval [0,1]. The probability that you have no accident on a path is simply the product of the probabilities that you have no accident on each street segment of the path.

Your goal is to find a path from (0,0) to (m,n) with the maximum probability of having no accident.

2. Study group lunch

Suppose you want to buy B burgers, C fries, and D drinks at your favourite fast-food place, for a study group you’re organizing (this question is most certainly not about good eating habits)! The unit price of each item is p b (for burgers), p c (for fries), and p d (for drinks). You also own n coupons N 1 ,…,N n . Each coupon N i is a combo that offers you b i burgers, c i fries, and d i drinks at price p i . Each coupon can only be used at most once. Note: All values are natural numbers, which means some of them could be equal to zero (e.g., it’s possible for a coupon to offer a deal that includes only drinks and fries, but no burger; it’s also possible for a coupon to offer more burgers, or fries, or drinks than you need).

What is the minimum amount of money you need to pay to get at least B burgers, C fries, and D drinks? It’s okay if you end up with more food (or drinks) than you need.

3. Homework planning

You have n assignments A 1 ,…,A n where A i = (p i ,t i ), p i ∈ Z + is the number of points earned if you complete the assignment, and t i ∈ R + is the time required to complete the assignment. You also have a total time T ∈ R + available to complete all the assignments.

Find a subset of assignments that you can complete within your time limit and that maximizes the total number of points obtained. (Note: you cannot use arbitrary real numbers as array indices.)


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关键词一 关键词二 关键词三 关键词四 关键词五 和法规和的发更好的风格和 ECON 615 FINC 612 CSC148 COMP 639 ACCT 203 ACCT 211 PSYC 101 MTH2009 COMP52315 PSYCO 432 statistics MATH4063 11 xxx 1 MA1MSP MAST30028 MATH3888 CS341 EEE30002 ES2F5 MCD4160 CC0933 ECON 1101 MCHM3001 CHEM3118 COMMGMT 2511 COMP41280 STAT 631 24T1 IRE379 SENG365 ECON433 FIT3139 MATH4602 LING5621M FINS5516 ECON3208 MN2177 L2 SM EEET1415 Finance DS4023 COMP3004 7CCSMRTS K1S5B6 Stat230 CSCI4211 CSI2132 ECON30130 MAS6100 ENVS222 COM2107 INFO1112 STAT 4004 FIT2100 comp2022 COMP4691 Physics 307 Econ 659 probability CSCI316 fir29 CSCI203 COMP3160 COMP6714 INFO1113 Physics 7B Physics Photonics S203031 STAT2005 COMP90015 CSCI 2110 CSCC46 Information CSC477 COMP4650 Statistical COMP 346 COMP1017 ELEC340 MATH1007 Programming function STAT 244 CS 134 Java cse13s Math 108A FW20 ECON3389 CSE 130 Science 331 COMP9020 engineering COSC 445 CSE 5523 GAME2012 visualization MATH 235 Math 370 CSC343 COGS 108 EE524 COMP10200 STAT 416 3FK4 MSCI 311 ECON6113 ACC40700 EMESTER1 MAS8383 ECO 512 STAT 8310 CMN3102 MA577 CMPT 225 COMP0045 Methods Equations MATH 113 Math 3283W ICS-33 EN4302/ENT603 BIA B350F MA318 MTHM506 MECH 5315M ECONOMICS MAS8382 COM 2004 PX3142 XJEL 3662 STAT 231 MGT B399F PX4131 COM2108 30AM MSCI521 ECONM1015 ACFI304 GR5241 MATH10101 ECON 2070 COMS31900 EFIM20011 CSE 250B ACSE-5 STAT4207 SOFT2412 ELEC 331 AY2020 MSIN0209 FIT2094 CS 241L ST404 CS 411 3D CA3 INF4002 COMP3506 SIT718 CS 188 CS 170 MATH 138 CSE 251A CMT118 DATA5207 CMPT307 CMPT459 T1 PGEE11108 COSC 3P32 ME 163 MATH96007 7QQMM203 EE6227 BA 574 STA 4234 ECO206Y1Y ECO2008 MT2300 MATH 11158 CS 527 MACM 316 CSE474 2DI70 ISE 525 COMP3411 EMAT30007 7CCSMBDT MFIN704 MFIN704W21 MfIB ECE 438 CS 436 F36 CS5344 FE 621A FE621 TBA 612 ECM3151 ECMM422 MF1 MSIN0107 ESSMENT CS 5854 MFIT 5008 MIPS R4000 ENG5274 BU52018 ENG2079 BIOA02 STA2570 F0 INF553 STAT 440 STAT3008 COMP9417 COMP6451 6COM1042 BU52006 ST303 HW-1 CISC-235 CS 510 MATH3161 ECN 140 ECE391 Comp 3613 CVEN 9625 PRG455 UESTION 1 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