CSCI 3110 Dalhousie Discrepancy Between a Map & the Adjacency Lists Project

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FM1998

Computer Science

CSCI 3110

Dalhousie University

CSCI

Description

This assignment is unusually short so that it can be completed,marked and returned before the deadlineto drop courses without academic penalty. It may seem pretty hard at first,but the trick is not to giveup, break things down into sub-problems, and think about whether you can solve each sub-problem (andpay attention to overflow!). .You should submit your code, in whatever programming language you can convince the TAs and markers toaccept. Good luck!

1.Use divide-and-conquer to count the valid 4-colourings of the map shown in Figure 1.(Apologies toNew Zealand and Antarctica!) In this case, let 's say a valid 4-colouring is an assignment of the coloursred, green,yellow and purple to the regions of the map (ignore water and the current colours) suchthat no two regions assigned the same colour share a border of positive length (they can touch at apoint) or have a line drawn between them. The adjacency-list representation of the correspondinggraph (with the vertices names A1 through F4) is on the back of this sheet and will be posted as a textfile on Brightspace. If you find a discrepancy between the map and the adjacency lists, please emailTravis as soon as possible!

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CSCI 3110 Assignment 1 posted: 05.05.2021 due: midnight 14.05.2021 Instructor: Travis Gagie You can work in groups of up to three people. One group member should submit a copy of the solutions on Brightspace, with all members’ names and banner numbers on it; the other group members should submit text files with all members’ names and banner numbers (otherwise Brightspace won’t let us assign them marks!). You may consult with other people but each group should understand the solutions: after discussions with people outside the groups, discard any notes and do something unrelated for an hour before writing up your solutions; it’s a problem if no one in a group can explain one of their answer. For programming questions you should submit your code, which should compile and run correctly to receive full marks. This assignment is unusually short so that it can be completed, marked and returned before the deadline to drop courses without academic penalty. It may seem pretty hard at first, but the trick is not to give up, break things down into sub-problems, and think about whether you can solve each sub-problem (and pay attention to overflow!). There is an optional tutorial on Friday to help you and two TA office hours next week, but the tutorial next week — on the day when this is due — will be for the next homework. You should submit your code, in whatever programming language you can convince the TAs and markers to accept. Good luck! 1. Use divide-and-conquer to count the valid 4-colourings of the map shown in Figure 1. (Apologies to New Zealand and Antarctica!) In this case, let’s say a valid 4-colouring is an assignment of the colours red, green, yellow and purple to the regions of the map (ignore water and the current colours) such that no two regions assigned the same colour share a border of positive length (they can touch at a point) or have a line drawn between them. The adjacency-list representation of the corresponding graph (with the vertices names A1 through F4) is on the back of this sheet and will be posted as a text file on Brightspace. If you find a discrepancy between the map and the adjacency lists, please email Travis as soon as possible! Figure 1: How many ways can this map be 4-coloured? 1 A1: A2: A3: A4: A5: A6: A2, A1, A2, A2, A1, A1, A5, A3, A5, A6 A2, A2, A6 A4, A5, A6, B7 B7, D5 A3, D5, D7, F2 A4 B1: B2, B3, B7, B11, D6 B2: B1, B3, B8, B9, B10, B11 B3: B1, B2, B7, B9 B4: B6, B8, B10, B12 B5: B6, B8 B6: B4, B5, B8, B12, E1 B7: A2, A3, B1, B3, D5, D6 B8: B2, B4, B5, B6, B10 B9: B2, B3, C2 B10: B2, B4, B8, B11, B12 B11: B1, B2, B10, D6 B12: B4, B6, B10 C1: C2: C3: C4: C3, B9, C1, C1, C4 C3, C4 C2, C4 C2, C3 D1: D2: D3: D4: D5: D6: D7: D2, D1, D1, D1, A3, B1, A5, D3, D4, D4, D2, A5, B7, D1, D4, D7 E5 D5, D6, D7 D3, D6 B7, D3, D6, D7 B11, D3, D4, D5 D3, D5 E1: E2: E3: E4: E5: E6: E7: E8: E9: B6, E1, E4, E3, D2, E1, E2, E4, E2, E2, E6, E9, E7, E6, E2, E4, E5, E3, E6 E7, F4 E8, E7, E5, E5, E7 E4, F1: F2: F3: F4: F2, A5, F1, E3, F3 F1, F3, F4 F2, F4 F2, F3 E9 E9 E8 E7 E6, E8, E9 E7 2 A1: A2, A5, A6 A2: A1, A3, A4, A5, A6, B7 A3: A2, A5, B7, D5 A4: A2, A6 A5: A1, A2, A3, D5, D7, F2 A6: A1, A2, A4 B1: B2, B3, B7, B11, D6 B2: B1, B3, B8, B9, B10, B11 B3: B1, B2, B7, B9 B4: B6, B8, B10, B12 B5: B6, B8 B6: B4, B5, B8, B12, E1 B7: A2, A3, B1, B3, D5, D6 B8: B2, B4, B5, B6, B10 B9: B2, B3, C2 B10: B2, B4, B8, B11, B12 B11: B1, B2, B10, D6 B12: B4, B6, B10 C1: C3, C4 C2: B9, C3, C4 C3: C1, C2, C4 C4: C1, C2, C3 D1: D2, D3, D4, D7 D2: D1, D4, E5 D3: D1, D4, D5, D6, D7 D4: D1, D2, D3, D6 D5: A3, A5, B7, D3, D6, D7 D6: B1, B7, B11, D3, D4, D5 D7: A5, D1, D3, D5 E1: B6, E2, E6 E2: E1, E6, E7, E9 E3: E4, E9, F4 E4: E3, E7, E8, E9 E5: D2, E6, E7, E8 E6: E1, E2, E5, E7 E7: E2, E4, E5, E6, E8, E9 E8: E4, E5, E7 E9: E2, E3, E4, E7 F1: F2, F3 F2: A5, F1, F3, F4 F3: F1, F2, F4 F4: E3, F2, F3 1 1
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