### Introduction

作业Python | 算法代做 | 程序代做 | assignment代写 – 本题是一个利用Python进行练习的代做, 对Python编程的流程进行训练解析, 是比较有代表性的Python等代写方向，涉及了一些算法问题

In this project, you will implement some new constraints and backtracking search algorithms.

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Files you'll edit:
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```
backtracki
ng.py
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Where all of the code related to backtracking search is located. You will
implement forward checking and gac search in this file.
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```
csp_proble
ms.py
```

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Where all of the code related implementing different CSP problems is
located. You will implement a new version of the nQueens CSP and a
CSP to solve the plane scheduling problem in this file.
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```
constraint
s.py
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Where all of the code related implementing various constraints is
located. You will implement the NValues constraint in this file.
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Files you can ignore:
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```
csp.py
File containing the definitions of Variables, Constraints, and CSP
classes.
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util.py Some basic utility functions.
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nqueens.py Solve nQueens problems.
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sudoku.py Solve sudoku problems.
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```
plane_sche
duling.py
Solve plane scheduling problems.
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autograder
.py
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Program for evaluating your solutions. As always your solution might
also be evaluated with additional tests besides those performed by the
autograder.
```

**Files to Edit and Submit:** You will fill in portions of backtraking.py, csp.py, and csp_problems.py during the assignment. You may also add other functions and code to these file so as to create a modular implementation. You will submit these file with your modifications. Please *do not* change the other files in this distribution.

**Evaluation:** Your code will be autograded for technical correctness. The tests in autograder.py will be run. Please *do not* change the names of any provided functions or classes within the code, or you will wreak havoc on the autograder.

### What to Submit

You will be using MarkUs to submit your assignment. You will submit three files:

- Your modified backtracking.py
- Your modified csp_problems.py
- Your modified constraints.py

### AutoGrader

autograder.py is not the same as the Berkeley autograder. You can only run the command

Python autograder.py -q qn

where qn is one of q1, q2, q3, q4, or q5. Or you can run the grader on all questions together with the command

python autograder.py

### CSPs

### Question 1 (4 points): Implementing a Table Constraint

backtracking.py already contains an implementation of BT (plain backtracking search) while csp_problems.pycontains an implementation of the nQueens problem. Try running

python nqueens.py 8

to solve the 8 queens problem using BT. If you run

python nqueens.py -c 8

the program will find all solutions to the 8-Queens problem. Try

python nqueens.py –help

to see the other arguments you can use. (However, you haven’t implemented FC nor GAC yet, so you can’t use these algorithms yet.) Try some different small numbers with the ‘-c’ option, to see how the number of solutions grows with the number of Queens. Also observe that even numbered queens are generally faster to solve, and the time to find a single solution for ‘BT’ grows quite quickly. Observe the number of nodes explored. Later once you have FC and GAC implemented you will see that they explore fewer nodes.

For this question look at constraint.py. There you will find the class QueensTableConstraint that you have to implement for this question. This class creates a table constraint to capture the nQueens constraint. Once you have that implemented you can run

python nqueens.py -t 8

to solve the nQueens CSP using your table constraint implementation. Check a number of sizes and ‘-c’ options: you should get the same solutions returned irrespective of whether or not you use ‘-t’. That is, your table constraint should yield the same behavior as the original QueensConstraint

### Question 2 (5 points): Forward Checking

In backtracking.py you will find the unfinished function FC. You have to complete this function. Note that the essential subroutine FCCheck has already been implemented for you. Note that your implementation must deal correctly with finding one or all solutions. Check how this is done in the already implemented BT algorithm…just be sure that you restore all pruned values even if FC is terminating after one solution.

After implementing FC you will be able to run

python nqueens.py -a FC 8

to solve 8-Queens with forward checking. Solve some different sizes and check how the number of nodes explored differs from when BT is used.

Also try solving sudoku using the command

python sudoku.py 1

Which will solve board #1 using Forward Checking. Try other boards (1 to 7). Use

python sudoku.py –help

to see the other arguments you can use.

Also try

python sudoku.py -a ‘BT’ 1

to see how BT performs compared to FC. Finally try

python sudoku.py -a ‘FC’ -c 1

To find all solutions using FC. Check if any of the boards 1-7 have more than one solution.

Note also that if you have a sudoku board you would like to solve, you can easily add it into sudoku.py and solve it. Look at the code in this file to see how input boards are formatted and placed in the list boards. Once a new board is added to the list boards it can be solved with the command python sudoku.py -a ‘FC’ k where k is the position of the new board in the list boards

### Question 3 (7 points): GacEnforce and GAC

In backtracking.py you will find unfinished GacEnforce and GAC routines. Complete these functions.

After finishing these routines you will be able to run

python nqueens.py -a GAC 8

Try different numbers of Queens and see how the number of nodes explored differs from when you run FC.

Does GAC also take less time than FC on sudoku? What about on nqueens?

Now try running

python sudoku.py -e 1

which will not do any backtracking search, it will only run GacEnforce at the root.

Try running only GacEnforce on each board to see which ones are solved by only doing GacEnforce.

### Question 4 (2 points): AllDiff for Sudoku

In csp_problems.py you will find the function sudokuCSP. This function takes a model parameter that is either ‘neq’ or ‘alldiff’. When model == ‘neq’ the returned CSP contains many binary not-equals constraints. But when model == ‘alldiff’ the model should contain 27 allDifferent constraints. Complete the implementation of sudokuCSP so it properly handles the case when model == ‘alldiff’ using allDifferent constraints instead of binary not-equals.

Note that this question is **very easy** as you can use the class AllDiffConstraint(Constraint) that is already implemented in constraints.py. However, you must successfully complete Question 3 to get any marks on this question.

### Question 5 (4 points): NValues Constraint

The NValues Constraint is a constraint over a set of variables that places a lower and an upper bound on the number of those variables taking on value from a specified set of values. In constraints.py you will find an incomplete implementation of class NValuesConstraint. In particular, the function hasSupport has not yet been implemented. Complete this implementation.

### Question 6 (10 points): Plane Scheduling

Implement a solver for the following plane scheduling problem by encoding the problem as a CSP and using your already developed code to find solutions.

You have a set of planes, and a set of flights each of which needs to be flown by some plane. The task is to assign to each plane a sequence of flights so that:

- Each plane is only assigned flights that it is capable of flying (e.g., small planes cannot fly trans-Atlantic flights).
- Each plane’s initial flight can only be a flight departing from that plane’s initial location.
- The sequence of flights flown by every plane must be feasible. That is, if F2 follows F1 in a plane’s sequence of flights then it must be that F2 can follow F1 (normally this would mean that F1 arrives at the same location that F2 departs).
- Certain flights terminate at a maintenance location. All planes must be serviced with a certain minimum frequency. If this minimum frequency is K then in the sequence of flights assigned to a plane at least one out every subsequence of K flights must be a flight

```
terminating at a maintenance location. Note that if a plane is only assigned J flights with J
< K, then it satisfies this constraint.
```

- Each flight must be scheduled (be part of some plane’s sequence of flights). And no flight can be scheduled more than once.
**Example**Say we have two planes AC-1 and AC-2, and 5 flights AC001, AC002, AC003, AC004, and AC005. Further: - AC-1 can fly any of these flights while AC-2 cannot fly AC003 (but can fly the others).
- AC-1 can start with flight AC001, while AC-2 can start with AC004 or AC005.
- AC002 can follow AC001, AC003 can follow AC002, and AC001 can follow AC (these form a one-way circuit since we can’t, e.g., fly AC003 first then AC002). In addition, AC004 can follow AC003, AC005 can follow AC004, and AC004 can follow AC005.
- AC003 and AC005 end at a maintenance location.
- The minimum maintenance frequency is 3. In this case a legal solution would be for AC-1’s schedule to be the sequence of flights [AC001, AC002, AC003, AC004] while AC-2’s schedule is [AC005] (notice that for AC-1 every subsequence of size 3 at least one flight ends at a maintenance location). Another legal schedule would be for AC-1 to fly [AC001, AC002, AC003, AC004, AC005] and AC-2 to fly [] (i.e., AC- does do any flights). Your task is to take a problem instance, where information like that given in the above example is specified, and build a CSP representation of the problem. You then solve the CSP using any of the search algorithms, and from the solution extract a legal schedule for each plane. Note that the set of constraints you have (and have built in the previous questions) are sufficient to model this problem (but feel free to implement further constraints if you need them for the CSP model you develop).

See plane_scheduling.py for the details of how problem instances are specified; csp_problems.py contains the class PlaneProblem for holding a specific problem.

You are to complete the implementation of solve_planes in the file csp_problems.py. This function takes a PlaneProblem, constructs a CSP, solves that CSP with backtracking search, converts the solutions of the CSP into the required format (see the solve_planes starter code for a specification of the output format) and then returns the solutions.

You can also test your code with plane_scheduling.py. The command

python plane_scheduling.py -a GAC -c K

where K is the problem number, will invoke your code (from csp_problems.py) on the specified problem. (Use python plane_scheduling.py –help for further information). It can be particularly useful to test your code on problems 1-4 as these problems only test one of the constraints you have to satisfy.

**A Few Hints:**

First you should decide on the variables and the domain of values for these variables that you want to use in your CSP model. You should design your variables so that it makes it easy to check the constraints. Avoid variables that require an exponential number of values: performing GAC on such constraints will be too expensive. A number of values equal to the number of flights times number of planes values would be ok.

Try not to use table constraints over large numbers of variables. Table constraints over two or three variables are fine: performing GAC on table constraints with large numbers of variables becomes very expensive.

In some models it is useful to observe that if plane P can fly up to K different flights, then the length of its sequence of flights is at most K. For example, in the example above, AC-1 can fly 5 different flights while AC-2 can fly 4 different flights. So clearly, the sequence of flights flown by AC-1 can’t be more than 5 long, and for AC-2 in sequence can’t be more than 4 long.

As an example of a set of variables and values that would be inadequate consider having a variable for every flight with values being the set of planes that can fly that flight. This a reasonable number of variables, and it makes the last constraint, that every flight is scheduled only once, automatically satisfied (since every variable can only have one value). However, these variables by themselves will not be sufficient, as we won’t be able to determine the sequencing of the set of flights assigned to a particular plane. Potentially, such variables might be useful, but other variables would have to be added to model the sequencing part of the CSP.