Python Answers

Create a maze without itertools and copy library Assign them (2, y) coordinates, where (0,0) is the upper-left corner of the map. In the example map above, we have lots of cells along the top edge; their coordinates are (0,0), (1,0), (2,0),(3,0),(4,0), (5,0),(6,0),... There are also quite a few along the left edge: (0,1),(0,2), (0,3), (0,4),(0,5).... The start point is at (4,0) and the end point is at (5,7). Required Dump Points As noted above, the "command" that the user types will tell you how far to run the algorithm, before you dump out a result. You must support the following commands; if the user types anything other than one of these (a blank line is OK), then report an error and terminate the program. For each of these commands, check the testcases to find the proper output.

Practice combining dictionaries with file input, practice with data visualization

Degree of Difficulty: Easy

1 Overview In this program, you will solve a maze. You will read the map up from a file, build a tree to represent the maze, and then search through the tree, to find a path from the start to the end. Name your program maze_solver.py

1.1 Dump Points Solving the maze takes several steps, so I've broken it into smaller pieces. For each piece, I've added a "dump" option - if I ask for that particular dump, then you will stop the algorithm at that point, print out what you have so far, and then terminate the program. I've done this for two reasons. First, I hope that it will help guide you through the solution - since each step will be relatively small. Second, if you complete only part of the algorithm but not all of it, you can still get partial credit, because we'll have testcases that will stop you, and check your code, at various points in the process. (Yes, this reduces your flexibility, and locks you into an algorithm

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Consider the equation   and the relation “(x, y) R (0, 2)”, where R is read as “has distance 1 of”. 

For example, “(0, 3) R (0, 2)”, that is, “(0, 3) has distance 1 of (0, 2)”. This relation can also be read as “the point (x, y) is on the circle of radius 1 with center (0, 2)”. In other words: “(x, y) satisfies this equation , if and only if, (x, y) R (0, 2)”. 

Does this equation determine a relation between x and y? Can the variable x can be seen as a function of y, like x=g(y)? Can the variable y be expressed as a function of x, like y= h(x)? If these are possible, then what will be the domains for these two functions? What are the graphs of these two functions? 

Are there points of the coordinate axes that relate to (0, 2) by means of R? 

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