mith College Computer Science Week 13 CSC111 Spring 2018 Dominique Thiébaut
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1 mith College Computer Science Week 13 CSC111 Spring 2018 Dominique Thiébaut
2 Recursion Continued
3 Visiting a Maze Start Exit
4
5 How do we represent a maze in Python?
6 mazetext = """ #########################...# ##############.########## #.#.#...#.#...# #.#.#.########.########.# #.#.#...#.# #.#.###.#####.#####.#...# #...#.#.#.#.##### #.#########.#.#.#.#...# #.#.#.#.#.#.#.#.#######.# #.#...#.#...#.. #.###############.#####.# #...#...# #.###########.#########.# #...#...# ######################### """ Step 1: String Definition
7 mazetext = """ ######################### # ############## ########## # # # # # # # # # ######## ######## # # # # # # # # ### ##### ##### # # # # # # # ##### # ######### # # # # # # # # # # # # # ####### # # # # # # # ############### ##### # # # # # ########### ######### # # # # ######################### """ Step 2: Replace dots by spaces
8 maze = [ '#########################', ' #', '############## ##########', '# # # # # #', '# # # ######## ######## #', '# # # # #', '# # ### ##### ##### # #', '# # # # # #####', '# ######### # # # # #', '# # # # # # # # ####### #', '# # # # # ', '# ############### ##### #', '# # #', '# ########### ######### #', '# # #', ######################### ] Step 3: Split into List of Strings
9 maze = [ '#########################', ' #', '############## ##########', '# # # # # #', '# # # ######## ######## #', '# # # # #', '# # ### ##### ##### # #', '# # # # # #####', '# ######### # # # # #', '# # # # # # # # ####### #', '# # # # # ', '# ############### ##### #', '# # #', '# ########### ######### #', '# # #', ######################### ] maze = [, -, -, - ] maze = [, -, ] Step 3: Split into List of Strings
10 maze = [ '#########################', ' #', '############## ##########', '# # # # # #', '# # # ######## ######## #', '# # # # #', '# # ### ##### ##### # #', '# # # # # #####', '# ######### # # # # #', '# # # # # # # # ####### #', '# # # # # ', '# ############### ##### #', '# # #', '# ########### ######### #', '# # #', ######################### ] maze[0] Result: Each row can be accessed with an index
11 maze = [ '#########################', ' #', '############## ##########', '# # # # # #', '# # # ######## ######## #', '# # # # #', '# # ### ##### ##### # #', '# # # # # #####', '# ######### # # # # #', '# # # # # # # # ####### #', '# # # # # ', '# ############### ##### #', '# # #', '# ########### ######### #', '# # #', ######################### ] maze[3] Result: Each row can be accessed with an index
12 maze[3][4] maze = [ '#########################', ' #', '############## ##########', '# # # # # #', '# # # ######## ######## #', '# # # # #', '# # ### ##### ##### # #', '# # # # # #####', '# ######### # # # # #', '# # # # # # # # ####### #', '# # # # # ', '# ############### ##### #', '# # #', '# ########### ######### #', '# # #', ######################### ] maze[3] Result: a 2-Dimensional Structure!
13 ######################### # ############## ########## # # # # # # # # # ######## ######## # # # # # # # # ### ##### ##### # # # # # # # ##### # ######### # # # # # # # # # # # # # ####### # # # # # # # ############### ##### # # # # # ########### ######### # # # # ######################### maze maze[3][4] each cell is defined by a row index, and a column index: maze[row][col] Result: a 2-Dimensional Array
14 Algorithm maze[i][j]
15 j i? maze[ i ][ j ]
16 j i? maze[ i ][ j+1 ] maze[ i ][ j ]
17 j i? maze[ i ][ j ]
18 j i? maze[ i ][ j ] maze[ i+1 ][ j ]
19 ######################### # ############## ########## # # # # # # # # # ######## ######## # # # # # # # # ### ##### ##### # # # # # # # ##### # ######### # # # # # # # # # # # # # ####### # # # # # # # ############### ##### # # # # # ########### ######### # # # # ######################### maze
20 impass v v v # # wall path... passage
21
22 Exploring the Code
23 Observing the Recursive Nature of visitmaze()
24 Fractal Trees
25 Let's Play with the Fractal Tree Make the order larger (e.g. 12) Make it draw the right side first Change the angle theta Make the drawing of a branch random Make the size of a branch very large Make the color proportional to the order of recursion
26 color_rgb( order*20, 255-order*20, 100 )
27 Examples
28
29 The result
30 color_rgb( 25*order, 25*order, *order )
31 Tough problems, simple solutions Recursive Functions Finding the Largest in a List Finding the Smallest in a List Factorial Traversing a Maze Recursive Trees Towers of Hanoi
32 We stopped here last time
33 Solving Problems Recursively: Towers of Hanoi A B C
34 The Legend of the Towers of Hanoi The puzzle was invented by the French mathematician Édouard Lucas in There is a story about an Indian temple in Kashi Vishwanath which contains a large room with three time-worn posts in it surrounded by 64 golden disks. Brahmin priests, acting out the command of an ancient prophecy, have been moving these disks, in accordance with the immutable rules of the Brahma, since that time. The puzzle is therefore also known as the Tower of Brahma puzzle. According to the legend, when the last move of the puzzle will be completed, the world will end. It is not clear whether Lucas invented this legend or was inspired by it. From Wikipedia,
35 Coding The Towers of Hanoi
36 How long would it take a good PC to move 64 disks on 3 pegs?
37 Timing Analysis
38
39
40 Final Exam
41 From Here to There
42 Most Important Tips
43 Most Important Tips Small, start small Don't work with the original data Take a small sample that is representative Take all the shortcuts possible
44 Most Important Tips Create small test data set with all possible cases for exceptions Make sure your program works with empty lists empty strings 0, 1 or n results
45 Most Important Tips Reuse code we have created before (solution programs, programs in the book) Solve only one problem at a time Do not be afraid of exceptions! "It would be nice if I could " > search python.org
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