CSCE 110 Programming I

Transcription

1 CSCE 110 Programming I Simulations and Plotting Data Dr. Tiffani L. Williams Department of Computer Science and Engineering Texas A&M University Spring 2014 Tiffani L. Williams (Texas A&M) CSCE 110) Spring / 21

2 We are now done with Part 1 of the course. We have covered the basics of Python. Now, it s time to look at different kinds of problems we can solve using our new found knowledge of Python. In this module, we will look at simulation and plotting data. Tiffani L. Williams (Texas A&M) CSCE 110) Spring / 21

3 Flipping a coin On average, how often will heads appear during a coin flip? How would you prove it? Tiffani L. Williams (Texas A&M) CSCE 110) Spring / 21

4 Fair coin experiments Listing 1: fair-coin.py 1 # A program that simulates the number of heads and tails that appear 2 # using a fair coin. 3 4 import random 5 6 def flip_coin (): 7 return random. choice ([ heads, tails ]) 8 9 def main ( coin_tosses ): 10 heads = 0 11 tails = 0 12 for i in range (0, coin_tosses ): 13 result = flip_coin () 14 if result == heads : 15 heads += 1 16 else : 17 tails += # Print results 20 print Total number of coin tosses : %d % ( coin_tosses ) 21 print Number of heads : %d (%.2 f percent ) \ 22 %( heads, float ( heads )/ coin_tosses * 100) 23 print Number of tails : %d (%.2 f percent ) \ 24 %( tails, float ( tails )/ coin_tosses * 100) main (10000) Tiffani L. Williams (Texas A&M) CSCE 110) Spring / 21

5 Unfair coin experiments Listing 2: unfair-coin.py 1 # A program that simulates the number of heads and tails that appear 2 # using an unfair coin. 3 4 import random 5 6 def flip_coin (): 7 return random. choice ([ heads, tails, tails, tails ]) 8 9 def main ( coin_tosses ): 10 heads = 0 11 tails = 0 12 for i in range (0, coin_tosses ): 13 result = flip_coin () 14 if result == heads : 15 heads += 1 16 else : 17 tails += # Print results 20 print Total number of coin tosses : %d % ( coin_tosses ) 21 print Number of heads : %d (%.2 f percent ) \ 22 %( heads, float ( heads )/ coin_tosses * 100) 23 print Number of tails : %d (%.2 f percent ) \ 24 %( tails, float ( tails )/ coin_tosses * 100) main (10000) Tiffani L. Williams (Texas A&M) CSCE 110) Spring / 21

6 Consider the following problem. On average, how many times do you need to roll a die before all six different numbers have turned up? Tiffani L. Williams (Texas A&M) CSCE 110) Spring / 21

7 We can use a computer to simulate the problem for us. Listing 3: rolling-all-numbers.py 1 import random 2 3 def roll_die (): 4 return random. randint (1,6) 5 6 def roll_all_numbers (): 7 rolled_value = [0,0,0,0,0,0,0] 8 number_rolls = while sum ( rolled_value )!= 6: 11 number = roll_die () 12 rolled_value [ number ] = 1 13 number_rolls += return number_rolls def conduct_simulation ( repetitions ): 18 total_rolls = 0 19 for i in range (0, repetitions ): 20 total_rolls += roll_all_numbers () 21 print Repetitions : % -8d \t Average rolls is %.1 f % ( 22 repetitions, float ( total_rolls ) / repetitions ) def main (): 25 for experiment in (1, 10, 100, 1000, 10000, ): 26 conduct_simulation ( experiment ) main () Tiffani L. Williams (Texas A&M) CSCE 110) Spring / 21

8 Sets A set is used to contain an unordered collection of objects. The elements of a set are never duplicated. To create a set, use the set() function and supply a sequence of items such as follows: Sets are unordered and cannot be indexed by numbers. Sets support a standard collection of operations, including union, intersection, difference, and symmetric difference. New items can be added to a set using add() or update(): Tiffani L. Williams (Texas A&M) CSCE 110) Spring / 21

9 Set Examples I 1 >>> a = [1, 2, 3, 4, 1, 3, " apple "] 2 >>> b = set (a) # convert the list a to a set 3 >>> b 4 set ([1, 2, 3, 4, apple ]) 5 >>> c = set ([" apple ", " banana ", 3]) 6 >>> c 7 set ([3, apple, banana ]) 8 >>> c. add (4) # add the integer 4 to the set c 9 >>> c 10 set ([3, 4, apple, banana ]) 11 >>> c.add (" banana ") # add " banana " to the set c 12 >>> c 13 set ([3, 4, apple, banana ]) 14 >>> b 15 set ([1, 2, 3, 4, apple ]) 16 >>> b. union (c) # union 17 set ([1, 2, 3, 4, apple, banana ]) 18 >>> b. intersection (c) # intersection 19 set ([3, 4, apple ]) 20 >>> b. difference (c) # set difference 21 set ([1, 2]) 22 >>> b. issubset (c) # subset 23 False 24 >>> b. issuperset (c) # superset 25 False 26 >>> d = set ([1,2]) 27 >>> d. issubset (b) # subset 28 True 29 >>> b Tiffani L. Williams (Texas A&M) CSCE 110) Spring / 21

10 Set Examples II 30 set ([1, 2, 3, 4, apple ]) 31 >>> b. pop () # arbitrarily select an item from the set b >>> b 34 set ([2, 3, 4, apple ]) 35 >>> b. remove (" apple ") # remove " apple " from the set b 36 >>> b 37 set ([2, 3, 4]) 38 >>> len (b) >>> b [1] 41 Traceback ( most recent call last ): 42 File "<string >", line 1, in <fragment > 43 TypeError : set object does not support indexing Tiffani L. Williams (Texas A&M) CSCE 110) Spring / 21

11 Consider the following problem. Let s assume you roll six dice at the same time. On average, how many times do you need to roll six dice before each of them has a different number? Tiffani L. Williams (Texas A&M) CSCE 110) Spring / 21

12 Computer programming comes to the rescue again. I Listing 4: six-dice-with-all-numbers.py 1 # Simulates the number of times we have to roll six dice so that each of them 2 # have different values. 3 import random 4 5 def roll_six_dice (): 6 roll = [] 7 for die in range (6): 8 roll += [ random. randint (1,6)] 9 return roll def roll_all_numbers (): 12 number_rolls = 0 13 roll = [] 14 while len ( roll )!= 6: 15 roll = set ( roll_six_dice ()) 16 number_rolls += 1 17 return number_rolls def conduct_simulation ( repetitions ): 20 total_rolls = 0 21 for i in range (0, repetitions ): 22 total_rolls += roll_all_numbers () 23 print Repetitions : % -8d \t Average rolls is %f % ( 24 repetitions, float ( total_rolls ) / repetitions ) def main (): Tiffani L. Williams (Texas A&M) CSCE 110) Spring / 21

13 Computer programming comes to the rescue again. II 27 for experiment in (1, 10, 100, 1000, 10000): 28 conduct_simulation ( experiment ) main () Tiffani L. Williams (Texas A&M) CSCE 110) Spring / 21

14 Simple Plotting Example (1) Listing 5: matplot-lib-example.py 1 import matplotlib. pyplot as plot 2 3 # plot values 4 plot.plot ( range (0,10), [9,4,5,2,3,5,7,12,2,3] ) 5 plot.plot ( range (0,10), [12,5,33,2,4,5,3,3,22,10] ) 6 7 # annotate our plot 8 plot. xlabel ( x axis ) 9 plot. ylabel ( y axis ) 10 plot. title ( a simple plot ) 11 plot. legend () 12 plot. grid ( True ) ## view our plot 15 plot. savefig ("sample -plot.pdf ") # saves file in PDF 16 #plot. savefig (" sample -plot.png ") # saves file in PNG format 17 #plot. savefig (" sample -plot.jpg ") # saves file in JPG 18 plot. show () # allows for interactive exploration of the plot Tiffani L. Williams (Texas A&M) CSCE 110) Spring / 21

15 Simple Plotting Example (2) 35 a simple plot y axis x axis Tiffani L. Williams (Texas A&M) CSCE 110) Spring / 21

16 Plotting Fair Coin Experiments (1) I Listing 6: fair-coin-plot-results.py 1 # Simulates the number of heads and tails that appear using a fair coin. 2 3 import random 4 import matplotlib. pyplot as plot 5 6 def plot_results ( heads_list, tails_list, x_axis ): 7 plot. plot ( x_axis, heads_list, label= heads, marker= o ) 8 plot. plot ( x_axis, tails_list, label= tails, marker= ^ ) 9 plot. xlabel ( Coin Tosses ) 10 plot. ylabel ( Percentage (%) ) 11 plot. legend () 12 plot. grid () 13 plot. ylim (0,80) 14 plot. xscale ( log ) 15 plot. savefig ("fair -coin -plot.pdf ") # saves file in PDF 16 plot. show () def flip_coin (): 19 return random. choice ([ heads, tails ]) def simulate ( coin_tosses ): 22 heads = 0 23 tails = 0 24 for i in range (0, coin_tosses ): 25 result = flip_coin () 26 if result == heads : Tiffani L. Williams (Texas A&M) CSCE 110) Spring / 21

17 Plotting Fair Coin Experiments (1) II 27 heads += 1 28 else : 29 tails += # Print results 32 print Total number of coin tosses : %d % ( coin_tosses ) 33 print Number of heads : %d (%.2 f percent ) %( 34 heads, float ( heads )/ coin_tosses * 100) 35 print Number of tails : %d (%.2 f percent ) %( 36 tails, float ( tails )/ coin_tosses * 100) return heads, tails def main (): 41 heads_y_axis = [] 42 tails_y_axis = [] 43 x_axis = [10, 100, 1000, 10000, , ] 44 for tosses in x_axis : 45 heads, tails = simulate ( tosses ) 46 # heads_y_axis += list ( heads ) 47 heads_y_axis += [ float ( heads )/ tosses * 100] 48 tails_y_axis += [ float ( tails )/ tosses * 100] plot_results ( heads_y_axis, tails_y_axis, x_axis ) main () Tiffani L. Williams (Texas A&M) CSCE 110) Spring / 21

18 Plotting Fair Coin Experiments (2) heads tails Percentage(%) Coin Tosses Tiffani L. Williams (Texas A&M) CSCE 110) Spring / 21

19 File Processing (1) Now, we are going to learn how to obtain input from a file. Consider the following file of planet names. The name of this file is planets.txt. 1 Mercury 2 Venus 3 Earth 4 Mars 5 Jupiter 6 Saturn 7 Uranus 8 Neptune Tiffani L. Williams (Texas A&M) CSCE 110) Spring / 21

20 File Processing (2) Let s read the contents of the planets.txt file and output the results to the screen. Listing 7: read-file-planets.py 1 # open file for reading 2 input_file = open ( planets. txt, r ) 3 4 # place contents of file into the variable lines 5 # the function readlines () returns the file contents as a list 6 lines = input_file. readlines () 7 8 # now iterate through the list as you normally would 9 for line in lines : 10 print "%s: %d" %( line, len (line )) # close the file 13 input_file. close () Tiffani L. Williams (Texas A&M) CSCE 110) Spring / 21

21 File Processing (3) Another version of our Python program for reading the planets.txt file. 1 input_file = open ( planets. txt, r ) 2 for line in input_file. readlines (): 3 strip_line = line. strip () # removes the new line character 4 print "%s: %d" %( strip_line, len ( strip_line )) 5 input_file. close () Tiffani L. Williams (Texas A&M) CSCE 110) Spring / 21