Elementary Python Programming

1. Elementary Python Programming

2. Quadratic Roots • Our goal is to write a simple Python script (program) to find the real roots of a quadratic equation. • Here is what a run of the program should look like.

3. First Steps We first print the program description: print("\nYou are to enter the", "coefficients a,b,c of the", "quadratic equation") print ("ax^2 + bx + c = 0 and the“, "solution will be presented\n")

4. First Steps Next, prompt for, and input, the coefficients: a = int(raw_input("Enter coefficient a: ")) b = int(raw_input("Enter coefficient b: ")) c = int(raw_input("Enter coefficient c: ")) Why did we use the int() converter? Because the raw_input() function always return a string.

5. Mathematical Solution

6. Branching • Notice that we must do different things depending on the truth value of an expression • Most programming languages provide for these situations by means of ifstatements • Python versions: if <condition>: <statements1>else: <statements2> if <condition1>: <statements1>elif <condition2>: <statements2> else: <statements3>

7. Square Roots • The square root function is not a Python built-in function • However, it is provided by the Python math module • So we must importthat module by placing the following statement at the top of our program file: import math • Now we may use the function sqrt to calculate a square root. • However, since it comes from an imported module, we must precede it by the module name and a .: math.sqrt()

8. Finishing the Script • So here is the final part of our script. d = b*b-4*a*c # the discriminant if d < 0: print('The equation has no real roots') elif d == 0: print('The equation has unique root',-b/(2*a)) else: r1 = (-b + math.sqrt(d))/(2*a) r2 = (-b - math.sqrt(d))/(2*a) print('The roots of the equation are',r1,r2)

9. A More Complicated Problem • We want to determine if a string could overlap itself. • For example s = 'abcdefabc' overlaps itself as follows: abcdefabcabcdefabc • So does the string t = 'abcda' : abcdaabcda • So we want to write a function that finds the minimum index i such that the first i characters are the same as the last i characters of a string.

10. A More Complicated Problem • We want to write a function that finds the smallest positive index i such that the first i characters of a string s are the same as the last i characters of s. • How can we describe the first i characters of string s? • s[:i], which is the same as s[0:i] and consists of the characters at indices 0,1, …,i-1. • The last i characters are given by s[-i:]. • The obvious approach is to • compare s[:1] with s[-1] • then compare s[:2] with s[-2] • and so on until we either find a match or our comparison index reaches len(s) • Most programming languages provide ways to do repeated execution, and the while construct is a common methodology

11. While Loops • The general form of a Python while statement is: while <condition>: <one or more statements> # body where <condition> is an expression that evaluates to either True or False. • Execution proceeds as follows: • <condition>is evaluated • if the result is False, execution continues with the statement after the while statement. • if the result is True, the body is executed and the condition is evaluated; • This continues until the condition becomes false.

12. While Loops • Very simple example to print the numbers from 1 to 3: i = 1 while i <= 3: print(i) i += 1 Loop unwound:Output i = 1 1 <= 3 True print(1) 1 i= 2 2 <= 3 True print(2) 2 i = 3 3 <= 3 True print(3) 3 i = 4 4 <= 3 False, so done

13. While Loops • So here is the code for our overlap function, which we would put in a file called, say, myoverlap.py. def overlaps(s): i = 1 while i < len(s) and s[:i] != s[-i:]:i += 1 if i == len(s): return -1 else: return i

14. Simple Assignment • Assignment: Right Triangle • In a file called rightTriangle.py, create a python script in the file that • prompts for and inputs three integers; • then prints a statement indicating whether the numbers are the lengths of the sides of a right triangle. • Your output should be one of the following: The numbers are the side lengths of a right triangle The numbers are not the side lengths of a right triangle Note: three numbers are the side lengths of a right triangle if and only the square of one of them is the sum of the squares of the others.

15. Random Module • The random module provides for the generation of (pseudo) random numbers • We will now illustrate the use of this module for a very, very simple simulation example. • The game of craps is played with two six-sided dice. • To start a game, the player rolls the dice and checks the total of the values on the up side of the two dice. • If the total is 7 or 11, the player wins immediately • If the total is 2, 3 or 12, the player loses immediately • Otherwise the total becomes the “point” • The player now continue to roll the dice until he hits either the point value or 7 • If he hits the point, he wins; if he hits 7, he loses

16. Craps Simulation • We will put our code in a file named craps.py • First, we create a function named roll_and report()that simulates a single roll of the dice. • The function will generate a random integer between 1 and 6 for the value on the first die • Then generate a second value for the second die • Finally, roll_and report()will report the die values and the total to the user and return the total • Next, we create a function play_game to simulate the playing of one game • The rest of our script consists of a call to the play_game function • We will ignore for now the value returned by play_game

17. Roll and Report Function import random # Now the methods from the random module are available def roll_and_report(): die1 = random.randint(1,6) # 1 ≤ die1 ≤ 6 die2 = random.randint(1,6) # 1 ≤ die2 ≤ 6 total = die1+die2 print( '\ndie1: ', die1, '\ndie2: ', die2, '\ntotal: ', total,'\n') return total

18. Function play_game def play_game(): print("Here we go with your first roll.") total = roll_and_report() if total == 7 or total == 11: print("Congratulations! You won the game on the first roll.\n") elif total == 2 or total == 3 or total == 12: print("Uh-oh, you lost the game on the first roll!\n") # The total now becomes the “point” and we continue rolling the dice

19. Function play_game else: raw_input("Hit enter to continue\n") # For better presentation on screen point = total print("You must roll a total of ", point, " to win") print("If you roll a 7 before ",point,", you lose") raw_input("\nHit enter to continue") total = roll_and_report() while total != 7 and total != point: total = roll_and_report() raw_input("\nHit enter to continue") if total == 7: print('\nGame over, you lose') return 0 else: print("\nYou hit the point, you win!") return 1

20. Rest of the Script print("\n\nWelcome to the Casino game of Craps") play_game()

21. Sample Runs of craps.py

22. Sample Runs of craps.py

23. Another Assignment • You are to modify the file craps.py so that the user plays a game, then is asked whether she wishes to play again (response should be ‘Y’ or ‘N’) • If ‘Y’, another game is played and the question asked again. • This continues until the player enters ‘N’ • Addendum: you might make your code a little more friendly by recognizing ‘y’ as ‘Y’ and ‘n’ as ‘N’.