Chapter 9, Problem 1PE

Program Plan Intro

Program plan:

• Import random.
• Define “main()” function.
  • Call the function “printIntro()”.
  • Get input using “getInputs()” function.
  • Call function “simNMatches()” to find the matches.
  • Call function “printSummary()”.
  • Define a function “printIntro()”.
    • Print the statements.
  • Define a function “getInputs()”.
  • Get the value for simulation parameter “a” from the user.
  • Get the value for simulation parameter “b” from the user.
  • Get the value for simulation parameter “n” from the user.
  • Returns the three simulation parameters.
  • Define a function “simNMatches()”.
    • Initialize values.
    • Iterate a for loop up to “n”.
      • Call the function “simOneMatch()”.
      • If condition.
      • Increment the value of “matchA” by 1.
      • Else.
      • Increment the value of “matchB” by 1.
      • Return the value of “matchA” and “matchB”.
  • Define a function “simOneMatch()”.
    • Initialize the values “wisnA” and “WinsB” as 0.
    • Accumulate number of games.
    • Iterate a while loop.
      • Call a function “simOneGame()”.
      • If condition.
        • Increment the value of “winA” by 1.
        • Increment the value of “x” by 1.
      • Else condition.
        • Increment the value of “winsB” by 1.
        • Increment the value of “x” by 1.
        • Return the value of “winsA” and “winsB”.
  • Define a function “simOneGame()”.
    • Call a function “findService()” to a value “serving”.
    • Initialize values.
    • Iterate a while loop.
      • If condition “serving == "A"”.
        • If condition “random() < probA”.
        • • Increment the value of “scoreA” by 1.
        • If not the condition.
        • • Assign a value “B” to a variable “serving”.
        • Else if condition.
        • • If condition “random() < probB” increment the value of “scoreB” by 1.
          • Increment the value of “scoreB” by 1.
        • If not the condition.
        • • assign a value “A” to a variable “serving”
            • Return “scoreA”, “scoreB”..
  • Define a function “findService()”.
    • If condition “x % 2 == 0”.
      • Return “A”.
        • • • If not the condition.
              • Return “B”.
  • Define a function “gameOver()”.
    • If the condition satisfies.
      • Return the value of “b”.
        • • • • Else if condition “b == 0 and a == 7”.
                • Return the value of “a”.
              • Else if condition “abs(a-b) >= 2”.
                • Return “True”.
              • If not the condition
                • Return a value “False”.
  • Define a function “printSummary()”.
    • Add the value of “matchA” and “matchB” and store in a variable “n”.
    • Print the value of “n”.
    • Print the value of “matchA”.
    • Print the value of “matchB”.
• main for function call

Program Description Answer

This is a revision of the racquetball simulation. The problem has two major changes:

The program has to calculate results for best of n games.

First service is alternated between A and B. The odd numbered games of the match are served first by A and even numbered games are first served by B.

Explanation of Solution

Program:

#import random

from random import random

#define main() function

def main():

    #call the function printIntro()

    printIntro()

  #get input using getInputs() function

    probA, probB, n = getInputs()

  #calling function simNMatches() to find the matches

    matchA, matchB = simNMatches(n, probA, probB)

  #call function printSummary()

    printSummary(matchA, matchB)

  #define a function printIntro()

def printIntro():

    print("This program simulates a game of racquetball between two")

    print('players called "A" and "B". The abilities of each player is')

    print("indicated by a probability (a number between 0 and 1) that")

    print("reflects the likelihood of a player winning the serve.")

    print("Player A has the first serve.")

#define a function getInputs()

def getInputs():

    #get the value for simulation parameter ‘a’ from the user

    a = eval(input("What is the prob. player A wins a serve? "))

    #get the value for simulation parameter ‘b’ from the user

    b = eval(input("What is the prob. player B wins a serve? "))

    #get the value for simulation parameter ‘n’ from the user

    n = eval(input("How many games to simulate? "))

    #Returns the three simulation parameters

    return a, b, n

#define a function simNMatches()

def simNMatches(n, probA, probB):

    #initialize values

    matchA = matchB = 0

    #iterate a for loop up to n

    for i in range(n):

        #call the function simOneMatch()

        winsA, winsB = simOneMatch(probA, probB)

        #if condition

        if winsA > winsB:

            #increment the value of matchA by 1

            matchA = matchA + 1

        #else

        else:

            #increment the value of matchB by 1

            matchB = matchB + 1

    #return the value of matchA and matchB

    return matchA, matchB

#define a function simOneMatch()

def simOneMatch(probA, probB):

    #initialize the values wisnA and WinsB as 0

    winsA = winsB = 0

    #accumulate number of games

    x = 1

    #iterate a while loop

    while winsA !=2 and winsB !=2:

        #calling a function simOneGame()

        scoreA, scoreB = simOneGame(probA, probB, x)

        #if condition

        if scoreA > scoreB:

            #increment the value of winA by 1

            winsA = winsA + 1

            #increment the value of x by 1

            x = x+1

        #else condition

        else:

            #increment the value of winsB by 1

            winsB = winsB + 1

            #increment the value of x by 1.

            x = x+1

    #return the value of winsA and winsB

    return winsA, winsB

#define a function simOneGame()

def simOneGame(probA, probB, x):

    #call a function findService() to a value “serving”

    serving = findService(x)

    #initialize values

    scoreA = 0

    scoreB = 0

    #iterate a while loop.

    while not gameOver(scoreA, scoreB):

        #if condition

        if serving == "A":

            #if condition

            if random() < probA:

                #increment the value of scoreA by 1

                scoreA = scoreA + 1

            #if not the condition

            else:

                #assign a value “B” to a variable “serving”

                serving = "B"

        #else if condition

        elif serving == "B":

            #if condition

            if random() < probB:

                #increment the value of scoreB by 1

                scoreB = scoreB + 1

            #if not the condition

            else:

                #assign a value “A” to a variable “serving”

                serving = "A"

    #return

    return scoreA, scoreB

#define a function findService()

def findService(x):

    #if condition

    if x % 2 == 0:

        #return “A”

        return "A"

    #if not the condition

    else:

        #return “B”

        return "B"

#define a function gameOver()

def gameOver(a, b):

    #if the condition satisfies

    if a == 0 and b == 7:

        #return the value of “b”

        return b == 7

    #else if condition

    elif b == 0 and a == 7:

        #return the value of a

        return a == 7

    #else if condition

    elif abs(a-b) >= 2:

        #return “True”

        return True

    #if not the condition

    else:

        #return a value “False”

        return False

#define a function printSummary()

# Prints a summary of wins for each players

def printSummary(matchA, matchB):

    #add the value of matchA and matchB and store in a variable n.

    n = matchA + matchB

    #print the value of n

    print("\nGames simulated: ", n)

    #print the value of matchA

    print("Wins for A: {0} ({1:0.1%})".format(matchA, matchA/n))

    #print the value of matchB

    print("Wins for B: {0} ({1:0.1%})".format(matchB, matchB/n))

# main for function call

if __name__ == '__main__': main()

Sample Output

Output:

This program simulates a game of racquetball between two

players called "A" and "B". The abilities of each player is

indicated by a probability (a number between 0 and 1) that

reflects the likelihood of a player winning the serve.

Player A has the first serve.

What is the prob. player A wins a serve? 0.5

What is the prob. player B wins a serve? 0.7

How many games to simulate? 2

Games simulated:  2

Wins for A: 1 (50.0%)

Wins for B: 1 (50.0%)