15-112 - Summer 1

Strings continued

String literals

The in operator

# for strings t and s, (t in s) is the same as 
# isSubstring(t, s) from homework 1-4.

print("h" in "hello")      # prints True
print("hell" in "hello")   # prints True
print("ll" in "hello")     # prints True
print("H" in "hello")      # prints False
print("" in "hello")       # prints True
print("k" not in "hello")  # prints True

Example: Caesar shift

def encrypt(message, shiftNum):
    result = ""
    for char in message:
        result += shift(char, shiftNum)
    return result

# Shift a single character by shiftNum.
# The following is a very "Pythonic" implementation.
def shift(c, shiftNum):
    shiftNum %= 26
    if (not c.alpha()): return c
    alph = string.ascii_lower if (c.islower())  else string.ascii_upper
    shiftedAlph = alph[shiftNum:] + alph[:shiftNum]
    return shiftedAlph[alph.find(c)]

# The following is a more standard approach.
def shift(c, shiftNum):
    shiftNum = shiftNum % 26
    if(not char.isalpha()): return char
    shifted = ord(char) + shiftNum
    if ( ((char <= 'Z') and (shifted > ord('Z'))) or
         ((char <= 'z') and (shifted > ord('z')))    ):
        return chr(shifted - 26)
    else:
        return chr(shifted)

Monte Carlo method

Odds of Mere winning

In the first bet, Mere rolls a dice 4 times. He wins if he gets a 1.

import random

def mereOdds():
    trials = 100*1000
    successes = 0
    for trial in range(trials):
        if(mereWins()):
            successes += 1
    return successes/trials

def mereWins():
    for i in range(4):
        dieValue = random.randint(1,6)
        if(dieValue == 1): return True
    return False

print(mereOdds())

In the second bet, Mere rolls two dice 24 times. He wins if he gets 1-1.

import random

def mereOdds():
    trials = 100*1000
    successes = 0
    for trial in range(trials):
        if(mereWins()):
            successes += 1
    return successes/trials

def mereWins():
    for i in range(24):
        dieValue1 = random.randint(1,6)
        dieValue2 = random.randint(1,6)
        if(dieValue1 == 1 and dieValue2 == 1): return True
    return False

print(mereOdds())

Birthday problem

Assume there are n people in a room. We want to estimate the probability that there are 2 people in the room who share a birthday.

import random

def birthdayOdds(n):
    trials = 10*1000
    successes = 0
    for trial in range(trials):
        if(trialSucceeds(n)): successes += 1
    return successes/trials

def trialSucceeds(n):
    seenBirthdays = ""
    for i in range(n):
        randomBirthday = "$" + str(random.randint(1,365)) + "$"
        if(randomBirthday in seenBirthdays): return True
        else: seenBirthdays += randomBirthday
    return False

for n in range(50):
    print(n, birthdayOdds(n))

Estimating Pi

import random

def estimatePi():
    throws = 100*1000
    numInCircle = 0   # successes
    for throw in range(throws):
        x = random.uniform(-1,1)
        y = random.uniform(-1,1)
        if(inUnitCircle(x,y)):  # trial succeeds
            numInCircle += 1
    return 4*numInCircle/throws

def inUnitCircle(x,y):
    return x**2 + y**2 <= 1

print(estimatePi())

Monty Hall problem

import random

# What are the odds of winning if you switch?
def montyHall():
    trials = 10*1000
    successes = 0
    for trial in range(trials):
        if(trialSucceeds()): successes += 1
    return successes/trials

def trialSucceeds():
    prize = random.randint(1,3)
    choice = random.randint(1,3)
    reveal = random.randint(1,3)
    while(reveal == prize or reveal == choice):
        reveal = random.randint(1,3)
    switch = (1+2+3) - reveal - choice
    return (switch == prize)

print(montyHall())

15-112 Fundamentals of Programming

Notes - Lecture 2.1