Functions

def clip(lo, x, hi):
    '''
    Takes in three numbers and returns a value based on the value of x.
    Returns:
     - lo, when x < lo
     - hi, when x > hi
     - x, otherwise
    '''
    # Your code here
    return min(hi,max(lo,x))

def evalQuadratic(a, b, c, x):
    '''
    a, b, c: numerical values for the coefficients of a quadratic equation
    x: numerical value at which to evaluate the quadratic.
    '''
    # Your code here
    return a * x**2 + b * x + c

def square(x):
    '''
    x: int or float.
    '''
    # Your code here
    return x**2

def odd(x):
    '''
    x: int or float.

    returns: True if x is odd, False otherwise
    '''
    # Your code here
    return (x%2)==1

def isVowel(char):
    '''
    char: a single letter of any case

    returns: True if char is a vowel and False otherwise.
    '''
    # Your code here
    return char in "aeiouAEIOU"

def isVowel(char):
    '''
    char: a single letter of any case

    returns: True if char is a vowel and False otherwise.
    '''
    # Your code here
    return "aeiouAEIOU".find(char) >=0

def credit_card(balance, annualInterestRate, monthlyPaymentRate) :
    """
    balance : float, outstanding balance on the credit card
    annualInterestRate : annual interest rate as a decimal
    monthlyPaymentRate : minimum monthly payment rate as a decimal
    """
    
    MONTHS = 12
    
    monthlyInterestRate = annualInterestRate / 12.0
    totalPaid = 0
        
    for month in range(MONTHS):
        monthlyPayment = round(balance * monthlyPaymentRate,2)
        totalPaid += monthlyPayment
        unpaidBalance = balance - monthlyPayment
        balance = unpaidBalance * (1 + monthlyInterestRate)
        print "Month:", month+1
        print "Minimum monthly payment:", monthlyPayment
        print "Remaining balance:", round(balance, 2)
        
    print "Total paid:", totalPaid
    print "Remaining balance:", round(balance, 2)

def payment12_10(balance, annualInterestRate) :
    """
    balance : float, outstanding balance on the credit card
    annualInterestRate : float, annual interest rate as a decimal

    Calculates the minimum fixed monthly payment needed in order pay off 
    a credit card balance within 12 months. 
    By a fixed monthly payment, we mean a single number which does not change 
    each month, but instead is a constant amount that will be paid each month.
    The monthly payment must be a multiple of $10 and is the same for all months. 
    Notice that it is possible for the balance to become negative using 
    this payment scheme, which is okay.
    """
    
    MONTHS = 12
    
    monthlyInterestRate = annualInterestRate / 12.0
    monthlyPayment = ((balance / MONTHS) // 10) * 10
    endBalance = balance
                   
    while endBalance > 0 : 
        #print "monthlyPayment :", monthlyPayment
        for dummy_month in range(MONTHS):
            endBalance = (endBalance - monthlyPayment) * (1 + monthlyInterestRate)
        if endBalance > 0 :
            monthlyPayment += 10
            endBalance = balance
            
    print "Lowest Payment:", monthlyPayment
    
def payment12(balance, annualInterestRate) :
    """
    balance : float, outstanding balance on the credit card
    annualInterestRate : float, annual interest rate as a decimal

    Calculates the minimum fixed monthly payment needed in order pay off 
    a credit card balance within 12 months. 
    By a fixed monthly payment, we mean a single number which does not change 
    each month, but instead is a constant amount that will be paid each month.
    The monthly payment WILL NOT BE LONGER a multiple of $10, 
    but is the same for all months. 
    Notice that it is possible for the balance to become negative using 
    this payment scheme, which is okay.
    """
    
    MONTHS = 12
    
    monthlyInterestRate = float(annualInterestRate) / MONTHS
    minMonthlyPayment = (balance / MONTHS)
    maxMonthlyPayment = (balance * (1 + monthlyInterestRate) ** MONTHS) / MONTHS
    endBalance = balance
    epsilon = 0.01                   
    
    monthlyPayment = (maxMonthlyPayment+minMonthlyPayment)/2
    
    while abs(endBalance) > epsilon : 
        #print "monthlyPayment :", monthlyPayment
        for dummy_month in range(MONTHS):
            endBalance = (endBalance - monthlyPayment) * (1 + monthlyInterestRate)
        if abs(endBalance) > epsilon :
            if endBalance > 0 :
                minMonthlyPayment = monthlyPayment
            else :
                maxMonthlyPayment = monthlyPayment
            monthlyPayment = (maxMonthlyPayment+minMonthlyPayment)/2
            endBalance = balance
            
            
    print "Lowest Payment:", round(monthlyPayment, 2)
    
#payment12(balance, annualInterestRate)    
payment12(320000, 0.2)
payment12(999999, 0.18)

# Radiation Exposure
def f(x):
    import math
    return 10*math.e**(math.log(0.5)/5.27 * x)
    
def radiationExposure(start, stop, step):
    count = 0
    i = start
    while i < stop:
        count += f(i)*step
        i += step
    return count

###
# Hangman

def isWordGuessed(secretWord, lettersGuessed):
    '''
    secretWord: string, the word the user is guessing
    lettersGuessed: list, what letters have been guessed so far
    returns: boolean, True if all the letters of secretWord are in lettersGuessed;
      False otherwise
    '''
    # FILL IN YOUR CODE HERE...
    for letter in secretWord:
        if not letter in lettersGuessed:
            return False
    return True

def getGuessedWord(secretWord, lettersGuessed):
    '''
    secretWord: string, the word the user is guessing
    lettersGuessed: list, what letters have been guessed so far
    returns: string, comprised of letters and underscores that represents
      what letters in secretWord have been guessed so far.
    '''
    # FILL IN YOUR CODE HERE...
    guessedWord = ''
    for letter in secretWord:
        if letter in lettersGuessed:
            guessedWord += letter + ' '
        else:
            guessedWord += '_ '
    return guessedWord
    
def getAvailableLetters(lettersGuessed):
    '''
    lettersGuessed: list, what letters have been guessed so far
    returns: string, comprised of letters that represents what letters have not
      yet been guessed.
    '''
    # FILL IN YOUR CODE HERE...
    availableLetters = ''
    for l in [l for l in string.ascii_lowercase if l not in lettersGuessed]:
        availableLetters += l
    return availableLetters

def sharp(x):
    """
    (int) -> int
    x# = ((((((2 ^ 3) ^ 4) ^ 5)  ...)  ...)     x-1) ^  x)
    """
    assert type(x)==int, "Argument should be an int"
    assert x>=2, "Argument should be >=2"
    if x == 2:
        return 2
    else:
        return sharp(x-1) ** x

def ndigits(x):
    """
    (int) -> int
    This function should return the number of digits in the integer x.
    """
    assert type(x)==int, "Argument should be an int"
    if x<0: 	# Check for negative ints
        x=-x
    if x<10:
        return 1
    else:
        return 1 + ndigits(x / 10)