lf7

# Problem Set 4
# Name: lf7
# Collaborators: Santa Claus, Rudolf and Sarah Palin
# Time: Some even finite sum of two prime numbers, in units of lightyears.

#
# Problem 1
#

def nestEggFixed(salary, save, growthRate, years):
    """
    - salary: the amount of money you make each year.
    - save: the percent of your salary to save in the investment account each
      year (an integer between 0 and 100).
    - growthRate: the annual percent increase in your investment account (an
      integer between 0 and 100).
    - years: the number of years to work.
    - return: a list whose values are the size of your retirement account at
      the end of each year.
    """
    # TODO: Your code here.
    n=0
    F=[(salary)*save*.01];
    while n+1<years:
        F.append(F[n]*(1+.01*growthRate)+F[0]);
        n=n+1;
    return F

        
        
    
    
    
    

def testNestEggFixed():
    salary     = 10000
    save       = 10
    growthRate = 15
    years      = 5
    savingsRecord = nestEggFixed(salary, save, growthRate, years)
    print savingsRecord
    # Output should have values close to:
    # [1000.0, 2150.0, 3472.5, 4993.375, 6742.3812499999995]
#testNestEggFixed()
#
# Problem 2
#

def nestEggVariable(salary, save, growthRates):
    # TODO: Your code here.
    """
    - salary: the amount of money you make each year.
    - save: the percent of your salary to save in the investment account each
      year (an integer between 0 and 100).
    - growthRate: a list of the annual percent increases in your investment
      account (integers between 0 and 100).
    - return: a list of your retirement account value at the end of each year.
    """
    n=0
    F=[(salary)*(save)*.01];
    while n+1<=len(growthRates)-1:
        F.append(F[n]*(1+.01*growthRates[n])+F[0]);
        n=n+1;
    return F



def testNestEggVariable0():
    salary      = 10000
    save        = 10
    growthRates = [3, 4, 5, 0, 3]
    savingsRecord = nestEggVariable(salary, save, growthRates)
    print('test 0')
    print savingsRecord
    # Output should have values close to:
    # [1000.0, 2040.0, 3142.0, 4142.0, 5266.2600000000002]

    # TODO: Add more test cases here.
def testNestEggVariable1():
    salary= 20000
    save=5
    growthRates=[3,4,5,0,3]
    savingsRecord= nestEggVariable(salary,save,growthRates)
    print('test 1')
    print savingsRecord

def testNestEggVariable2():
    salary= 20000
    save=10
    growthRates=[3,4,5,0,3]
    savingsRecord= nestEggVariable(salary,save,growthRates)
    print('test 2')
    print savingsRecord

def testNestEggVariable3():
    salary= 30000
    save=10
    growthRates=[3,4,5,0,3]
    savingsRecord= nestEggVariable(salary,save,growthRates)
    print('test 3')
    print savingsRecord

##testNestEggVariable0();
##testNestEggVariable1();
##testNestEggVariable2();
##testNestEggVariable3();
#
# Problem 3
#

def postRetirement(savings, growthRates, expenses):
    """
    - savings: the initial amount of money in your savings account.
    - growthRate: a list of the annual percent increases in your investment
      account (an integer between 0 and 100).
    - expenses: the amount of money you plan to spend each year during
      retirement.
    - return: a list of your retirement account value at the end of each year.
    """
    # TODO: Your code here.
    n=0
    F=[savings*(1+.01*growthRates[n])-expenses];
    for n in range(0,len(growthRates)-1):
        F.append(F[n]*(1+.01*growthRates[n+1])-expenses);
        n=n+1;
    return F


def testPostRetirement0():
    savings     = 100000
    growthRates = [10, 5, 0, 5, 1]
    expenses    = 30000
    savingsRecord = postRetirement(savings, growthRates, expenses)
    print '\n PR 0= ',savingsRecord
    # Output should have values close to:
    # [80000.000000000015, 54000.000000000015, 24000.000000000015,
    # -4799.9999999999854, -34847.999999999985]

    # TODO: Add more test cases here.
def testPostRetirement1():
    savings     = 200000
    growthRates = [3, 5, 0, 5, 1,3,6,1,2,4,5,10]
    expenses    = 30000
    savingsRecord = postRetirement(savings, growthRates, expenses)
    print '\n PR 1= ',savingsRecord

def testPostRetirement2():
    savings     = 100000
    growthRates = [10, 15, 10, 25, 11]
    expenses    = 30000
    savingsRecord = postRetirement(savings, growthRates, expenses)
    print '\n PR 2= ',savingsRecord

##testPostRetirement0()
##testPostRetirement1()
##testPostRetirement2()

#
# Problem 4
#

def findMaxExpenses(salary, save, preRetireGrowthRates, postRetireGrowthRates,
                    epsilon):
    """
    - salary: the amount of money you make each year.
    - save: the percent of your salary to save in the investment account each
      year (an integer between 0 and 100).
    - preRetireGrowthRates: a list of annual growth percentages on investments
      while you are still working.
    - postRetireGrowthRates: a list of annual growth percentages on investments
      while you are retired.
    - epsilon: an upper bound on the absolute value of the amount remaining in
      the investment fund at the end of retirement.
    """
    # TODO: Your code here.
        #little check before the program is started;
    assert epsilon > 0, 'Episolon must be greater than zero, not ' + str(epsilon)

    savings = nestEggVariable(salary, save, preRetireGrowthRates)[-1]
    low = 0
    high = savings + epsilon
    guess = low+(low - high)/2.0 #mid point
    endRetirement = postRetirement(savings, postRetireGrowthRates, guess)[-1]
    
    while abs(endRetirement) > epsilon:
        if endRetirement > epsilon:     
            low = guess
        else:
            high = guess
        guess = low+(high - low)/2.0
        endRetirement = postRetirement(savings, postRetireGrowthRates, guess)[-1]
    return guess




#       Binary Search Example from the lecture for reference

'''def bsearch(growthRates, epsilon, growthRates[n], len(growthRates)-1, calls):
                               print growthRates,len(growthRates)-1 , calls
                                if (last - first) < 2: return s[first] == e or s[last] == e
                                mid = first + (last - first)/2
                                if s[mid] == e: return True
                                if s[mid] > e: return bsearch(s, e, first, mid - 1, calls+1)
                                return bsearch(s, e, mid + 1, last, calls + 1)
                             '''   



def testFindMaxExpenses0():
    salary                = 10000
    save                  = 10
    preRetireGrowthRates  = [3, 4, 5, 0, 3]
    postRetireGrowthRates = [10, 5, 0, 5, 1]
    epsilon               = .01
    expenses = findMaxExpenses(salary, save, preRetireGrowthRates,
                               postRetireGrowthRates, epsilon)
    print 'findMax0= ',expenses
def testFindMaxExpenses1():
    salary                = 100000
    save                  = 10
    import random;
    a=random.randrange(0,15,1)
    preRetireGrowthRates  = [a]
    while len(preRetireGrowthRates)<20:
        preRetireGrowthRates.append(a);
    postRetireGrowthRates = [10, 5, 0, 5, 1,4,2,9,4]
    epsilon               = .01
    expenses = findMaxExpenses(salary, save, preRetireGrowthRates,
                               postRetireGrowthRates, epsilon)
    print 'findMax1= ',expenses
def testFindMaxExpenses2():
    salary                = 30000
    save                  = 10
    import random;
    a=random.randrange(0,15,1)
    preRetireGrowthRates  = [a]
    while len(preRetireGrowthRates)<20:
        preRetireGrowthRates.append(a);
    postRetireGrowthRates = [10, 5, 0, 5, 1]
    epsilon               = .01
    expenses = findMaxExpenses(salary, save, preRetireGrowthRates,
                               postRetireGrowthRates, epsilon)
    print 'findMax2= ',expenses



testFindMaxExpenses0()
testFindMaxExpenses1()
testFindMaxExpenses2()

    # Output should have a value close to:
    # 1229.95548986

    # TODO: Add more test cases here.