#################################################
#Week 1 _ Loops
#################################################

import math

#################################################
# Helper functions
#################################################

def almostEqual(d1, d2, epsilon=10**-7):
    # note: use math.isclose() outside 15-112 with Python version 3.5 or later
    return (abs(d2 - d1) < epsilon)


#################################################
# Problems
#################################################

def digitCount(n):
    return 42

def gcd(x, y):
    return 42

def nthAdditivePrime(n):
    return 42

def nthPerfectNumber(n):
    return 42

def longestIncreasingRun(n):
    return 42

def nthLeftTruncatablePrime(n):
    return 42

def nthCarolPrime(n):
    return 42

def sumOfSquaresOfDigits(n):
    return 42

def isHappyNumber(n):
    return 42

def nthHappyNumber(n):
    return 42


def mostFrequentDigit(n):
    return 42

def nthPowerfulNumber(n):
    return 42

#################################################
# Test Functions
#################################################

def testDigitCount():
    print('Test digitCount()...', end='')
    assert(digitCount(0) == 1)
    assert(digitCount(5) == 1)
    assert(digitCount(-5) == 1)
    assert(digitCount(42) == 2)
    assert(digitCount(-42) == 2)
    assert(digitCount(121) == 3)
    assert(digitCount(-121) == 3)
    assert(digitCount(-10002000) == 8)
    print('Passed')


def testGcd():
    print('Testing gcd()... ', end='')
    assert(gcd(3, 3) == 3)
    assert(gcd(3**6, 3**6) == 3**6)
    assert(gcd(3**6, 2**6) == 1)
    assert (gcd(2*3*4*5,3*5) == 15)
    x = 1568160 # 2**5 * 3**4 * 5**1 *        11**2
    y = 3143448 # 2**3 * 3**6 *        7**2 * 11**1
    g =    7128 # 2**3 * 3**4 *               11**1
    assert(gcd(x, y) == g)
    print('Passed.')

def testNthAdditivePrime():
    print('Testing nthAdditivePrime()... ', end='')
    assert(nthAdditivePrime(0) == 2)
    assert(nthAdditivePrime(1) == 3)
    assert(nthAdditivePrime(5) == 23)
    assert(nthAdditivePrime(10) == 61)
    assert(nthAdditivePrime(15) == 113)
    print('Passed.')

def testNthPerfectNumber():
    print('Testing nthPerfectNumber()... ', end='')
    assert(nthPerfectNumber(0) == 6)
    assert(nthPerfectNumber(1) == 28)
    assert(nthPerfectNumber(2) == 496)
    assert(nthPerfectNumber(3) == 8128) # this can be slow
    print('Passed.')

def testLongestIncreasingRun():
    print('Testing longestIncreasingRun()... ', end='')
    assert(longestIncreasingRun(27648923679) == 23679)
    assert(longestIncreasingRun(123345) == 345)
    assert(longestIncreasingRun(1232) == 123)
    assert(longestIncreasingRun(0) == 0)
    assert(longestIncreasingRun(1) == 1)
    assert(longestIncreasingRun(10012301230123) == 123)
    assert(longestIncreasingRun(12345678987654321) == 123456789)
    print('Passed.')

def testNthLeftTruncatablePrime():
    print('Testing nthLeftTruncatablePrime()... ', end='')
    assert(nthLeftTruncatablePrime(0) == 2)
    assert(nthLeftTruncatablePrime(10) == 53)
    assert(nthLeftTruncatablePrime(1) == 3)
    assert(nthLeftTruncatablePrime(5) == 17)
    print('Passed.')

def testNthCarolPrime():
    print('Testing nthCarolPrime()... ', end='')
    assert(nthCarolPrime(0) == 7)
    assert(nthCarolPrime(1) == 47)
    assert(nthCarolPrime(3) == 3967)
    assert(nthCarolPrime(6) == 16769023)
    print('Passed.')

def testSumOfSquaresOfDigits():
    print("Testing sumOfSquaresOfDigits()...", end="")
    assert(sumOfSquaresOfDigits(5) == 25)   # 5**2 = 25
    assert(sumOfSquaresOfDigits(12) == 5)   # 1**2 + 2**2 = 1+4 = 5
    assert(sumOfSquaresOfDigits(234) == 29) # 2**2 + 3**2 + 4**2 = 4+9+16 = 29
    print("Passed.")

def testIsHappyNumber():
    print("Testing isHappyNumber()...", end="")
    assert(isHappyNumber(-7) == False)
    assert(isHappyNumber(1) == True)
    assert(isHappyNumber(2) == False)
    assert(isHappyNumber(97) == True)
    assert(isHappyNumber(98) == False)
    assert(isHappyNumber(404) == True)
    assert(isHappyNumber(405) == False)
    print("Passed.")

def testNthHappyNumber():
    print("Testing nthHappyNumber()...", end="")
    assert(nthHappyNumber(0) == 1)
    assert(nthHappyNumber(1) == 7)
    assert(nthHappyNumber(2) == 10)
    assert(nthHappyNumber(3) == 13)
    assert(nthHappyNumber(4) == 19)
    assert(nthHappyNumber(5) == 23)
    assert(nthHappyNumber(6) == 28)
    assert(nthHappyNumber(7) == 31)
    print("Passed.")


def testMostFrequentDigit():
    print('Testing mostFrequentDigit()... ', end='')
    assert(mostFrequentDigit(0) == 0)
    assert(mostFrequentDigit(1223) == 2)
    assert(mostFrequentDigit(12233) == 2)
    assert(mostFrequentDigit(-112233) == 1)
    assert(mostFrequentDigit(1223322332) == 2)
    assert(mostFrequentDigit(123456789) == 1)
    assert(mostFrequentDigit(1234567789) == 7)
    assert(mostFrequentDigit(1000123456789) == 0)
    print('Passed.')

def testNthPowerfulNumber():
    print('Testing nthPowerfulNumber()... ', end='')
    assert(nthPowerfulNumber(0) == 1)
    assert(nthPowerfulNumber(1) == 4)
    assert(nthPowerfulNumber(2) == 8)
    assert(nthPowerfulNumber(3) == 9)
    assert(nthPowerfulNumber(4) == 16)
    assert(nthPowerfulNumber(5) == 25)
    assert(nthPowerfulNumber(10) == 64)
    assert(nthPowerfulNumber(15) == 121)
    assert(nthPowerfulNumber(20) == 196)
    print('Passed.')

#################################################
# testAll and main
#################################################

def testAll():
    testDigitCount()
    testGcd()
    testNthAdditivePrime()
    testNthPerfectNumber()
    testLongestIncreasingRun()
    testNthLeftTruncatablePrime()
    testNthCarolPrime()
    testSumOfSquaresOfDigits()
    testIsHappyNumber()
    testNthHappyNumber()
    testMostFrequentDigit()
    testNthPowerfulNumber()

def main():
    testAll()

if __name__ == '__main__':
    main()