# Loopy exercises: Answers

# -------------------------- 1. fred(q) ----------------

def fred(q):
    return q*q-3

# -------------------------- 2. sumFredWhile(n) ----------

def sumFredWhile(n):
    the_sum=0
    i=0
    while i<n:
        the_sum += fred(i)
        i += 1
    return the_sum
    
# --------------------------- 3. sumFredFor(n) -----------
    
def sumFredFor(n):
    the_sum=0
    for i in range(n):
        the_sum += fred(i)
    return the_sum

#------------------------------ 4. sumFredBetween(low,high) -----

def sumFredBetween(low,high):
    return sumFredFor(high+1) - sumFredFor(low)


# --------------------------- 5. sumFredBetween2(a,b) ---------

def sumFredBetween2(a,b):
    if a<=b:
        return sumFredBetween(a,b)
    return sumFredBetween(b,a)

# ---------------------------- 6. factorPairs(n) ------------

def factorPairs(n):
    for i in range(1,int(n**0.5)+1):
        if n%i == 0:
            print i,n/i

# ---------------------------- 7. isPrime(n) --------------------

def isPrime(n):
    if n==2 or n==3:
        return True
    if n%2==0:
        return False
    highest=int(n**0.5)+1
    i=3
    while i<highest:
        if n%i==0:
            return False
        i += 2
    return True

# --------------------------- 8. LargestPrimeFactor(n) -----------

# Helper function: smallestFactor(n)
def smallestFactor(n):
    if isPrime(n):
        return n
    if n%2==0:
        return 2
    for i in range(3,int(n**0.5)+1,2):
        if n%i==0:
            return i

def largestPrimeFactor(n):
    sofar=1
    while True:
        factor=smallestFactor(n)  # find the next factor
        if factor>sofar:  # if it's larger than the one we already have, keep it
            sofar=factor
        if factor==n:  # if the factor is the number itself, then we're done
            return sofar
        n /= factor  # now reduce the number by that factor, and start again
        
# --------------------------------- 9. Prime or not? ----------------
## 98767 False
## 987127 True
## 135797533 True
## 12345678911 False
## 12345677654381 True