igorvanloo

def prime_factors(n):
    factors = []
    d = 2
    while n > 1:
        while n % d == 0:
            factors.append(d)
            n /= d
        d = d + 1
        if d*d > n:
            if n > 1: 

igorvanloo

#Returns a list of True and False indicating if a number is prime, for example list[7] = True, list[8] = False
def list_primality(n):
  result = [True] * (n + 1)
  result[0] = result[1] = False
  for i in range(int(math.sqrt(n)) + 1):
    if result[i]:
      for j in range(2 * i, len(result), i):
        result[j] = False
  return result

igorvanloo

def Partition(goal, alist):
  ways = [1] + [0] * (goal)
  for options in alist:
     for i in range(len(ways) - options):
        ways[i + options] += ways[i]
  return ways[-1]-1 

'''
Sample Output for partitioning 5:

igorvanloo

def compute():
    matrix = [[131, 673, 234, 103,18],
              [201, 96, 342, 965, 150],
              [630, 803, 746, 422, 111],
              [537, 699, 497, 121, 956],
              [805, 732, 524, 37, 331]]
    y = len(matrix)
    x = len(matrix[0])
    for i in (range(x)):
        for j in (range(y)):

igorvanloo

def compute():
    start = 101010100
    end = 1389026620
    while start < end:
        if str((start+30)**2)[::2] == "1234567890":
            start += 30
            break
        if str((start+70)**2)[::2] == "1234567890":
            start += 70
            break

igorvanloo

def Number_to_english(x):
    if x < 20:
        return ONES[x]
    elif 20 <= x < 100:
        return TENS[x // 10] + ONES[x % 10]
    elif 100 <= x < 1000:
        if x == 100:
            return "onehundred"
        else:
            if x % 100 == 0:

igorvanloo

def top_to_bottom(tri):
    for i in range(1,len(tri)):
        a = len(triangle[i])
        for j in range(0, a):
            if j == 0:
                tri[i][j] += tri[i-1][j]
            elif j == a-1:
                tri[i][j] += tri[i-1][j-1]
            else:
                tri[i][j] += max(tri[i-1][j],tri[i-1][j-1])