collatz_problem

def map_builder(chain, map_dct):
        '''
        (list, dictionary) -> dictionary
        
        Precondition: chain[0] is a number equall to existing key in dictionary.
        This function takes arguments chain (list of numbers) and map_dct (dictionary {num:num}) 
        and creates new entries in dictionary with keys equal to numbers from chain[1:] and values
        assigned to sum of preexisted key's value and 1, 2,...n according to the position of 
        the element in chain.
        '''
 
	for (i, j) in zip(chain[1:], range(1,len(chain))):
	    map_dct[i] = map_dct[chain[0]] + j
	return map_dct
    
def hailstone_seq(n):
    '''
    (int) -> dictionary
    For each element from range(2, n+1) this function create dictionary with keys corresponding to 
    the element and value corresponding to the length of the hailstone sequence generated by this
    number. All the numbers which appears in hailstone sequence during calculations are excluded 
    from the input set n {[2...n]} (we already know length for every such chain).
    '''
    map_dct = {1:1}                     
    n = set(range(2, n+1))
    chain = [n.pop()]
    while len(n) >= 0:
        if chain[0] in map_dct:                        # Found number in map_dct?
            map_dct = map_builder(chain, map_dct)      # Assign length values for rest of numbers
            n -= set(chain)                            # Delete all numbers from the input set
            if len(n) == 0:                            # Stop if the sat is empty
                break
            chain = [n.pop()]                          # Take the element from input set
            continue                                   # Why did I write it here?! Aliens!
        else:
            chain.insert(0, chain[0]%2 == 0 and chain[0]//2 or int(chain[0]*3+1)) #Find next element

    golden_key = max(map_dct, key = map_dct.get)       # Find key with max value
    print("It's a nummber " + str(golden_key) +        # Say how do you love her!
          "\nChain length is " + str(map_dct[golden_key]))