문제적 남자 : 브레인 유랑단 13회, 신비로운 문제

hotbrains-s2-13.py

# https://www.youtube.com/watch?v=Hx58twR_VY0

NUMBERS = ["zero", "one", "two", "three", "four", "five", "six", "seven", "eight", "nine", "ten", "eleven", "twelve", "thirteen", "fourteen", "fifteen", "sixteen", "seventeen", "eighteen", "nineteen", "twenty", "twentyone", "twentytwo", "twentythree", "twentyfour", "twentyfive", "twentysix", "twentyseven", "twentyeight", "twentynine", "thirty", "thirtyone", "thirtytwo", "thirtythree", "thirtyfour", "thirtyfive", "thirtysix", "thirtyseven", "thirtyeight", "thirtynine", "forty", "fortyone", "fortytwo", "fortythree", "fortyfour", "fortyfive", "fortysix", "fortyseven", "fortyeight", "fortynine", "fifty", "fiftyone", "fiftytwo", "fiftythree", "fiftyfour", "fiftyfive", "fiftysix", "fiftyseven", "fiftyeight", "fiftynine", "sixty", "sixtyone", "sixtytwo", "sixtythree", "sixtyfour", "sixtyfive", "sixtysix", "sixtyseven", "sixtyeight", "sixtynine", "seventy", "seventyone", "seventytwo", "seventythree", "seventyfour", "seventyfive", "seventysix", "seventyseven", "seventyeight", "seventynine", "eighty", "eightyone", "eightytwo", "eightythree", "eightyfour", "eightyfive", "eightysix", "eightyseven", "eightyeight", "eightynine", "ninety", "ninetyone", "ninetytwo", "ninetythree", "ninetyfour", "ninetyfive", "ninetysix", "ninetyseven", "ninetyeight", "ninetynine"]


# create square to be equal sums
def makeSquare(a, b, c, d):
    return [a, b, c, d, a+d+-c, b+2*c-2*d, b+c-d, 2*c-d, a-2*c+2*d]


# all sum of rows are same?
def isMagicSquare(grid):
    chk = {}
    colsum = [0, 0, 0]
    for i in range(len(grid)):
        # each number in cell should be unique
        if grid[i] in chk or grid[i] <= 0 or grid[i] >= 100:
            return False
        colsum[i % 3] += grid[i]
        chk[grid[i]] = True
    _sum = sum(grid[:3])
    for i in range(0, 3):
        if _sum != sum(grid[3*i:3*(i+1)]):
            return False
        if _sum != colsum[i]:
            return False
    if _sum != grid[0]+grid[4]+grid[8]: return False
    if _sum != grid[2]+grid[4]+grid[6]: return False
    return True


def isValid(grid):
    if not isMagicSquare(grid):
        return False
    square2 = [len(NUMBERS[x]) for x in grid]
    return isMagicSquare(square2)


def print_grid(grid):
    for i in range(3):
        row = grid[3*i:3*(i+1)]
        print(' '.join(list(map(str, row))))


def hash(grid):
    return '-'.join(sorted(list(map(str,grid))))


used_number = {}
used_set = {}
MAX_N = 100
for a in range(1, MAX_N):
    used_number[a] = True
    for b in range(1, MAX_N):
        if b in used_number: continue
        used_number[b] = True
        for c in range(1, MAX_N):
            if c in used_number: continue
            used_number[c] = True
            for d in range(1, MAX_N):
                if d in used_number: continue
                grid = makeSquare(a, b, c, d)
                if isValid(grid):
                    cur_set = hash(grid)
                    if cur_set in used_set: continue
                    used_set[cur_set] = True
                    print_grid(grid)
                    print("")
            del used_number[c]
        del used_number[b]
    del used_number[a]