Wine glass solution

solution.txt

1-st pouring
n=1
0.500

2-nd pouring
n=2
                1

        0.500           0.500

3-rd pouring
n=2
                1

        1               1

4-th pouring
n=4
                                1

                        1               1

                0.750           1               0.750

        0               0.250           0.250           0

5-th pouring
n=5
                                1

                        1               1

                1               1               1

        0.350           1               1               0.350

0               0.275           0.550           0.275           0

6-th pouring
n=6
                                                1

                                        1               1

                                1               1               1

                        1               1               1               1

                0               1               1               1               0

        0               0.125           0.875           0.875           0.125           0

7-th pouring
n=8
                                                                1

                                                        1               1

                                                1               1               1

                                        1               1               1               1

                                0.525           1               1               1               0.525

                        0               1               1               1               1               0

                0               0.087           1               1               1               0.087           0

        0               0               0.169           0.919           0.919           0.169           0               0

wine-glass.py

# problem : wine glass
# source : https://www.facebook.com/groups/ThaiPGAssociateSociety/posts/2392759474268641/
# coded by : kang

from decimal import Decimal
import math

def normalize(layer: list):
    return [min(glass, Decimal(1)) for glass in layer]

def pour_wine(a: Decimal):
    glasses = None
    n = 1

    # current layer
    cl = [a]
    glasses = normalize(cl)
    last_layer = False
    while not last_layer:
        last_layer = True
        # next layer
        nl: list = []
        for i, c in enumerate(cl):
            # solution of the new glass in next layer
            s = c - 1 if c >= 1 else Decimal(0)
            s = s / 2
            if s > 0:
                last_layer = False
            if i == 0:
                nl.append(s)
            else:
                nl[-1] += s
            nl.append(s)
            i += 1
        cl = nl
        if not last_layer:
            n += 1
            glasses += normalize(nl)
    return glasses, n

##### unit-tests #####
(glasses, n) = pour_wine(Decimal(0.5))
assert glasses == [Decimal(0.5)]
assert n == 1

(glasses, n) = pour_wine(Decimal(2))
assert glasses == [Decimal(1), Decimal("0.5"), Decimal("0.5")]
assert n == 2

(glasses, n) = pour_wine(Decimal(3))
assert glasses == [Decimal(1), Decimal(1), Decimal(1)]
assert n == 2

(glasses, n) = pour_wine(Decimal(6))
assert glasses == [
    Decimal(1),
    Decimal(1), Decimal(1),
    Decimal("0.75"), Decimal(1), Decimal("0.75"),
    Decimal(0), Decimal("0.25"), Decimal("0.25"), Decimal(0),]
assert n == 4

(glasses, n) = pour_wine(Decimal("9.8"))
assert glasses == [
    Decimal(1),
    Decimal(1), Decimal(1),
    Decimal(1), Decimal(1), Decimal(1),
    Decimal('0.35'), Decimal(1), Decimal(1), Decimal('0.35'),
    Decimal('0'), Decimal('0.275'), Decimal('0.550'), Decimal('0.275'), Decimal('0')]
assert n == 5

def display_glasses(glasses: list, n: int):
    print(f"n={n}")

    # deep copy
    glasses = list(glasses)

    spacer = "\t"
    # NOTE: for debugging purpose
    # spacer = "s"

    # normalized n
    nn = n + 1 if n % 2 == 0 else n
    for i in range(1, n+1):
        # partial glasses (layer)
        pg = glasses[:i]
        # leading spaces between layer
        ls = (spacer * 2 * int(math.floor((nn - i)/2)))
        if len(pg) % 2 == 0:
            ls += spacer

        print(ls, end="")
        for g in pg:
            format_string = "%.3f" if 0 < g < 1 else "%d"
            print(format_string % g, end=spacer*2)
        print("\n")

        glasses = glasses[i:]


# NOTE: for debugging purpose
# glasses == [
#     Decimal(1),
#     Decimal(1), Decimal(1),
#     Decimal(1), Decimal(1), Decimal(1),
#     Decimal('0.35'), Decimal(1), Decimal(1), Decimal('0.35'),
#     Decimal('0'), Decimal('0.275'), Decimal('0.550'), Decimal('0.275'), Decimal('0')]
# n = 5
# display_glasses(glasses, n)

# glasses = [Decimal(1), Decimal(1), Decimal(1)]
# n = 2
# display_glasses(glasses, n)


##### real application #####
print("1-st pouring")
display_glasses(*pour_wine(Decimal(0.5)))

print("2-nd pouring")
display_glasses(*pour_wine(Decimal(2)))

print("3-rd pouring")
display_glasses(*pour_wine(Decimal(3)))

print("4-th pouring")
display_glasses(*pour_wine(Decimal(6)))

print("5-th pouring")
display_glasses(*pour_wine(Decimal("9.8")))

print("6-th pouring")
display_glasses(*pour_wine(Decimal("15")))

print("7-th pouring")
display_glasses(*pour_wine(Decimal("23.4")))