考起碩士生的小一數學題(ppp)解法

題目

Rules

1. A, C, E, G != 0
2. 所有數字既range係[0, 9]
3. 數字冇重覆

Code

#!/usr/bin/env pypy3
from itertools import permutations

def check(i):
    if i[0] == 0 or i[2] == 0 or i[4] == 0 or i[6] == 0:
        return
    ab = i[0] * 10 + i[1]
    cd = i[2] * 10 + i[3]
    ef = i[4] * 10 + i[5]
    if ab - cd != ef:
        return
    gh = i[6] * 10 + i[7]
    ppp = i[8] * 100 + i[8] * 10 + i[8]
    if ef + gh == ppp:
        print("{0} - {1} = {2}, {2} + {3} = {4}".format(ab, cd, ef, gh, ppp))

if __name__ == '__main__':
    for i in permutations(range(0, 10), 9):
        check(i)

如果已知ppp = 111

#!/usr/bin/env pypy3
from itertools import permutations

def check(i):
    if i[0] == 0 or i[2] == 0 or i[4] == 0 or i[6] == 0:
        return
    ab = i[0] * 10 + i[1]
    cd = i[2] * 10 + i[3]
    ef = i[4] * 10 + i[5]
    if ab - cd != ef:
        return
    gh = i[6] * 10 + i[7]
    ppp = 111
    if ef + gh == ppp:
        print("{0} - {1} = {2}, {2} + {3} = {4}".format(ab, cd, ef, gh, ppp))

if __name__ == '__main__':
    for i in permutations(list(range(2, 10)) + [0], 9):
        check(i)

答案

85 - 46 = 39, 39 + 72 = 111
86 - 54 = 32, 32 + 79 = 111
90 - 27 = 63, 63 + 48 = 111
90 - 63 = 27, 27 + 84 = 111
95 - 27 = 68, 68 + 43 = 111
pypy3 ./primary-math.py  0.10s user 0.02s system 98% cpu 0.123 total

結論

出題果個正一戇鳩。

高效率版本

用左加強版解法既algorithm解一解原題目。唔知點解python3快過pypy3。

 #!/usr/bin/env python3
from itertools import permutations

PPP = 111

def check_last_4(i):
    if i[0] == 0 or i[2] == 0:
        return 0
    EF, GH = i[0] * 10 + i[1], i[2] * 10 + i[3]
    if EF + GH == PPP:
        return EF
    return 0

def check_first_4(i, EF):
    if i[0] == 0 or i[2] == 0:
        return 0
    AB, CD = i[0] * 10 + i[1], i[2] * 10 + i[3]
    if AB - CD == EF:
        return 1

if __name__ == '__main__':
    for i in permutations(set(range(10)) - {1}, 4):
        EF = check_last_4(i)
        if EF == 0:
            continue
        for j in permutations(set(range(10)) - set(i) - {1}, 4):
            if check_first_4(j, EF):
                print(j, i)

結果

(9, 0, 6, 3) (2, 7, 8, 4)
(8, 6, 5, 4) (3, 2, 7, 9)
(8, 5, 4, 6) (3, 9, 7, 2)
(9, 0, 2, 7) (6, 3, 4, 8)
(9, 5, 2, 7) (6, 8, 4, 3)
python ./eff.py  0.05s user 0.00s system 98% cpu 0.055 total