Problem: To make it difficult to withdraw money, a certain bank allows its customers to withdraw only one of the following amounts in one operation:    * 1 yen (the currency of Japan)    * 6 yen, 6^2(=36) yen, 6^3(=216) yen, ...    * 9 yen, 9^2(=81) yen, 9^3(=729) yen, ...  At least how many operations are required to withdraw exactly N yen in total?  It is not allowed to re-deposit the money you withdrew.

Submission attempts (in order):
num = [i for i in range(0,100001)]

for j in range(1,100001):
        num[j] = j//6 + num[j%6]

for j in range(1,100001):
        num[j] = min(num[j],j//9+num[j%9])

for j in range(1,100001):
        num[j] = min(num[j],j//36+num[j%36])

for j in range(81,324):
        num[j] = min(num[j],1+num[j-81])
for j in range(162,324):
        num[j] = min(num[j],2+num[j-162])
for j in range(243,324):
        num[j] = min(num[j],3+num[j-243])
for j in range(324,100001):
        num[j] = (j//324)*4 + num[j%234]

for j in range(216,648):
        num[j] = min(num[j],1+num[j-216])
for j in range(432,648):
        num[j] = min(num[j],2+num[j-216*2])
for j in range(648,100001):
        num[j] = (j//648)*3 + num[j%648]

for i in range(1,8):
        for j in range(729*i,729*8):
                num[j] = min(num[j],i+num[j-729*i])
for j in range(729*8,100001):
        num[j] = (j//(729*8))*8+num[j%(729*8)]

MoneyYouCanGet = [6**4,9**4,6**5,6**6,9**5]

for i in MoneyYouCanGet:
        for j in range(1,100001):
                k = 1
                while k*i<j:
                        num[j] = min(num[j],k+num[j-k*i])
                        k += 1

N = int(input())
print(num[N])

num = [i for i in range(0,100001)]

for j in range(1,100001):
        num[j] = j//6 + num[j%6]

for j in range(1,100001):
        num[j] = min(num[j],j//9+num[j%9])

for j in range(1,100001):
        num[j] = min(num[j],j//36+num[j%36])

for j in range(81,324):
        num[j] = min(num[j],1+num[j-81])
for j in range(162,324):
        num[j] = min(num[j],2+num[j-162])
for j in range(243,324):
        num[j] = min(num[j],3+num[j-243])
for j in range(324,100001):
        num[j] = min(num[j],(j//324)*4 + num[j%234])

for j in range(216,648):
        num[j] = min(num[j],1+num[j-216])
for j in range(432,648):
        num[j] = min(num[j],2+num[j-216*2])
for j in range(648,100001):
        num[j] = min(num[j],(j//648)*3 + num[j%648])

for i in range(1,8):
        for j in range(729*i,729*8):
                num[j] = min(num[j],i+num[j-729*i])
for j in range(729*8,100001):
        num[j] = min(num[j],(j//(729*8))*8+num[j%(729*8)])

for i in range(1,9):
        for j in range((6**4)*i,(6**4)*9):
                num[j] = min(num[j],i+num[j-(6**4)*i])
for j in range((6**4)*9,100001):
        num[j] = min(num[j],(j//((6**4)*9))*9+num[j%((6**4)*9)])

for i in range(1,2**4):
        for j in range((9**4)*i,(9**4)*(2**4)):
                num[j] = min(num[j],i+num[j-(9**4)*i])
for j in range((9**4)*(2**4),100001):
        num[j] = min(num[j],(j//((9**4)*(2**4)))*(2**4)+num[j%((6**4)*(2**4))])

MoneyYouCanGet = [6**5,6**6,9**5]

for i in MoneyYouCanGet:
        for j in range(1,100001):
                k = 1
                while k*i<j:
                        num[j] = min(num[j],k+num[j-k*i])
                        k += 1

N = int(input())
print(num[N])

SixNum = [i for i in range(0,100001)]
for i in range(1,7):
        for j in range(1,100001):
                SixNum[j] = min(SixNum[j],j//(6**i) + SixNum[j%(6**i)])

NineNum = [i for i in range(0,100001)]
for i in range(1,6):
        for j in range(1,100001):
                NineNum[j] = min(NineNum[j],j//(9**i) + NineNum[j%(9**i)])

N = int(input())
ans = 100001
for i in range(0,N+1):
        ans = min(ans,SixNum[i]+NineNum[N-i])
print(ans)

Verdicts: Time Limit Exceeded

Runtime Error

Accepted