Problem:


Score : 300 points

Problem Statement

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.

Constraints

1 \leq N \leq 100000

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

If at least x operations are required to withdraw exactly N yen in total, print x.

Sample Input 1

127

Sample Output 1

4

By withdrawing 1 yen, 9 yen, 36(=6^2) yen and 81(=9^2) yen, we can withdraw 127 yen in four operations.

Sample Input 2

3

Sample Output 2

3

By withdrawing 1 yen three times, we can withdraw 3 yen in three operations.

Sample Input 3

44852

Sample Output 3

16



Sample input:
127


Sample output:
4

Submission status: Accepted

Solution code:
#!/usr/bin/env python3
import sys, math, itertools, heapq, collections, bisect, functools, copy
input = lambda: sys.stdin.buffer.readline().rstrip().decode('utf-8')
sys.setrecursionlimit(10**7)
inf = float('inf')
mod = 10**9+7
ans = inf ; count = 0; pro = 1

n=int(input())
count=0
# @functools.lru_cache(maxsize=None)
memo=[0]*(n+1)
memo[0]=0
def func(n):
    if memo[n] or n==0:return memo[n]
    # print(n)
    # global count
    # count+=1
    # if count%10==0:print(count)
    if n==0:
        return 0
    re=inf
    k=s=1
    while 9**s<=n:
        re=min(re,func(n-9**s)+1)
        s+=1
    while 6**k<=n:
        re=min(re,func(n-6**k)+1)
        k+=1
    re=min(re,func(n-1)+1)
    memo[n]=re
    return re
    
print(func(n))
# print(memo)

Submission status: Accepted

Solution code:
#!/usr/bin/env python3
import sys, math, itertools, heapq, collections, bisect, functools, copy
input = lambda: sys.stdin.buffer.readline().rstrip().decode('utf-8')
sys.setrecursionlimit(10**7)
inf = float('inf')
mod = 10**9+7
ans = inf ; count = 0; pro = 1

n=int(input())
count=0
# @functools.lru_cache(maxsize=None)
memo=[0]*(n+1)
memo[0]=0
def func(n):
    if memo[n] or n==0:return memo[n]
    # print(n)
    # global count
    # count+=1
    # if count%10==0:print(count)
    if n==0:
        return 0
    re=inf
    k=s=1
    while 6**k<=n:
      re=min(re,func(n-6**k)+1)
      k+=1
    while 9**s<=n:
      re=min(re,func(n-9**s)+1)
      s+=1

    re=min(re,func(n-1)+1)
    memo[n]=re
    return re
    
print(func(n))
# print(memo)

Submission status: Accepted

Solution code:
N = int(input())
res = N
for i in range(N+1):
    cc = 0
    t = i
    while t > 0:
        cc += t % 6
        t //= 6
    t = N - i
    while t > 0:
        cc += t % 9
        t //= 9
    res = min(res, cc)
print(int(res))

Submission status: Accepted

Solution code:
N=int(input())
ans = N
for i in range(N+1):
    t=i
    cnt=0
    while t>0:
        cnt += t%6
        t //= 6
    k=N-i
    while k>0:
        cnt += k%9
        k //= 9
    ans = min(ans,cnt)
print(ans)

Submission status: Accepted

Solution code:

args = int(input())

ans = float('inf')
for i in range(args+1):
    count = 0

    args_six = i
    while args_six >= 6:
        count += args_six % 6
        args_six //= 6
    count += args_six

    args_nine = args - i
    while args_nine >= 9:
        count += args_nine % 9
        args_nine //= 9
    count += args_nine
    ans = min(ans, count)

print(ans)

Submission status: Accepted

Solution code:
N = int(input())
dp = [float("inf")]*(N + 1)
dp[0] = 0
pull_list_9 = [9**i for i in range(1, 6)]
pull_list_6 = [6**i for i in range(1, 7)]
pull_list = pull_list_9 + pull_list_6 + [1]
p_s = sorted(pull_list)

for i in range(1, N + 1):
  for j in p_s:
    if i - j < 0:
      break
    dp[i] = min(dp[i], dp[i-j] + 1)

print(dp[-1])

Submission status: Accepted

Solution code:
def main(sample_file = ''):

    """ convenient functions
    # for i, a in enumerate(iterable)
    # q, mod = divmod(a, b)
    # divmod(x, y) returns the tuple (x//y, x%y)
    # Higher-order function: reduce(operator.mul, xyz_count, 1)
    # manage median(s) using two heapq https://atcoder.jp/contests/abc127/tasks/abc127_f
    """

    """convenient decorator
    # @functools.lru_cache():
    # to facilitate use of recursive function
        # ex:
        # from functools import lru_cache
        # import sys
        # sys.setrecursionlimit(10**9)
        # @lru_cache(maxsize=None)
        # def fib(n):
        #     if n < 2:
        #         return n
        #     return fib(n-1) + fib(n-2)
        # print(fib(1000))
    """
    
    # import numpy as np
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product # https://docs.python.org/ja/3/library/itertools.html
    # accumulate() returns iterator! to get list: list(accumulate())
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  # prime factor
        b, e = 2, 0  # base, exponent
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        # TODO: How should I do when n - r is negative?
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict # https://docs.python.org/ja/3/library/collections.html#collections.deque
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest # https://docs.python.org/ja/3/library/heapq.html
    from copy import deepcopy, copy # https://docs.python.org/ja/3/library/copy.html
    import operator
    from operator import itemgetter #sort 
    # ex1: List.sort(key=itemgetter(1))
    # ex2: sorted(tuples, key=itemgetter(1,2))
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd # Deprecated since version 3.5: Use math.gcd() instead.
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)
    
    # first create factorial_list
    # fac_list = mod_factorial_list(n)
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    modpow = lambda a, n, p = MOD: pow(a, n, p) # Recursive function in python is slow!
    def modinv(a, p = MOD):
        # evaluate reciprocal using Fermat's little theorem:
        # a**(p-1) is identical to 1 (mod p) when a and p is coprime
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        # fac_list = modfactorial_list(100)
        # print(modcomb(100, 5, modfactorial_list(100)))
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something
        >>  else:
        >>      do something
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    # Graph: https://en.wikipedia.org/wiki/Directed_graph
    # Bellman-Ford: O(|V||E|). Use this if there exists an edge with negative length in the graph
    # After N steps, the shortest path has converded if there doesn't exist an cycle of edges with negative
    # Watch out: d[N] == d[2*N] doesn't necessarily mean the graph doesn't have negative cycle
    # ref: https://www.youtube.com/watch?v=1Z6ofKN03_Y

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    """ initialize variables and set inputs
    # initialize variables
        # to initialize list, use [0] * n
        # to initialize two dimentional array:
            # ex) [[0] * N for _ in range(N)]
            # ex2) dp = [[0] * (N+1) for _ in range(W*2)]
    # set inputs
        # put inputs between specific values (almost as quickly)
        # ex) S = [-INF] + [int(r()) for _ in range(A)] + [INF]
        # open(0).read() is sometimes useful:
        # ex) n, m, *x = map(int, open(0).read().split())
        #     min(x[::2]) - max(x[1::2])
        # ex2) *x, = map(int, open(0).read().split())
        #     don't forget to add comma after *x if only one variable is used
    # preprocessing
        # transpose = [x for x in zip(*data)]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [(1, 4, 7), (2, 5, 8), (3, 6, 9)]
        # flat = [flatten for inner in data for flatten in inner]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [1, 2, 3, 4, 5, 6, 7, 8, 9]
    # calculate and output
        # output pattern
        # ex1) print(*l) => when l = [2, 5, 6], printed 2 5 6
    """

    # functions to read input
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    R = lambda: list(map(int, r().split()))
    Rmap = lambda: map(int, r().split())
    Rfloat = lambda: list(map(float, r().split()))
    Rtuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    # single int: int(r())
    # single string: r()
    # single float: float(r())
    # line int: R()
    # line string: r().split()
    # line (str, int, int): [j if i == 0 else int(j) for i, j in enumerate(r().split())]
    # lines int: [R() for _ in range(n)]
    """

    # for test
    if sample_file:
        sys.stdin = open(sample_file)
        
    # ----------------------------------
    # main

    N = r_int()
    dp = [[0] * (14) for _ in range(10**5+1)]
    for i in range(10**5+1):
        dp[i][0] = i
    unit_money = [6**i for i in range(1, 7)] + [9**i for i in range(1,6)]

    for col, unit in enumerate(unit_money, start=1):
        for i in range(10**5+1):
            dp[i][col] = dp[i][col-1]
            if i >= unit:
                dp[i][col] = min(dp[i][col], dp[i-unit][col]+1)
    print(dp[N][11])

    # to finish code, use return instead of exit()
    # end of main
    # ----------------------------------

    """memo: how to use defaultdict of list
    # initialize
    Dic = defaultdict(list)
    # append / extend
    Dic[x].append(y)
    # three methods for loop: keys(), values(), items()
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    # to make binary digits text
    >>> a = 5
    >>> bin_str_a = format(a, '#06b')
    >>> print(bin_str_a)
    0b0101 # first 2 strings (='0b') indicates it is binary
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
from collections import deque
import math

n = int(input())

#引き出せる金額の準備
a1 = [1]
a6 = [6**x for x in range(1, int(math.log(10**6, 6))+1)]
a9 = [9**x for x in range(1, int(math.log(10**6, 9))+1)]
b = a1+a6+a9
b.sort()

# n円引き出すための引き出し回数
dp = [-1] *(n+1)
dp[0]  = 0

# 探索キューを初期値ゼロで用意
d = deque([0])

# キューがなくなるまでループ
for _ in range(10**12):
    # キューが無いなら終了
    if len(d) == 0:
        break
        
    # キューから取り出し
    tmp = d.pop()
    
    # +1回で引き出せる範囲をDPにメモ
    for x in b:
        if tmp+x > n:
            break
        if dp[tmp+x] == -1:
            dp[tmp+x] = dp[tmp]+1
            d.appendleft(tmp+x)

print(dp[n])

Submission status: Accepted

Solution code:
# Strange Bank
N = int(input())

dp = ['inf']*(N+1)

init = 6 if N > 5 else N+1
for n in range(init):
	dp[n] = n

for n in range(6,N+1):
	cnd = [dp[n-1]+1]
	for i in range(1,7):
		if n > 6**i-1:
			cnd.append(dp[n-6**i]+1)
	for j in range(1,6):
		if n > 9**j-1:
			cnd.append(dp[n-9**j]+1)
	dp[n] = min(cnd)
	
print(dp[N])

Submission status: Accepted

Solution code:
N = int(input())
dp = [100000] * (N + 1)
dp[0] = 0
dp[1] = 1
for i in range(1, N + 1):
    dp[i] = dp[i - 1] + 1
    # 6
    prev = 6
    while i - prev >= 0:
        dp[i] = min(dp[i], dp[i - prev] + 1)
        prev *= 6
    # 9
    prev = 9
    while i - prev >= 0:
        dp[i] = min(dp[i], dp[i - prev] + 1)
        prev *= 9
print(dp[N])

Submission status: Accepted

Solution code:
N = int(input())
ans = float('inf')
for i in range(N+1):
    count = 0
    n = i
    while n > 0:
        count += n % 6
        n //= 6
    n = N-i
    while n > 0:
        count += n % 9
        n //= 9
    ans = min(ans, count)

print(ans)

Submission status: Accepted

Solution code:
from itertools import count

n = int(input())

dp = [0]*(n+1)

#[1,6,36,9,81]などのn以下で使える数字を出力してくれる。
def it(n):
  yield 1
  m = 6
  while m <= n:
    yield m
    m *= 6
  m = 9
  while m <= n:
    yield m
    m *= 9

#1~nまでの数をループで回す
for i in range(1,n+1):
  #print(list(t for t in it(i)))
  #使える数字全部使ってそこまでのdpを
  dp[i] = min(dp[i-t] for t in it(i))+1
  
print(dp[n])

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(10**6)
from functools import lru_cache

@lru_cache(maxsize=None)
def solve(val , now):
    if val < 6 or now == 0:
        ret_val = val
    # 何もしない
    elif val < counts[now]:
        ret_val = solve(val , now - 1)
    # 何もしない or 手を加えるの小さい方
    else:
        ret_val = min(solve(val , now - 1) , solve(val - counts[now] , now) + 1)
    return ret_val

N = int(input())
coins = [1,6,9]
counts = [1]
for i in range(1,3):
    for j in range(1,N):
        if coins[i] ** j <= N:
            counts.append(coins[i] ** j)
        else:
            break
#print(counts)
print(solve(N , len(counts) - 1))

Submission status: Accepted

Solution code:
N = int(input())

M1 = [6**i for i in range(7)]
M2 = [9**i for i in range(6)]
M = list(set(M1 + M2))
M.sort()
#print(M)


dp = [0 for i in range(N+1)]
dp[0] = 1

for i in range(1, N+1):
    if i in M:
        dp[i] = 1
    else:
        dp[i] = min(dp[i-1] + 1, dp[i])
    for j in M:
        if i + j <= N:
            if dp[i+j] == 0:
                dp[i+j] = dp[i] + 1
            else:
                dp[i+j] = min(dp[i] + 1, dp[i+j])

            #print(i, dp[i+j])
#print(dp)
print(dp[N])

Submission status: Accepted

Solution code:
INF = float('inf')
N = int(input())

dp = [INF for _ in range(N+1)]
dp[0] = 0

for i in range(1, N+1):
    # 1円玉を使う場合
    dp[i] = min(dp[i], dp[i-1] + 1)
    # 6べき円玉を使う場合
    power = 6
    while power <= i:
        dp[i] = min(dp[i], dp[i-power] + 1)
        power *= 6
    # 9べき円玉を使う場合
    power = 9
    while power <= i:
        dp[i] = min(dp[i], dp[i-power] + 1)
        power *= 9

print(dp[N])

Submission status: Accepted

Solution code:

def examC(inf):
    N = I()
    A = []
    A.append(1)
    for i in range(1, 7):
        A.append(6 ** i)
    for i in range(1, 6):
        A.append(9 ** i)
    A.sort()
    dp = [10 * 5 + 10] * (N + 1)
    dp[0] = 0
    for i in range(1, N + 1):
        for s in range(len(A)):
            if i - A[s] >= 0:
                dp[i] = min(dp[i - A[s]] + 1, dp[i])
    ans = dp[N]
    print(ans)

import sys,copy,bisect,itertools,heapq,math
from heapq import heappop,heappush,heapify
from collections import Counter,defaultdict,deque
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))
def LSI(): return list(map(str,sys.stdin.readline().split()))
def LS(): return sys.stdin.readline().split()
def SI(): return sys.stdin.readline().strip()
mod = 10**9 + 7
inf = float('inf')

examC(inf)

Submission status: Accepted

Solution code:
n = int(input())

ans = float("inf")

for i in range(n+1):
    kari = 0

    a = i
    while a >= 6:
        kari += a % 6
        a //= 6
    kari += a

    b = n - i
    while b >= 9:
        kari += b % 9
        b //= 9
    kari += b

    ans = min(ans, kari)

print(ans)

Submission status: Accepted

Solution code:
def nbasesum(value,n):
    nbasevalue = 0
    while value > 0:
        nbasevalue += value%n
        value //= n
    return nbasevalue

N = int(input())
ans = nbasesum(N,9)

for i in range(N+1):
    c6 = i
    c9 = N-i
    ans = min(ans, nbasesum(c9,9)+nbasesum(c6,6))

print(ans)

Submission status: Accepted

Solution code:
def nbasesum(value,n):
    nbasevalue = 0
    while value >= n:
        nbasevalue += value%n
        value //= n
    nbasevalue += value
    return nbasevalue

N = int(input())
ans = nbasesum(N,9)

for i in range(N+1):
    c6 = i
    c9 = N-i
    ans = min(ans, nbasesum(c9,9)+nbasesum(c6,6))

print(ans)

Submission status: Accepted

Solution code:
from collections import Counter,defaultdict,deque
import sys
import bisect
import math
import itertools
import string
import queue
import copy
# import numpy as np
# import scipy
from itertools import permutations, combinations
from heapq import heappop, heappush
# input = sys.stdin.readline
sys.setrecursionlimit(10**8)
mod = 10**9+7
 
def inp(): # n=1
    return int(input())
def inpm(): # x=1,y=2
    return map(int,input().split())
def inpl(): # a=[1,2,3,4,5,...,n]
    return list(map(int, input().split()))
def inpls(): # a=['1','2','3',...,'n']
    return list(input().split())
def inplm(n): # x=[] 複数行
    return list(int(input()) for _ in range(n))
def inpll(n): # [[1,1,1,1],[2,2,2,2],[3,3,3,3]]
    return [list(map(int, input().split())) for _ in range(n)]

def main():
    n=inp()
    ans=n
    for t in range(min(5,n//46656)+1):
        x1 = n-t*46656
        for s in range(min(5,x1//7776)+1):
            x2=x1-7776*s
            for r in range(min(5,x2//1296)+1):
                x3=x2-1296*r
                for q in range(min(5,x3//216)+1):
                    x4=x3-216*q
                    for p in range(min(5,x4//36)+1):
                        x5=x4-36*p
                        for o in range(min(5,x5//6)+1):
                            x6=x5-6*o
                            n1=x6//59049
                            x6-=59049*n1
                            n2=x6//6561
                            x6-=6561*n2
                            n3=x6//729
                            x6-=729*n3
                            n4=x6//81
                            x6-=81*n4
                            n5=x6//9
                            x6-=9*n5
                            ans=min(ans,o+p+q+r+s+t+n1+n2+n3+n4+n5+x6)
    print(ans)

if __name__ == "__main__":
    main()

Submission status: Accepted

Solution code:
n = int(input())

max_N = 1000000
memo = [False]*max_N
import sys
import threading
sys.setrecursionlimit(100000)
threading.stack_size(128*1024*1024)


# 貰う DPではなく、再帰を使ったメモ化再帰
from functools import lru_cache

lru_cache(maxsize=100000)
def f(n):
	if n < 6:
		return n
	if memo[n]:
		# print(f"at n: {n}, memo[n]:", memo[n])
		return memo[n]
	
	ans = n
	# メモ化
	x = 6
	while x <= n:
		ans = min(ans, f(n-x)+1)
		x *= 6
	
	x = 9
	while x <= n:
		ans = min(ans, f(n-x)+1)
		x *= 9
	
	memo[n] = ans
	return ans

def main():
	print(f(n))
	
threading.Thread(target=main).start()

Submission status: Accepted

Solution code:
N = int(input())
dp = dict()

dp[0] = 0
# 貰う DP --- dp[n] に遷移を集める
for n in range(1, N+1):
  dp[n] = dp[n-1] + 1
  
  # メモ化
  x = 6
  while x <= n:
    dp[n] = min(dp[n], dp[n-x]+1)
    x *= 6
  
  x = 9
  while x <= n:
    dp[n] = min(dp[n], dp[n-x]+1)
    x *= 9
    
  # dp[n] = ans
  
print(dp[N])

Submission status: Accepted

Solution code:
N = int(input())
dp = dict()

dp[0] = 0
for n in range(1, N+1):
  ans = dp[n-1] + 1
  
  # メモ化
  x = 6
  while x <= n:
    ans = min(ans, dp[n-x]+1)
    x *= 6
  
  x = 9
  while x <= n:
    ans = min(ans, dp[n-x]+1)
    x *= 9
    
  dp[n] = ans
  
print(dp[N])

Submission status: Accepted

Solution code:
n=int(input())

m=n//6+n%6
for i in range(n+1):
  c=0
  t=i
  while t>0:
    c+=t%6
    t//=6
  t=n-i
  while t>0:
    c+=t%9
    t//=9
  m=min(m,c)

print(m)

Submission status: Accepted

Solution code:
def pow_n(n,k): #kをnで何科いわれるか
    pow_n = 0
    while k //n != 0:
        pow_n += 1
        k = k//n
    return(pow_n)

n = int(input())
dp= [0]*(n+1)
dp[0] = 0
#print(pow_n(6,39),pow_n(9,33))
for i in range(1,n+1):
    pow_6 = pow_n(6,i)
    pow_9 = pow_n(9,i)
    dp[i] = dp[i-1]+1
    for j in range(1,pow_6+1):
        dp[i] = min(dp[i],dp[i-6**j]+1)
    for j in range(1,pow_9+1):
        dp[i] = min(dp[i],dp[i-9**j]+1)
#print(dp[21],dp[15],dp[12])
print(dp[n])

Submission status: Accepted

Solution code:
N=int(input())
dp=[i for i in range(N+1)]
n=1
while n<=N:
  n*=6
  for j in range(N-n+1):
    dp[j+n]=min(dp[j+n],dp[j]+1)
    
n=1
while n<=N:
  n*=9
  for j in range(N-n+1):
    dp[j+n]=min(dp[j+n],dp[j]+1)

print(dp[N])

Submission status: Accepted

Solution code:
n=int(input())
dp=[10**6]*(n+1)
dp[0]=0
for i in range(n+1):
	j=0
	while i-6**j>=0:
		dp[i]=min(dp[i-6**j]+1,dp[i])
		j+=1
	j=0
	while i-9**j>=0:
		dp[i]=min(dp[i-9**j]+1,dp[i])
		j+=1
print(dp[-1])

Submission status: Accepted

Solution code:
n = int(input())
ans = float("inf")
for i in range(n):
    if i * 9 > n:
        break
    j = (n-(i*9)) // 6
    k = (n-(i*9)) % 6

    tmp = 0
    tmp += k
    while i:
        tmp += i % 9
        i = i // 9
    while j:
        tmp += j % 6
        j = j // 6
    if tmp < ans:
        ans = tmp

print(ans)

Submission status: Accepted

Solution code:
import sys
import math
if sys.platform =='ios':
  sys.stdin=open('Untitled.txt')
input = sys.stdin.readline


N = int(input())
dp = [float("INF") for _ in range(N+1)]
dp[0] = 0

MAX_JOU = int(math.ceil(math.log(N, 6)))

a_six = [6**x for x in range(MAX_JOU+1)]
a_nine = [9**x for x in range(MAX_JOU+1)]

for i in range(N+1):
    if (i-1 >= 0):
            dp[i] = min(dp[i], dp[i-1]+1)
    for six in a_six:
        if (i-six >= 0):
            dp[i] = min(dp[i], dp[i-six]+1)
    for nine in a_nine:
        if (i-nine >= 0):
            dp[i] = min(dp[i], dp[i-nine]+1)

print(dp[-1])

Submission status: Accepted

Solution code:
from sys import stdin
N = int(stdin.readline().rstrip())

dp = [99999999]*(N+1)
dp[0] = 0
for i in range(0, N):
    dp[i+1] = min(dp[i] + 1, dp[i+1])
    k = 6
    while i+k <= N:
        dp[i+k] = min(dp[i]+1, dp[i+k])
        k *= 6
    k = 9
    while i+k <= N:
        dp[i+k] = min(dp[i]+1, dp[i+k])
        k *= 9
print(dp[N])

Submission status: Accepted

Solution code:
n = int(input())
mn = 1e10

for i in range(n+1):
    ans = 0
    a, b = i, n-i

    while a>=6:
        a, mo = divmod(a, 6)
        ans += mo
    ans += a

    while b>=9:
        b, mo = divmod(b, 9)
        ans += mo
    ans += b

    mn = min(mn, ans)
print(mn)

Submission status: Accepted

Solution code:
n = int(input())
mn = 1e10

for i in range(n+1):
    ans = 0
    a, b = i, n-i

    di, mo = divmod(a, 6)
    ans += mo
    while di>=6:
        di, mo = divmod(di, 6)
        ans += mo
    ans += di

    di, mo = divmod(b, 9)
    ans += mo
    while di>=9:
        di, mo = divmod(di, 9)
        ans += mo
    ans += di

    mn = min(mn, ans)
print(mn)