Problem:


Score : 400 points

Problem Statement

In this problem, we only consider strings consisting of lowercase English letters.

Strings s and t are said to be isomorphic when the following conditions are satisfied:

|s| = |t| holds.

For every pair i, j, one of the following holds:

s_i = s_j and t_i = t_j.

s_i \neq s_j and t_i \neq t_j.

For example, abcac and zyxzx are isomorphic, while abcac and ppppp are not.

A string s is said to be in normal form when the following condition is satisfied:

For every string t that is isomorphic to s, s \leq t holds. Here \leq denotes lexicographic comparison.

For example, abcac is in normal form, but zyxzx is not since it is isomorphic to abcac, which is lexicographically smaller than zyxzx.

You are given an integer N.
Print all strings of length N that are in normal form, in lexicographically ascending order.

Constraints

1 \leq N \leq 10

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N

Output

Assume that there are K strings of length N that are in normal form: w_1, \ldots, w_K in lexicographical order.
Output should be in the following format:

w_1
:
w_K

Sample Input 1

1

Sample Output 1

a

Sample Input 2

2

Sample Output 2

aa
ab



Sample input:
1


Sample output:
a

Submission status: Accepted

Solution code:
# coding: utf-8
# Your code here!
n=int(input())
alps=[chr(ord("a")+x) for x in range(26)]
def dfs(s,mx):
    if len(s)==n:
        print(s)
    else:
        for i in range(mx+1):
            if (i==mx):
                dfs(s+alps[i],mx+1)
            else:
                dfs(s+alps[i],mx)
                
                
dfs("",0)

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_float = lambda: float(r())
    R = lambda: list(map(int, r().split()))
    R_str = lambda: r().split()
    R_map = lambda: map(int, r().split())
    R_float = lambda: list(map(float, r().split()))
    R_tuple = 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()
    task = [('a', 1)]
    abc = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j']
    while task:
        s, l = task.pop()
        if len(s) == N:
            print(s)
        else:
            for i in range(l, -1, -1):
                u = ''.join((s, abc[i]))
                if i == l:
                    task.append((u, l+1))
                else:
                    task.append((u, l))
    
    #%%
    # 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:
N = int(input())
def dfs(s):
  if len(s) == N:
    print(s)
    return
  else:
    for i in range(ord("a"), ord("z")+1):
      if i < ord(max(list(s)))+2:
        dfs(s+chr(i))
      else:
        return
dfs("a")

Submission status: Accepted

Solution code:
N = int(input())
def dfs(s):
  if len(s) == N:
    print(s)
    return
  else:
    for i in range(ord("a"), ord("z")+1):
      if max(list(s)) != chr(i-2):
        dfs(s+chr(i))
      else:
        return
dfs("a")

Submission status: Accepted

Solution code:
import sys 
sys.setrecursionlimit(4100000)

N = int(input())

def dfs(i,s):
    if len(s) == N:
        
        return print(s)
    
    for x in range(97,i + 1):
        t = s + chr(x)
        
        dfs(max(x + 1,i),t)
    
    
dfs(ord("a"),"")

Submission status: Accepted

Solution code:
N = int(input())

dp = [[] for _ in range(N)]
dp[0].append('a')

for i in range(1, N):
    for strings in dp[i-1]:
        j = 97
        while j <= ord(max(strings))+1:
            nextstr = strings
            nextstr += chr(j)
            dp[i].append(nextstr)
            j += 1

dp[N-1].sort()

for strings in dp[N-1]:
    print(strings)

Submission status: Accepted

Solution code:
def write(r):
    b=[chr(x+97) for x in r]
    print("".join(b))


def add(a,j):
    for c in a[j]:
        for d in range(max(c)+2):
            e=c+[d]
            a[j+1].append(e)
    

n=int(input())
a=[[] for x in range(n)]
a[0]=[[0]]
for j in range(n-1):
    add(a,j)
for r in a[n-1]:
    write(r)

Submission status: Accepted

Solution code:
s = input().split()
n = int(s[0])

st = ['a','b','c','d','e','f','g','h','i','j','k']

#initialize
inis = [1,1,1,1,1,1,1,1,1,1,1]

def print_str( arry , num):
   str_a = ''
   for i in range(num):
     #print(arry,i)
     str_a = str_a + st[arry[i]-1]
   print(str_a)

# len = 1 .. 10
def do_number_n( len ):
   global inis
   tsti = 0
   k = len - 1    
   print_str( inis , len)
   while True:
      inis[k] += 1
      for j in range(k,0,-1):
         #print(inis[0:j],j)
         if ( max(inis[0:j]) + 2 ) <= inis[j]  :
         #if ( inis[j-1] + 2 ) <= inis[j]  :
            inis[j-1] += 1
            inis[j] = 1
         #print('test:  {},{},   {}'.format(j,k,inis))
            
      #最後まで行った。
      if inis[0] > 1 :
         return        
      print_str( inis , len)
  
def main():
  do_number_n(n)
    
main()

Submission status: Accepted

Solution code:
n = int(input())
a = list(chr(i*97) for i in range(10))
ans = 'a'

def dfs():
    global ans, n
    if len(ans) == n:
        print(ans)
    else:
        max1 = 'a'
        for i in range(len(ans)):
            max1 = max(max1, ans[i])
        for i in range(ord(max1) - 95):
            ans += chr(i+97)
            dfs()
            ans = ans[:-1]

dfs()

Submission status: Accepted

Solution code:
N = int(input())
from collections import deque

def func(S):
  q = deque([S])
  while q:
    x = q.popleft()
    if len(x) == N:
      print(x)
    else:
      for char_no in range(ord('a'), max([ ord(i) for i in x ])+2):
        y = x + chr(char_no)
        q.append(y)


start = 'a'
func(start)

Submission status: Accepted

Solution code:
N=int(input())

def dfs(s, mx):
    if len(s) == N:
        print(s)
    else:
        for o in range(ord('a'),ord(mx)+1):
            dfs(s + chr(o), chr(ord(mx)+1) if o==ord(mx) else mx)


dfs("",'a')

Submission status: Accepted

Solution code:
import string
N=int(input())
A=string.ascii_letters
ans=["a"]*N
Ans=[1]*N

def search(n):
    if n!=N-1:
        for i in range(max(Ans)+1):
            Ans[n]=i+1
            ans[n]=A[i]
            search(n+1)
            Ans[n+1:]=[1]*(N-n-1)
    else:
        for i in range(max(Ans)+1):
            Ans[n]=i+1
            ans[n]=A[i]
            print("".join(ans))

if N==1:
    print("a")
else:
    search(1)

Submission status: Accepted

Solution code:
N = int(input())

alphabet = [chr(97+i) for i in range(min(N,26))]
# print(alphabet)

dp = [[None]*N for _ in range(N)]
dp[0][0] = [alphabet[0]]
for i in range(1,N):
	dp[0][i] = []
# print(dp)


for n in range(1,N):
	for k in range(N):
		# dp[n][k] = dp[n-1][k]*k + dp[n-1][k-1]
		dp[n][k] = []
		for s in dp[n-1][k]:
			# print([s + alphabet[i] for i in range(k+1)])
			dp[n][k] += [s + alphabet[i] for i in range(k+1)]
		for s in dp[n-1][k-1]:
			dp[n][k] += [s + alphabet[k]]

# print(dp)
ans = []
for k in range(N):
	ans += dp[N-1][k]
ans = sorted(ans)

for s in ans:
	if len(s)!=0:
		print(s)

Submission status: Accepted

Solution code:
def solve():
    N = int(input())
    # ord("a") Unicode コードポイントを返す
    codepoint = ord("a")
 
    # たどるグラフの深さ
    i = 1
    # 標準形文字列とその次の辞書順
    ans = [["a", 1]]
    # 一つづつ潜る
    while i < N:
        # 次の深さをtmpとする
        tmp = []
        # 各ノード
        for w, j in ans:
            # 辞書順で追加していく
            for k in range(j+1):
                if k != j:
                    tmp.append([w + chr(codepoint+k), j])
                # 辞書順のインクリメント
                else:
                    tmp.append([w + chr(codepoint+k), j+1])
        ans = tmp
        i += 1
 
    [print(a[0]) for a in ans]
 
    # Solve
if __name__ == "__main__":
    solve()

Submission status: Accepted

Solution code:
string=['a','b','c','d','e','f','g','h','i','j']
N=int(input())
res=[]
def dfs(ss):
  if len(ss)==N:
    ss=''.join(ss)
    res.append(ss)
  else:
    for i in range(string.index(max(ss))+2):
      a=ss+[string[i]]
      dfs(a)
  return res
ans=dfs(['a'])
for i in range(len(ans)):
  print(ans[i])

Submission status: Accepted

Solution code:
import math


def div_with_mod(x, y, mod):
    # Fermat's little theorem
    return x*pow(y, mod - 2, mod)


def comb(n, r, mod):
    # calculates C(n,r) with mod (assuming mod is prime)
    nc = n
    for rc in range(1, r):
        nc -= 1
        n = n*nc % mod
        r = r*rc % mod

    return div_with_mod(n, r, mod)


def solve():
    N = int(input())
    # ord("a") Unicode コードポイントを返す
    codepoint = ord("a")

    def dfs(word, dep):
        if len(word) == N:
            return print(word)

        for i in range(dep):
            dfs(word + chr(codepoint+i), dep)

        dfs(word + chr(codepoint+dep), dep+1)

    dfs("a", 1)


# Solve
if __name__ == "__main__":
    solve()

Submission status: Accepted

Solution code:
import sys

input = sys.stdin.readline
# sys.setrecursionlimit(10 ** 8)

N = int(input())


def dfs(s, mx):
    if len(s) == N:
        print(s)
        return
    for c in range(ord("a"), mx + 2):
        t = s
        t += chr(c)
        dfs(t, max(c, mx))


dfs("", ord("a") - 1)

Submission status: Accepted

Solution code:
N = int(input())
s = 'abcdefghijklmn'


def f(d, now, kind):
    if d == N:
        print(now)
        return
    for i in range(kind):
        f(d + 1, now + s[i], kind)
    f(d + 1, now + s[kind], kind + 1)

f(0, '', 0)

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(500000)

N = int(input())
global ans
ans = []
def dfs(now,rank,root_,m):
    root = root_[:]
    if rank == N:
        root.append(now)
        ans.append(''.join([chr(i+ord('a')) for i in root]))
    else:
        root.append(now)
        for i in range(m+2):
            dfs(i,rank+1,root,max(m,i))

dfs(0,1,[],0)
ans.sort()
print(*ans,sep='\n')

Submission status: Accepted

Solution code:
import math


def div_with_mod(x, y, mod):
    # Fermat's little theorem
    return x*pow(y, mod - 2, mod)


def comb(n, r, mod):
    # calculates C(n,r) with mod (assuming mod is prime)
    nc = n
    for rc in range(1, r):
        nc -= 1
        n = n*nc % mod
        r = r*rc % mod

    return div_with_mod(n, r, mod)


def solve():
    N = int(input())
    # ord("a") Unicode コードポイントを返す
    codepoint = ord("a")

    # たどるグラフの深さ
    i = 1
    # 標準形文字列とその次の辞書順
    ans = [["a", 1]]
    # 一つづつ潜る
    while i < N:
        # 次の深さをtmpとする
        tmp = []
        # 各ノード
        for w, j in ans:
            # 辞書順で追加していく
            for k in range(j+1):
                if k != j:
                    tmp.append([w + chr(codepoint+k), j])
                # 辞書順のインクリメント
                else:
                    tmp.append([w + chr(codepoint+k), j+1])
        ans = tmp
        i += 1

    [print(a[0]) for a in ans]

    # Solve
if __name__ == "__main__":
    solve()

Submission status: Accepted

Solution code:
def getStr(vars):
    if len(vars)==N:
        print(getPrintStr(vars))
        return
    
    vars.append(0)
    for i in range(0,max(vars)+2):
        vars[-1] = i
        #print(":", i, vars)
        getStr(vars)
    del vars[-1]
    return

def getPrintStr(vars):
    ret = ""
    for i in range(len(vars)):
        ret += "abcdefghijkl"[vars[i]]
    return ret

N = int(input())
 
getStr([0])

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
from operator import itemgetter
sys.setrecursionlimit(10000000)
INF = 10**30

S = "abcdefghijkl"
N = 0
def rec(s):
    if len(s) == N:
        print(''.join(s))
        return
    for i in range(len(set(s))+1):
        s.append(S[i])
        rec(s)
        s.pop()
    

def main():
    global N
    N = int(input().strip())
    rec([])

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
N = int(input())

def f(s, mx):
    if len(s) == N:
        print(s)
        return
    for i in range(mx+1):
        f(s + chr(ord("a") + i), max(mx, i+1))

f("", 0)

Submission status: Accepted

Solution code:
n = int(input())
dic = {0:'a',1:'b',2:'c',3:'d',4:'e',5:'f',6:'g',7:'h',8:'i',9:'j'}
ans = [["a",1]]
for i in range(1,n):
    tmp=[]
    for prev,val in ans:
        for j in range(val+1):
            tmp.append([prev+dic[j],val]) if j!=val else tmp.append([prev+dic[j],val+1])
    ans=tmp
ans=sorted(ans,key=lambda x:x[0])
for i in range(len(ans)):
    print(ans[i][0])

Submission status: Accepted

Solution code:
N=int(input())
dic={0:'a',1:'b',2:'c',3:'d',4:'e',5:'f',6:'g',7:'h',8:'i',9:'j'}
ans=[["a",1]]
for i in range(1,N):
    tmp=[]
    for prev,val in ans:
        for j in range(val+1):
            if j!=val:
                tmp.append([prev+dic[j],val])
            else:
                tmp.append([prev+dic[j],val+1])
    ans=tmp
ans=sorted(ans,key=lambda x:x[0])
for i in range(len(ans)):
    print(ans[i][0])

Submission status: Accepted

Solution code:
def standard_form(N):
    # 長さNの標準形を返す。
    if N == 1:
        return ["a"]
    ans = []
    std_forms = standard_form(N - 1)
    max_char_idx = 2

    for std_form in std_forms:
        max_char_idx = max([ord(ch) for ch in std_form])

        for i in range(ord('a'), max_char_idx + 2):
            append_char = chr(i)
            ans.append(std_form + append_char)

    return ans


if __name__ == '__main__':
    N = int(input())
    ans = standard_form(N)
    ans.sort()
    for a in ans:
        print(a)

Submission status: Accepted

Solution code:
import math


def div_with_mod(x, y, mod):
    # Fermat's little theorem
    return x*pow(y, mod - 2, mod)


def comb(n, r, mod):
    # calculates C(n,r) with mod (assuming mod is prime)
    nc = n
    for rc in range(1, r):
        nc -= 1
        n = n*nc % mod
        r = r*rc % mod

    return div_with_mod(n, r, mod)


def solve():
    N = int(input())
    list = [chr(ord("a")+i) for i in range(10)]

    def dfs(w, i):
        if len(w) == N:
            return print(w)

        for j in range(i):
            dfs(w+list[j], i)

        dfs(w + list[i], i + 1)

    dfs("", 0)


# Solve
if __name__ == "__main__":
    solve()

Submission status: Accepted

Solution code:
alp='abcdefghijklmnopqrstuvwxyz'

def f(N, s, x):
  if len(s)==N:
    print(s)
    return
  for i in range(x+2):
    f(N, s+alp[i], max(x, i))
    
f(int(input()), 'a', 0)

Submission status: Accepted

Solution code:
def dfs(N, s, maxc):
    if len(s) == N:
        print(s)
    else:
        for i in range(ord(maxc)-ord('a') + 2):
            ord_c = ord('a')+i
            dfs(N, s+chr(ord_c), chr(max(ord_c, ord(maxc))))

N = int(input())
dfs(N, 'a', 'a')

Submission status: Accepted

Solution code:
import string

n = int(input())
s = string.ascii_letters[:n]

ans_list = ['a']
for i in range(n-1):
    ans_list = [ans + c for ans in ans_list for c in s[:len(set(ans)) + 1]]

print(*ans_list, sep='\n')

Submission status: Accepted

Solution code:
# D
N = int(input())

al = [chr(ord('a') + i) for i in range(26)]

ans = ['a']
for i in range(N-1):
    tmp = []
    for s in ans:
        stop = ord(max(s)) + 1
        for i in range(ord('a'), stop+1):
            tmp.append(s + chr(i))
    ans = tmp
for s in ans:
    print(s)

Submission status: Accepted

Solution code:
# coding: utf-8
# Your code here!
N=int(input())

cand=["a"]

num=98
for i in range(N-1):
    #print(i)
    temp=[]
    for item in cand:
        ma=0
        for c in item:
            ma=max(ma,ord(c))
        for i in range(ma-95):
            temp.append(item+chr(i+97))
    num+=1
    cand=temp[:]

for item in cand:
    print(item)

Submission status: Accepted

Solution code:
N=int(input())

alphabets = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j']

a="a"

def dfs(n):
  if n == 1:
    return["a"]

  if n == 2:
    return["aa","ab"]
  else:
    characters = alphabets[0:n]
    result = []
    for r in dfs(n-1):#n=3の時は["aa","ab"]
      done = False
      for char in characters:#"a","b","c",,,
        if char in r:#char="a" が r="aa"に入っていたら
          result.append(r + char)#("aa"+"a"="aaa")
        else:#入っていないなら
          if not done:#もしdone=Falseなら
            result.append(r + char)#"aab"
            done =True
          else:
            break
    return result

print("\n".join(dfs(N)))

Submission status: Accepted

Solution code:
# D
N = int(input())

al = [chr(ord('a') + i) for i in range(26)]

def dfs(S, i):
    if len(S) == N:
        yield S
        return
    for j in range(i):
        for w in dfs(S + al[j], i):
            yield w
    for w in dfs(S + al[i], i + 1):
        yield w

for w in dfs('', 0):
    print(w)