Problem:


Score : 400 points

Problem Statement

A positive integer X is said to be a lunlun number if and only if the following condition is satisfied:

In the base ten representation of X (without leading zeros), for every pair of two adjacent digits, the absolute difference of those digits is at most 1.

For example, 1234, 1, and 334 are lunlun numbers, while none of 31415, 119, or 13579 is.

You are given a positive integer K. Find the K-th smallest lunlun number.

Constraints

1 \leq K \leq 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

K

Output

Print the answer.

Sample Input 1

15

Sample Output 1

23

We will list the 15 smallest lunlun numbers in ascending order:

1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
21,
22,
23.

Thus, the answer is 23.

Sample Input 2

1

Sample Output 2

1

Sample Input 3

13

Sample Output 3

21

Sample Input 4

100000

Sample Output 4

3234566667

Note that the answer may not fit into the 32-bit signed integer type.



Sample input:
15


Sample output:
23

Submission status: Accepted

Solution code:
from queue import Queue
k = int(input())
q = Queue()
for i in range(1,10):
    q.put(i)
for i in range(k):
    x = q.get()
    if x % 10 != 0:
        q.put(x*10+x%10-1)
    q.put(x*10+x%10)
    if x % 10 != 9:
        q.put(x*10+x%10+1)
print(x)

Submission status: Accepted

Solution code:
import queue
K = int(input())
q = queue.Queue()
for i in range(1,10):
    q.put(i)
for j in range(K-1):
    x = q.get()
    if x%10 != 0:
        q.put(10*x+x%10-1)
    q.put(10*x+x%10)
    if x%10 != 9:
        q.put(10*x+x%10+1)
x = q.get()
print(x)

Submission status: Accepted

Solution code:
from collections import deque

from collections import deque


def main():
    K = int(input())

    q = deque()

    for i in range(1, 10):
        q.append(i)

    while True:
        v = q.popleft()
        K -= 1
        if K == 0:
            print(v)
            exit()
        u = v % 10
        nv = v * 10 + u

        if u == 0:
            q.append(nv)
            q.append(nv + 1)
        elif u == 9:
            q.append(nv - 1)
            q.append(nv)
        else:
            q.append(nv - 1)
            q.append(nv)
            q.append(nv + 1)


main()

Submission status: Accepted

Solution code:
# editorial準拠
def main():
    from collections import deque
    K = int(input())

    q = deque([1, 2, 3, 4, 5, 6, 7, 8, 9])
    cnt = 0
    while q:
        x = q.popleft()
        cnt += 1
        if cnt == K:
            print(x)
            return

        y = x % 10
        z = 10*x + y
        if y != 0:
            q.append(z-1)
        q.append(z)
        if y != 9:
            q.append(z+1)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import queue

N = int(input())
q = queue.Queue()
for i in range(1, 10):
    q.put(i)

ans = 0
for i in range(N):
    ans = q.get()
    m = ans % 10
    if ans % 10 != 0:
        q.put(ans * 10 + m - 1)
    q.put(ans * 10 + m)
    if ans % 10 != 9:
        q.put(ans * 10 + m + 1)

print(ans)

Submission status: Accepted

Solution code:
k = int(input())

from collections import deque
queue = deque(range(1,10))
count = 0

while count < k:
    tmp = queue.popleft()
    tail = tmp%10
    if tail != 0:
        queue.append(tmp*10+tail-1)
    queue.append(tmp*10+tail)
    if tail != 9:
        queue.append(tmp*10+tail+1)
    count += 1
    
print(tmp)

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-
N = int(input())

if N <= 12:
    print(N)
else:
    str_ans = "12"
    counter = 12
    while counter < N:
        len_ans = len(str_ans)
        low_nine_num = 0
        for i in range(len_ans):
            if str_ans[len_ans - i - 1] == "9":
                low_nine_num += 1
            else:
                break
        if low_nine_num == len_ans:
            str_ans = "1" + "0" * len_ans
        else:
            chenged_top_num = -1
            low_digit_num = -1
            if low_nine_num == len_ans - 1:
                chenged_top_num = int(str_ans[len_ans - low_nine_num - 1])
                low_digit_num = len_ans - 1
            else:
                for i in range(len_ans - low_nine_num):
                    if i == len_ans - low_nine_num - 1 :
                        if chenged_top_num == -1:
                            chenged_top_num = int(str_ans[0])
                            low_digit_num = len_ans - 1
                    else:
                        compare_high_num = int(str_ans[-1 * (i + 2 + low_nine_num)])
                        compare_low_num = int(str_ans[-1 * (i + 1 + low_nine_num)])
                        if compare_high_num - compare_low_num != 0 and compare_high_num - compare_low_num != 1:
                            chenged_top_num = compare_high_num
                            low_digit_num = i + 1 + low_nine_num
    #                         print("A", str_ans, compare_high_num, low_digit_num)
                        else:
                            chenged_top_num = compare_low_num
                            low_digit_num = i + low_nine_num
    #                         print("B", str_ans, compare_high_num, low_digit_num)
                            break

                            
            temp_str_ans = str_ans[:len_ans - low_digit_num - 1] # not chenged
            temp_str_ans += str(chenged_top_num + 1)
            for i in range(low_digit_num):
                temp_str_ans += str(max(chenged_top_num - i, 0))
            str_ans = temp_str_ans
        
        counter += 1
#         print(counter, str_ans, low_nine_num, low_digit_num)
    
    print(int(str_ans))

Submission status: Accepted

Solution code:
K = int(input())
table = [1, 2, 3, 4, 5, 6, 7, 8, 9]
for i in table:
  if len(table) > K:
    break
  x = i % 10
  for j in range(max(0, x - 1), min(x + 2, 10)):
    table.append(i * 10 + j)
print(table[K-1])

Submission status: Accepted

Solution code:
from collections import deque
k=int(input())
d=deque([1,2,3,4,5,6,7,8,9])

for i in range(k):
  x=d.popleft()
  if x%10!=0:
    d.append(10*x+x%10-1)
  d.append(10*x+x%10)
  if x%10!=9:
    d.append(10*x+x%10+1)
print(x)

Submission status: Accepted

Solution code:
K=int(input())

lunlun=[[0 for i in range(0,10)] for i in range(0,13)]
for i in range(0,10):
    lunlun[1][i]=1
for i in range(2,13):
    for j in range(0,10):
        if j==0:
            lunlun[i][j]=lunlun[i-1][0]+lunlun[i-1][1]
        else:
            ans=0
            ans+=lunlun[i-1][j-1]+lunlun[i-1][j]
            if 9>j:
                ans+=lunlun[i-1][j+1]

            lunlun[i][j]=ans

def condition(num):
    s=str(num)
    n=len(s)
    ans=0
    dp=[0 for i in range(0,n+1)]
    dp[n]=1
    for k in range(0,n-1):
        i=n-1-k
        j=int(s[i-1])
        ans=0
        if j>0:
            if int(s[i])>j-1:
                ans+=lunlun[n-i][j-1]
            elif int(s[i])==j-1:
                ans+=dp[i+1]

        if int(s[i])>j:
            ans+=lunlun[n-i][j]
        elif int(s[i])==j:
            ans+=dp[i+1]

        if 9>j:
            if int(s[i])>j+1:
                ans+=lunlun[n-i][j+1]
            elif int(s[i])==j+1:
                ans+=dp[i+1]

        dp[i]=ans

    ans=0
    for i in range(1,int(s[0])):
        ans+=lunlun[n][i]
    ans+=dp[1]
    for i in range(1,n):
        for j in range(1,10):
            ans+=lunlun[i][j]

    return ans>=K
start=1
end=10**12
while end-start>1:
    test=(end+start)//2
    if condition(test):
        end=test
    else:
        start=test

if condition(start):
    print(start)
else:
    print(end)