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.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)


import java.io.*;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.TreeSet;

/**
 * @author tutuz on 2020/04/05
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyInput in = new MyInput(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskX solver = new TaskX();
        solver.solve(1, in, out);
        out.close();
    }

    static int INF = 1 << 30;
    static long LINF = 1L << 55;
    static int MOD = 1000000007;
    static int[] mh4 = {0, -1, 1, 0};
    static int[] mw4 = {-1, 0, 0, 1};
    static int[] mh8 = {-1, -1, -1, 0, 0, 1, 1, 1};
    static int[] mw8 = {-1, 0, 1, -1, 1, -1, 0, 1};

    static TreeSet<Long> set = new TreeSet<>();
    static long max = (long) Math.pow(10, 12);

    static class TaskX {

        public void solve(int testNumber, MyInput in, PrintWriter out) {
            int k = in.nextInt();
            TreeSet<Long> set = new TreeSet<>();

            ArrayDeque<Long> q = new ArrayDeque<>();

            for (long i = 1; i < 10; i++) {
                q.addLast(i);
                set.add(i);
            }

            while (set.size() <= 100010) {
                long num = q.removeFirst();
                String str = String.valueOf(num);
                char cc = str.charAt(str.length() - 1);
                int c = cc - '0';
                if (c == 0) {
                    if (!set.contains(Long.parseLong(str + "0"))) {
                        q.addLast(Long.parseLong(str + "0"));
                        set.add(Long.parseLong(str + "0"));
                    }

                    if (!set.contains(Long.parseLong(str + "1"))) {
                        q.addLast(Long.parseLong(str + "1"));
                        set.add(Long.parseLong(str + "1"));
                    }
                } else if (0 < c && c <= 8) {
                    for (int i = -1; i <= 1; i++) {
                        final long o = Long.parseLong(str + (c + i));
                        if (!set.contains(o)) {
                            q.addLast(o);
                            set.add(o);
                        }
                    }
                } else if (c == 9) {
                    if (!set.contains(Long.parseLong(str + "8"))) {
                        q.addLast(Long.parseLong(str + "8"));
                        set.add(Long.parseLong(str + "8"));
                    }

                    if (!set.contains(Long.parseLong(str + "9"))) {
                        q.addLast(Long.parseLong(str + "9"));
                        set.add(Long.parseLong(str + "9"));
                    }
                }
            }

            out.println(set.toArray()[k - 1]);

        }
    }

    static class MyInput {
        private final BufferedReader in;
        private static int pos;
        private static int readLen;
        private static final char[] buffer = new char[1024 * 8];
        private static char[] str = new char[500 * 8 * 2];
        private static boolean[] isDigit = new boolean[256];
        private static boolean[] isSpace = new boolean[256];
        private static boolean[] isLineSep = new boolean[256];

        static {
            for (int i = 0; i < 10; i++) {
                isDigit['0' + i] = true;
            }
            isDigit['-'] = true;
            isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true;
            isLineSep['\r'] = isLineSep['\n'] = true;
        }

        public MyInput(InputStream is) {
            in = new BufferedReader(new InputStreamReader(is));
        }

        public int read() {
            if (pos >= readLen) {
                pos = 0;
                try {
                    readLen = in.read(buffer);
                } catch (IOException e) {
                    throw new RuntimeException();
                }
                if (readLen <= 0) {
                    throw new EndOfFileRuntimeException();
                }
            }
            return buffer[pos++];
        }

        public int nextInt() {
            int len = 0;
            str[len++] = nextChar();
            len = reads(len, isSpace);
            int i = 0;
            int ret = 0;
            if (str[0] == '-') {
                i = 1;
            }
            for (; i < len; i++)
                ret = ret * 10 + str[i] - '0';
            if (str[0] == '-') {
                ret = -ret;
            }
            return ret;
        }

        public long nextLong() {
            int len = 0;
            str[len++] = nextChar();
            len = reads(len, isSpace);
            int i = 0;
            long ret = 0;
            if (str[0] == '-') {
                i = 1;
            }
            for (; i < len; i++)
                ret = ret * 10 + str[i] - '0';
            if (str[0] == '-') {
                ret = -ret;
            }
            return ret;
        }

        public char nextChar() {
            while (true) {
                final int c = read();
                if (!isSpace[c]) {
                    return (char) c;
                }
            }
        }

        public String nextString() {
            return new String(nextChars());
        }

        public char[] nextChars() {
            int len = 0;
            str[len++] = nextChar();
            len = reads(len, isSpace);
            return Arrays.copyOf(str, len);
        }

        public char[][] next2DChars(int h, int w) {
            char[][] s = new char[h][w];
            for (int i = 0; i < h; i++) {
                s[i] = nextChars();
            }
            return s;
        }

        int reads(int len, boolean[] accept) {
            try {
                while (true) {
                    final int c = read();
                    if (accept[c]) {
                        break;
                    }
                    if (str.length == len) {
                        char[] rep = new char[str.length * 3 / 2];
                        System.arraycopy(str, 0, rep, 0, str.length);
                        str = rep;
                    }
                    str[len++] = (char) c;
                }
            } catch (EndOfFileRuntimeException e) {
            }
            return len;
        }

        public int[] nextIntArray(final int n) {
            final int[] res = new int[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextInt();
            }
            return res;
        }

        public int[] nextIntArray1Index(final int n) {
            final int[] res = new int[n + 1];
            for (int i = 1; i < n + 1; i++) {
                res[i] = nextInt();
            }
            return res;
        }

        public int[] nextIntArrayDec(final int n) {
            final int[] res = new int[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextInt() - 1;
            }
            return res;
        }

        public long[] nextLongArray(final int n) {
            final long[] res = new long[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextLong();
            }
            return res;
        }

        public long[] nextLongArray1Index(final int n) {
            final long[] res = new long[n + 1];
            for (int i = 1; i < n + 1; i++) {
                res[i] = nextLong();
            }
            return res;
        }

        public long[] nextLongArrayDec(final int n) {
            final long[] res = new long[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextLong() - 1;
            }
            return res;
        }

        public double nextDouble() {
            return Double.parseDouble(nextString());
        }

        public double[] nextDoubleArray(int n) {
            double[] res = new double[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextDouble();
            }
            return res;
        }

        static class EndOfFileRuntimeException extends RuntimeException {
        }

    }
}