Problem:
Score : 700 points

Problem Statement

Find the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Constraints

2 \leq K \leq 10^5

K is an integer.

Input

Input is given from Standard Input in the following format:

K

Output

Print the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Sample Input 1

6

Sample Output 1

3

12=6×2 yields the smallest sum.

Sample Input 2

41

Sample Output 2

5

11111=41×271 yields the smallest sum.

Sample Input 3

79992

Sample Output 3

36

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


import java.io.IOException;
import java.io.InputStream;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.NoSuchElementException;

public class Main implements Runnable {
	public static void main(String[] args) {
		// long t = System.currentTimeMillis();
		new Thread(null, new Main(), "", Runtime.getRuntime().maxMemory()).start();
		// System.err.println(System.currentTimeMillis() - t);
	}

	public void run() {
		// 和xで余り0を構成できるか

		Scanner sc = new Scanner();
		int K = sc.nextInt();
		solve(K);
	}

	void solve(int K) {
		int[] f = new int[K];
		Arrays.fill(f, Integer.MAX_VALUE / 3);
		ArrayDeque<Integer> que = new ArrayDeque<>();
		f[1] = 1;
		f[10 % K] = 1;
		que.add(1);
		que.add(10 % K);
		while (!que.isEmpty()) {
			int v = que.poll();
			if (f[10 * v % K] > f[v]) {
				f[10 * v % K] = f[v];
				que.addFirst(10 * v % K);
			}
			if (f[(v + 1) % K] > f[v] + 1) {
				f[(v + 1) % K] = f[v] + 1;
				que.addLast((v + 1) % K);
			}
		}
		System.out.println(f[0]);
	}

	class Scanner {
		private final InputStream in = System.in;
		private final byte[] buffer = new byte[1024];
		private int ptr = 0;
		private int buflen = 0;

		private boolean hasNextByte() {
			if (ptr < buflen) {
				return true;
			} else {
				ptr = 0;
				try {
					buflen = in.read(buffer);
				} catch (IOException e) {
					e.printStackTrace();
				}
				if (buflen <= 0) {
					return false;
				}
			}
			return true;
		}

		private int readByte() {
			if (hasNextByte())
				return buffer[ptr++];
			else
				return -1;
		}

		private boolean isPrintableChar(int c) {
			return 33 <= c && c <= 126;
		}

		public boolean hasNext() {
			while (hasNextByte() && !isPrintableChar(buffer[ptr]))
				ptr++;
			return hasNextByte();
		}

		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (isPrintableChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}

		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			long n = 0;
			boolean minus = false;
			int b = readByte();
			if (b == '-') {
				minus = true;
				b = readByte();
			}
			if (b < '0' || '9' < b) {
				throw new NumberFormatException();
			}
			while (true) {
				if ('0' <= b && b <= '9') {
					n *= 10;
					n += b - '0';
				} else if (b == -1 || !isPrintableChar(b)) {
					return minus ? -n : n;
				} else {
					throw new NumberFormatException();
				}
				b = readByte();
			}
		}

		public int nextInt() {
			long nl = nextLong();
			if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
				throw new NumberFormatException();
			return (int) nl;
		}

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

	static void tr(Object... objects) {
		System.out.println(Arrays.deepToString(objects));
	}

}