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  1. Prepare
  2. Mathematics
  3. Fundamentals
  4. Special Multiple
  5. Discussions

Special Multiple

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148 Discussions

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  • polat_ernez
     + 2 comments
    def solve(n):
    i = 0
    while True:
        i += 1
        x = int(bin(i)[2:]) * 9
        if x % n == 0:
            return str(x)

  • CS_2212256_T
     + 0 comments
    import java.math.BigInteger;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;

public class Solution {
    static final int LIMIT = 500;
    static final int[] DIGITS = { 0, 9 };

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int T = sc.nextInt();
        for (int tc = 0; tc < T; tc++) {
            int N = sc.nextInt();
            System.out.println(solve(N));
        }

        sc.close();
    }

    static BigInteger solve(int N) {
        boolean[] visited = new boolean[N];

        Queue<BigInteger> queue = new LinkedList<BigInteger>();
        queue.offer(BigInteger.valueOf(DIGITS[0]));
        while (true) {
            BigInteger head = queue.poll();

            for (int digit : DIGITS) {
                if (head.equals(BigInteger.ZERO) && digit == 0) {
                    continue;
                }

                BigInteger next = head.multiply(BigInteger.TEN).add(BigInteger.valueOf(digit));

                int remainder = next.mod(BigInteger.valueOf(N)).intValue();
                if (remainder == 0) {
                    return next;
                } else if (!visited[remainder]) {
                    visited[remainder] = true;
                    queue.offer(next);
                }
            }
        }
    }
}

  • rajmurmu101
     + 0 comments
    def solve(n):
    queue = deque(['9'])
    visited = set()
    
    while queue:
        current = queue.popleft()
        
        current_num = int(current)
        
        if current_num % n == 0:
            return current
            
        next_num1 = current + '0'
        next_num2 = current + '9'
        
        if next_num1 not in visited:
            queue.append(next_num1)
            visited.add(next_num1)
            
        if next_num2 not in visited:
            queue.append(next_num2)
            visited.add(next_num2)

  • spawnisback
     + 0 comments

    The multiple sought belongs to the list: {9x1, 9x10, 9x11, 9x100, 9x101, ...} We notice that {1, 10, 11, 100, 101, ...} are the binary writings of the numbers {1, 2, 3, 4, 5, ...}

    def solve(n):
    i = 1
    res = 9*int(bin(i)[2:])
    while res % n:
        i = i + 1
        res = 9*int(bin(i)[2:])
    return str(res)

  • kerimsaltoglu1
     + 0 comments

    There is an error with fptr.write(result + '\n'). Change it to fptr.write(str(result) + '\n'). The correct code is below.

        def solve(n):
        if 9 % n == 0:
                print(9)
                return 9

        curr_str = ['9']
        next_str = []
        found = False

        while not found:
            for curr in curr_str:
                    a = curr + '0'
                    b = curr + '9'

                    if int(a) % n == 0:
                            print(int(a))
                            found = True
                            return int(a)

                    if int(b) % n == 0:
                            print(int(b))
                            found = True
                            return int(b)

                    next_str.append(str(a))
                    next_str.append(str(b))

        curr_str = next_str
        next_str = []

    if name == 'main': fptr = open(os.environ['OUTPUT_PATH'], 'w')

    t = int(input().strip())

for t_itr in range(t):
    n = int(input().strip())

    result = solve(n)
    # fptr.write(result + '\n')
    # add str(result) because otherwise it does not work
    fptr.write(str(result) + '\n')

fptr.close()