// Two-star problem
// Problem 10127 Ones
/*
This program is written by
Prof. Chua-Huang Huang
Department of Information Engineering and Computer Science
Feng Chia University
Taichung, Taiwan
Disclaimer:
The programming problem is downloaded from UVa Online Judge (https://uva.onlinejudge.org/).
The program solution is provided for helping students to prepare Collegiate Programming
Examination (CPE). The author does not guarantee the program is completely correct to pass
UVa Online Judge platform or CPE examination platform.
This program is not intended for a student to copy only. He/She should practice the
programming problem himself/herself. Only use the program solution as a reference.
The author is not responsible if the program causes any damage of your computer or
personal properties.
No commercial use of this program is allowed without the author's written permission.
*/
#include
#include
// This problem is sovled using congruence theorem.
// For an integer a, if a%n=r, then (a+b)%n=(r+b)%n and (a*b)%n=(r*b)%n.
// Hence, if a%n=r, then (a*b+c)%n=(r*b+c)%n.
// Initially, set a=1, b=10 and c=1.
// In the following program, at the end of every iteration a is an integer of all 1's. Also,
// initialize ones to 1 and increment ones in every iteration, then,
// after the end of the j-th iteration, ones is j+1 and a has j+1 1's.
int main(void) {
int n; // Input integer.
int r; // All ones, with the congurence value.
int ones; //Number of ones.
while (scanf("%d", &n)==1) { // Input an integer if there is any.
r = 1 % n; // Initial congruent number, a is 1.
ones = 1; // Count one 1's.
while (r!=0) { // When r==0, 111.1 is divided by n.
r = r * 10 + 1; // Add one more 1 to a; b==10 and c==1.
ones++; // Increment number of 1's
r = r % n; // Congruent number of 111...1, the number of 1 is the value of ones.
}
printf("%d\n", ones); // Ouput the number of 1's.
}
return 0;
}