Program for Number of solutions to Modular Equations in C/C++?

CC++Server Side ProgrammingProgramming

Here we will see one interesting problem related to modular equations. Suppose we have two values A and B. We have to find number of possible value that the variable X can take, such that (A mod X) = B holds.

Suppose A is 26, and B is 2. So the preferred value for X will be {3, 4, 6, 8, 12, 24} So the count will be 6. That is the answer. Let us see the algorithm to get better idea.

Algorithm

possibleWayCount(a, b) −

begin
   if a = b, then there are infinite solutions
   if a < b, then there are no solutions
   otherwise div_count := find_div(a, b)
   return div_count
end

find_div(a, b) −

begin
   n := a – b
   div_count := 0
   for i in range 1 to square root of n, do
      if n mode i is 0, then
         if i > b, then
            increase div_count by 1
         end if
         if n / i is not same as i and (n / i) > b, then
            increase div_count by 1
         end if
      end if
   done
end

Example

#include <iostream>
#include <cmath>
using namespace std;
int findDivisors(int A, int B) {
   int N = (A - B);
   int div_count = 0;
   for (int i = 1; i <= sqrt(N); i++) {
      if ((N % i) == 0) {
         if (i > B)
            div_count++;
         if ((N / i) != i && (N / i) > B) //ignore if it is already counted
            div_count++;
      }
   }
   return div_count;
}
int possibleWayCount(int A, int B) {
   if (A == B) //if they are same, there are infinity solutions
      return -1;
   if (A < B) //if A < B, then there are two possible solutions
      return 0;
   int div_count = 0;
   div_count = findDivisors(A, B);
   return div_count;
}
void possibleWay(int A, int B) {
   int sol = possibleWayCount(A, B);
   if (sol == -1)
      cout << "For A: " << A << " and B: " << B << ", X can take infinite values greater than " << A;
   else
      cout << "For A: " << A << " and B: " << B << ", X can take " << sol << " values";
}
int main() {
   int A = 26, B = 2;
   possibleWay(A, B);
}

Output

For A: 26 and B: 2, X can take 6 values
raja
Published on 20-Aug-2019 11:19:05
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