N-th multiple in sorted list of multiples of two numbers in C++

You are given three numbers. You need to find the n-th multiple from the multiples of the first two numbers. Let's see an example to understand it more clearly.

Input

x = 2
y = 3
n = 7

Output

10

The first n ****multiples of 2 are 2 4 6 8 10 12 14

The first n ****multiples of 3 ****are 3 6 9 12 15 18 21

If combine both multiples and sort them we get 2 3 4 6 8 9 10 12 14 15 18 21 and the nth number from the list is 10.

Algorithm

• Initialise a vector to store all the multiples.
• Find the first n ****multiples of x and add them to the above vector.
• Now, find the first n multiples of y.
  • Add them to the vector if it is not already present in the vector.
• Sort the multiples.
• Print the nth multiple from the vector.

Implementation

Following is the implementation of the above algorithm in C++

#include<bits/stdc++.h>
using namespace std;
int findNthMultiple(int x, int y, int n) {
   vector<int> multiples;
   for (int i = 1; i <= n; i++) {
      multiples.push_back(x * i);
   }
   sort(multiples.begin(), multiples.end());
   for (int i = 1, k = n; i <= n && k; i++) {
      if (!binary_search(multiples.begin(), multiples.end(), y * i)) {
         multiples.push_back(y * i);
         sort(multiples.begin(), multiples.end());
      }
   }
   return multiples[n - 1];
}
int main() {
   int x = 2, y = 3, n = 7;
   cout << findNthMultiple(x, y, n) << endl;
   return 0;
}

Output

f you run the above code, then you will get the following result.

10