Minimum Insertions to Make a Co-Prime Array in C++

In this section we will see another interesting problem. Suppose we have an array of N elements. We have to find minimum number of intersection points to make this array as co-prime array. In the co-prime array gcd of every two consecutive elements is 1. We have to print the array also.

Suppose we have elements like {5, 10, 20}. This is not co-prime array. Now by inserting 1 between 5, 10 and 10, 20, it will be co-prime array. So the array will be like {5, 1, 10, 1, 20}

Algorithm

makeCoPrime(arr, n):
begin
   count := 0
   for i in range 1 to n, do
      if gcd of arr[i] and arr[i – 1] is not 1, then increase count by 1
   done
   display count value
   display the first element of arr
   for i in range 1 to n, do
      if gcd of arr[i] and arr[i – 1] is not 1, then display 1
   display element arr[i]
   done
end

Example

 Live Demo

#include <iostream>
#include <algorithm>
using namespace std;
int makeCoPrime(int arr[], int n){
   int count = 0;
   for(int i = 1; i<n; i++){
      if(__gcd(arr[i], arr[i - 1]) != i){
         count++;
      }
   }
   cout << "Number of intersection points: " << count << endl;
   cout << arr[0] << " ";
   for(int i = 1; i<n; i++){
      if(__gcd(arr[i], arr[i - 1]) != i){
         cout << 1 << " ";
      }
      cout << arr[i] << " ";
   }
}
int main() {
   int A[] = {2, 7, 28};
   int n = sizeof(A)/sizeof(A[0]);
   makeCoPrime(A, n);
}

Output

Number of intersection points: 1
2 7 1 28