# Minimum insertions to make a Co-prime array

Given an array of N elements, find the minimum number of insertions to convert the given array into a co-prime array. Print the resultant array also.

Co-prime Array : An array in which every pair of adjacent elements are co-primes. i.e, .

Examples :

```Input : A[] = {2, 7, 28}
Output : 1
Explanation :
Here, 1st pair = {2, 7} are co-primes( gcd(2, 7) = 1).
2nd pair = {7, 28} are not co-primes, insert 9
between them. gcd(7, 9) = 1 and gcd(9, 28) = 1.

Input : A[] = {5, 10, 20}
Output : 2
Explanation :
Here, there is no pair which are co-primes.
Insert 7 between (5, 10) and 1 between (10, 20).
```

## Recommended: Please solve it on PRACTICE first, before moving on to the solution.

Observe that to make a pair to become co-primes we have to insert a number which makes the newly formed pairs co-primes. So, we have to check every adjacent pair for their co-primality and insert a number if required. Now, what is the number that should be inserted? Let us take two numbers a and b. If any of a or b is 1, then GCD(a, b) = 1. So, we can insert ONE(1) at every pair. For efficiency we use euler’s gcd function .

Below is the implementation of the above approach:

## C++

 `// CPP program for minimum insertions to ` `// make a Co-prime Array. ` `#include ` `using` `namespace` `std; ` ` `  `void` `printResult(``int` `arr[], ``int` `n) ` `{ ` `    ``// Counting adjacent pairs that are not ` `    ``// co-prime. ` `    ``int` `count = 0; ` `    ``for` `(``int` `i = 1; i < n; i++)      ` `        ``if` `(__gcd(arr[i], arr[i - 1]) != 1) ` `            ``count++; ` ` `  `    ``cout << count << endl; ``// No.of insertions ` `    ``cout << arr << ``" "``; ` `    ``for` `(``int` `i = 1; i < n; i++)  ` `    ``{ ` `        ``// If pair is not a co-prime insert 1. ` `        ``if` `(__gcd(arr[i], arr[i - 1]) != 1) ` `            ``cout << 1 << ``" "``; ` `        ``cout << arr[i] << ``" "``; ` `    ``} ` `} ` ` `  `// Driver Function ` `int` `main() ` `{ ` `    ``int` `A[] = { 5, 10, 20 }; ` `    ``int` `n = ``sizeof``(A) / ``sizeof``(A); ` `    ``printResult(A, n); ` `    ``return` `0; ` `} `

## Java

 `//Java program for minimum insertions ` `// to make a Co-prime Array. ` `import` `java.io.*; ` ` `  `class` `GFG { ` `     `  `    ``// Recursive function to return  ` `    ``// gcd of a and b ` `    ``static` `int` `gcd(``int` `a, ``int` `b) ` `    ``{ ` `        ``// Everything divides 0  ` `        ``if` `(a == ``0` `|| b == ``0``) ` `        ``return` `0``; ` `     `  `        ``// base case ` `        ``if` `(a == b) ` `            ``return` `a; ` `     `  `        ``// a is greater ` `        ``if` `(a > b) ` `            ``return` `gcd(a-b, b); ` ` `  `        ``return` `gcd(a, b-a); ` `    ``} ` `     `  `    ``static` `void` `printResult(``int` `arr[], ``int` `n) ` `    ``{ ` `         `  `        ``// Counting adjacent pairs that are not ` `        ``// co-prime. ` `        ``int` `count = ``0``; ` ` `  `        ``for` `(``int` `i = ``1``; i < n; i++)      ` `            ``if` `(gcd(arr[i], arr[i - ``1``]) != ``1``) ` `                ``count++; ` `     `  `        ``// No.of insertions ` `        ``System.out.println(count );  ` `        ``System.out.print (arr[``0``] + ``" "``); ` ` `  `        ``for` `(``int` `i = ``1``; i < n; i++)  ` `        ``{ ` `             `  `            ``// If pair is not a co-prime insert 1. ` `            ``if` `(gcd(arr[i], arr[i - ``1``]) != ``1``) ` `                ``System.out.print( ``1` `+ ``" "``); ` `            ``System.out.print(arr[i] + ``" "``); ` `        ``} ` `    ``} ` `     `  `    ``// Driver Function ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `A[] = { ``5``, ``10``, ``20` `}; ` `        ``int` `n = A.length; ` `        ``printResult(A, n); ` `    ``} ` `} ` ` `  `/*This code is contributed by Nikita Tiwari.*/`

## Python3

 `# Python3 code for minimum insertions ` `# to make a Co-prime Array. ` `from` `fractions ``import` `gcd ` ` `  `def` `printResult(arr, n): ` ` `  `    ``# Counting adjacent pairs that  ` `    ``# are not co-prime. ` `    ``count ``=` `0` `    ``for` `i ``in` `range``(``1``,n): ` `        ``if` `(gcd(arr[i], arr[i ``-` `1``]) !``=` `1``): ` `            ``count``+``=``1` `     `  `    ``print``(count)     ``# No.of insertions ` `    ``print``( arr[``0``], end ``=` `" "``) ` `    ``for` `i ``in` `range``(``1``,n): ` `         `  `        ``# If pair is not a co-prime insert 1. ` `        ``if` `(gcd(arr[i], arr[i ``-` `1``]) !``=` `1``): ` `            ``print``(``1``, end ``=` `" "``) ` `        ``print``(arr[i] , end ``=` `" "``) ` `         `  `# Driver Code ` `A ``=` `[ ``5``, ``10``, ``20` `] ` `n ``=` `len``(A) ` `printResult(A, n)  ` ` `  `# This code is contributed by "Sharad_Bhardwaj". `

## C#

 `// C# program for minimum insertions ` `// to make a Co-prime Array. ` `using` `System; ` ` `  `class` `GFG { ` ` `  `    ``// Recursive function to return ` `    ``// gcd of a and b ` `    ``static` `int` `gcd(``int` `a, ``int` `b) ` `    ``{ ` `        ``// Everything divides 0 ` `        ``if` `(a == 0 || b == 0) ` `            ``return` `0; ` ` `  `        ``// base case ` `        ``if` `(a == b) ` `            ``return` `a; ` ` `  `        ``// a is greater ` `        ``if` `(a > b) ` `            ``return` `gcd(a - b, b); ` ` `  `        ``return` `gcd(a, b - a); ` `    ``} ` ` `  `    ``static` `void` `printResult(``int``[] arr, ``int` `n) ` `    ``{ ` `        ``// Counting adjacent pairs that  ` `        ``// are not co-prime. ` `        ``int` `count = 0; ` ` `  `        ``for` `(``int` `i = 1; i < n; i++) ` `            ``if` `(gcd(arr[i], arr[i - 1]) != 1) ` `                ``count++; ` ` `  `        ``// No.of insertions ` `        ``Console.WriteLine(count); ` `        ``Console.Write(arr + ``" "``); ` ` `  `        ``for` `(``int` `i = 1; i < n; i++) { ` ` `  `            ``// If pair is not a co-prime insert 1. ` `            ``if` `(gcd(arr[i], arr[i - 1]) != 1) ` `                ``Console.Write(1 + ``" "``); ` `            ``Console.Write(arr[i] + ``" "``); ` `        ``} ` `    ``} ` ` `  `    ``// Driver Function ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int``[] A = { 5, 10, 20 }; ` `        ``int` `n = A.Length; ` `        ``printResult(A, n); ` `    ``} ` `} ` ` `  `/*This code is contributed by vt_m.*/`

## PHP

 ` ``\$b``) ` `        ``return` `gcd(``\$a` `- ``\$b``, ``\$b``); ` ` `  `    ``return` `gcd(``\$a``, ``\$b` `- ``\$a``); ` `} ` ` `  `function` `printResult(``\$arr``, ``\$n``) ` `{ ` `    ``// Counting adjacent pairs  ` `    ``// that are not co-prime. ` `    ``\$count` `= 0; ` ` `  `    ``for` `(``\$i` `= 1; ``\$i` `< ``\$n``; ``\$i``++) ` `        ``if` `(gcd(``\$arr``[``\$i``],  ` `                ``\$arr``[``\$i` `- 1]) != 1) ` `            ``\$count``++; ` ` `  `    ``// No.of insertions ` `    ``echo` `\$count``, ``"\n"``; ` `    ``echo` `\$arr`` , ``" "``; ` ` `  `    ``for` `(``\$i` `= 1; ``\$i` `< ``\$n``; ``\$i``++) ` `    ``{ ` ` `  `        ``// If pair is not a  ` `        ``// co-prime insert 1. ` `        ``if` `(gcd(``\$arr``[``\$i``],  ` `                ``\$arr``[``\$i` `- 1]) != 1) ` `            ``echo` `1 , ``" "``; ` `        ``echo` `\$arr``[``\$i``] , ``" "``; ` `    ``} ` `} ` ` `  `// Driver Code ` `\$A` `= ``array``(5, 10, 20); ` `\$n` `= sizeof(``\$A``); ` `printResult(``\$A``, ``\$n``); ` ` `  `// This code is contributed ` `// by ajit ` `?> `

Output:

```2
5 1 10 1 20
```

Time Complexity : O(n).

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