Print N lines of 4 numbers such that every pair among 4 numbers has a GCD K

Given N and K, the task is to print N lines where each line contains 4 numbers such that every among those 4 numbers has a GCD K and the maximum number used in N*4 should be minimized.

Note: In case of multiple outputs, print any one.

Examples:



Input: N = 1, K = 1
Output: 1 2 3 5
Every pair among 1, 2, 3 and 5 gives a GCD K and the largest number among these is 5 which the minimum possible.

Input: 2 2
Output:
2 4 6 22
14 18 10 16

In the above input, the maximum number is 22, which is the minimum possible to make 2 lines of 4 numbers.

Approach: The first observation is that if we can solve the given problem for K=1, we can solve the problem with GCD K by simply multiplying the answers with K. We know that any three consecutive odd numbers have a GCD 1 always when paired, so three numbers of every line can be easily obtained. Hence the lines will look like:

1 3 5 _ 
7 9 11 _ 
13 15 17 _  
.
.
.

An even number cannot be inserted always, because inserting 6 in third line will give GCD(6, 9) as 3. So the best number that can be inserted is a number between the first two off numbers of every line. Hence the pattern looks like:

1 2 3 5  
7 8 9 11  
13 14 15 17  
.
.
.

To obtain given GCD K, one can easily multiply K to the obtained numbers. Hence for i-th line:

  1. the first number will be k * (6*i+1)
  2. the second number will be k * (6*i+1)
  3. the third number will be k * (6*i+3)
  4. the fourth number will be k * (6*i+5)

The maximum number among N*4 numbers will be k * (6*i – 1)

Below is the implementation of the above approach.

C++

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// C++ implementation of the
// above approach
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to print N lines
void printLines(int n, int k)
{
    // Iterate N times to print N lines
    for (int i = 0; i < n; i++) {
        cout << k * (6 * i + 1) << " "
             << k * (6 * i + 2) << " "
             << k * (6 * i + 3) << " "
             << k * (6 * i + 5) << endl;
    }
}
// Driver Code
int main()
{
    int n = 2, k = 2;
    printLines(n, k);
    return 0;
}

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Java

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// Java implementation of the
// above approach
  
import java.util.*;
import java.lang.*;
import java.io.*;
  
class GFG
{
// Function to print N lines
static void printLines(int n, int k)
{
    // Iterate N times to print N lines
    for (int i = 0; i < n; i++) {
        System.out.println ( k * (6 * i + 1) + " "
            + k * (6 * i + 2) + " "
            + k * (6 * i + 3) + " "
            + k * (6 * i + 5) );
    }
}
// Driver Code
public static void main(String args[])
{
    int n = 2, k = 2;
    printLines(n, k);
}
}

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Python 3

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# Python implementation of the
# above approach. 
  
# Function to print N lines 
def printLines(n, k) :
  
    # Iterate N times to print N lines
    for i in range(n) :
        print( k * (6 * i + 1),
                k * (6 * i + 2),
               k * (6 * i + 3),
               k * (6 * i + 5))
          
# Driver code     
if __name__ == "__main__" :
  
    n, k = 2, 2
    printLines(n, k)
  
# This code is contributed by ANKITRAI1

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PHP

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<?php
// Function to print N lines
function printLines($n, $k)
{
    // Iterate N times to print N lines
    for ($i = 0; $i < $n; $i++) 
    {
        echo ($k * (6 * $i + 1));
        echo (" ");
        echo ($k * (6 * $i + 2));
        echo (" ");
        echo ($k * (6 * $i + 3)); 
        echo (" ");
        echo ($k * (6 * $i + 5));
        echo ("\n");
    }
}
  
// Driver Code
$n = 2;
$k = 2;
printLines($n, $k);
      
// This code is contributed 
// by Shivi_Aggarwal
?>

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C#

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// C# implementation of the
// above approach
using System;
  
class GFG
{
// Function to print N lines
static void printLines(int n, int k)
{
    // Iterate N times to print N lines
    for (int i = 0; i < n; i++)
    {
        Console.WriteLine ( k * (6 * i + 1) + " " +
                            k * (6 * i + 2) + " " +
                            k * (6 * i + 3) + " "
                            k * (6 * i + 5) );
    }
}
  
// Driver Code
public static void Main()
{
    int n = 2, k = 2;
    printLines(n, k);
}
}
  
// This code is contributed
// by Akanksha Rai(Abby_akku)

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Output:

2 4 6 10
14 16 18 22

Time Complexity: O(4*N)



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Striver(underscore)79 at Codechef and codeforces D

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