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.
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
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:
- the first number will be k * (6*i+1)
- the second number will be k * (6*i+1)
- the third number will be k * (6*i+3)
- 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.
2 4 6 10 14 16 18 22
Time Complexity: O(4*N)
- Print a pair of numbers with the given Sum and Product
- Check if a given pair of Numbers are Betrothed numbers or not
- Check if the given two numbers are friendly pair or not
- Find original numbers from gcd() every pair
- Angle between a Pair of Lines in 3D
- Pair of prime numbers with a given sum and minimum absolute difference
- Print numbers such that no two consecutive numbers are co-prime and every three consecutive numbers are co-prime
- Print numbers with digits 0 and 1 only such that their sum is N
- Print first N Mosaic numbers
- Program to print first n Fibonacci Numbers | Set 1
- Print all integers that are sum of powers of two given numbers
- Program to print first N Prime numbers
- Print k numbers where all pairs are divisible by m
- Print all numbers less than N with at-most 2 unique digits
- Print prime numbers in a given range using C++ STL
- Print squares of first n natural numbers without using *, / and -
- Print N numbers such that their sum is a Perfect Cube
- Print N distinct numbers following the given operations
- Print the kth common factor of two numbers
- Program to print non square numbers
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.