Skip to content
Related Articles
Create an array of size N with sum S such that no subarray exists with sum S or S-K
• Last Updated : 04 May, 2021

Given a number N and an integer S, the task is to create an array of N integers such that sum of all elements equals to S and print an element K where 0 ≤ K ≤ S, such that there exists no subarray with sum equals to K or (S – K)
If no such array is possible then print “-1”.
Note: There can be more than one value for K. You can print any one of them.
Examples:

Input: N = 1, S = 4
Output: {4}
K = 2
Explanation:
There exists an array {4} whose sum is 4.
From all possible value of K i.e., 0 ≤ K ≤ 4, K = 1, 2, and 3 satisfy the given conditions.
For K = 2, there is no subarray whose sum is 2 or S – K i.e., 4 – 2 = 2.
Input: N = 3, S = 8
Output: {2, 2, 4}
K = 1
Explanation:
There exists an array {2, 2, 4} and there exists K as 1 such that there is no subarray whose sum is 1 and S – K i.e., 8 – 1 = 7.

Approach: To solve the problem mentioned above we have to observe that:

1. If 2 * N > S then there is no array possible.
For Example:

For N = 3 and S = 4, then the possible arrays are {1, 2, 1}, {1, 1, 2}, {2, 1, 1}.
The possible values for K are 0, 1, 2, 3 (0 < = k < = S).
But there is no value for K which satisfy the condition.
So the solution to this is not possible.

1.
2. An array is only possible if 2 * N <= S and the array can be created using elements (N-1) times 2 and the last element as S – (2 * (N – 1)) and K will always be 1.

Below is the implementation of the above approach:

## C++

 `// C++ for the above approach``#include``using` `namespace` `std;``    ` `// Function to create an array with``// N elements with sum as S such that``// the given conditions satisfy``void` `createArray(``int` `n, ``int` `s)``{``    ` `    ``// Check if the solution exists``    ``if` `(2 * n <= s)``    ``{` `        ``// Print the array as``        ``// print (n-1) elments``        ``// of array as 2``        ``for``(``int` `i = 0; i < n - 1; i++)``        ``{``           ``cout << ``"2"` `<< ``" "``;``           ``s -= 2;``        ``}` `        ``// Print the last element``        ``// of the array``        ``cout << s << endl;` `        ``// Print the value of k``        ``cout << ``"1"` `<< endl;``    ``}``    ``else``    ` `        ``// If solution doesnot exists``        ``cout << ``"-1"` `<< endl;``}` `// Driver Code``int` `main()``{``    ` `    ``// Given N and sum S``    ``int` `N = 1;``    ``int` `S = 4;` `    ``// Function call``    ``createArray(N, S);``}` `// This code is contributed by Ritik Bansal`

## Java

 `// Java for the above approach``class` `GFG{``    ` `// Function to create an array with``// N elements with sum as S such that``// the given conditions satisfy``static` `void` `createArray(``int` `n, ``int` `s)``{` `    ``// Check if the solution exists``    ``if` `(``2` `* n <= s)``    ``{` `        ``// Print the array as``        ``// print (n-1) elments``        ``// of array as 2``        ``for` `(``int` `i = ``0``; i < n - ``1``; i++)``        ``{``            ``System.out.print(``2` `+ ``" "``);``            ``s -= ``2``;``        ``}` `        ``// Print the last element``        ``// of the array``        ``System.out.println(s);` `        ``// Print the value of k``        ``System.out.println(``1``);``    ``}``    ``else``    ` `        ``// If solution doesnot exists``        ``System.out.print(``"-1"``);``}` `// Driver Code``public` `static` `void` `main(String[] args)``{` `    ``// Given N and sum S``    ``int` `N = ``1``;``    ``int` `S = ``4``;` `    ``// Function call``    ``createArray(N, S);``}``}` `// This code is contributed by 29AjayKumar`

## Python3

 `# Python3 for the above approach` `# Function to create an array with``# N elements with sum as S such that``# the given conditions satisfy``def` `createArray(n, s):`` ` `    ``# Check if the solution exists``    ``if` `(``2` `*` `n<``=` `s):            ``        ` `        ``# Print the array as``        ``# print (n-1) elments``        ``# of array as 2``        ``for` `i ``in` `range``(n``-``1``):``            ``print``(``2``, end ``=``" "``)``            ``s``-``=` `2``            ` `        ``# Print the last element``        ``# of the array``        ``print``(s)``        ` `        ``# Print the value of k``        ``print``(``1``)``    ``else``:``        ``# If solution doesnot exists``        ``print``(``'-1'``)`  `# Driver Code` `# Given N and sum S ``N ``=` `1``S ``=` `4` `# Function call``createArray(N, S)`

## C#

 `// C# program for the above approach``using` `System;``class` `GFG{``    ` `// Function to create an array with``// N elements with sum as S such that``// the given conditions satisfy``static` `void` `createArray(``int` `n, ``int` `s)``{``    ` `    ``// Check if the solution exists``    ``if` `(2 * n <= s)``    ``{` `        ``// Print the array as``        ``// print (n-1) elments``        ``// of array as 2``        ``for``(``int` `i = 0; i < n - 1; i++)``        ``{``           ``Console.Write(2 + ``" "``);``           ``s -= 2;``        ``}` `        ``// Print the last element``        ``// of the array``        ``Console.WriteLine(s);` `        ``// Print the value of k``        ``Console.WriteLine(1);``    ``}``    ``else``    ` `        ``// If solution doesnot exists``        ``Console.Write(``"-1"``);``}` `// Driver Code``public` `static` `void` `Main()``{` `    ``// Given N and sum S``    ``int` `N = 1;``    ``int` `S = 4;` `    ``// Function call``    ``createArray(N, S);``}``}` `// This code is contributed by Code_Mech`

## Javascript

 ``
Output:
```4
1```

Time Complexity: O(N)
Auxiliary Space: O(1)

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with industry experts, please refer Geeks Classes Live

My Personal Notes arrow_drop_up