# Check if array can be divided into two sub-arrays such that their absolute difference is K

Given an array arr[] and an integer K, the task is to find whether the array can be divided into two sub-arrays such that the absolute difference of the sum of the elements of both the sub-arrays is K.

Examples:

Input: arr[] = {2, 4, 5, 1}, K = 0
Output: Yes
{2, 4} and {5, 1} are the two possible sub-arrays.
|(2 + 4) – (5 + 1)| = |6 – 6| = 0

Input: arr[] = {2, 4, 1, 5}, K = 2
Output: No

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

• Assume there exists an answer, let the sum of elements of the sub-array (with smaller sum) is S.
• Sum of the elements of the second array will be S + K.
• And, S + S + K must be equal to sum of all the elements of the array say totalSum = 2 *S + K.
• S = (totalSum – K) / 2
• Now, traverse the array till we achieve a sum of S starting from the first element and if its not possible then print No.
• Else print Yes.

Below is the implementation of the above approach:

 `#include ` `using` `namespace` `std; ` ` `  `// Function that return true if it is possible ` `// to divide the array into sub-arrays ` `// that satisfy the given condition ` `bool` `solve(``int` `array[], ``int` `size, ``int` `k) ` `{ ` `    ``// To store the sum of all the elements ` `    ``// of the array ` `    ``int` `totalSum = 0; ` `    ``for` `(``int` `i = 0; i < size; i++) ` `        ``totalSum += array[i]; ` ` `  `    ``// Sum of any sub-array cannot be ` `    ``// a floating point value ` `    ``if` `((totalSum - k) % 2 == 1) ` `        ``return` `false``; ` ` `  `    ``// Required sub-array sum ` `    ``int` `S = (totalSum - k) / 2; ` ` `  `    ``int` `sum = 0; ` `    ``for` `(``int` `i = 0; i < size; i++) { ` `        ``sum += array[i]; ` `        ``if` `(sum == S) ` `            ``return` `true``; ` `    ``} ` ` `  `    ``return` `false``; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `array[] = { 2, 4, 1, 5 }; ` `    ``int` `k = 2; ` `    ``int` `size = ``sizeof``(array) / ``sizeof``(array); ` `    ``if` `(solve(array, size, k)) ` `        ``cout << ``"Yes"` `<< endl; ` `    ``else` `        ``cout << ``"No"` `<< endl; ` `} `

 `/*package whatever //do not write package name here */` ` `  `import` `java.io.*; ` ` `  `class` `GFG  ` `{ ` `     `  `// Function that return true if it is possible ` `// to divide the array into sub-arrays ` `// that satisfy the given condition ` `static` `boolean` `solve(``int` `array[], ``int` `size, ``int` `k) ` `{ ` `    ``// To store the sum of all the elements ` `    ``// of the array ` `    ``int` `totalSum = ``0``; ` `    ``for` `(``int` `i = ``0``; i < size; i++) ` `        ``totalSum += array[i]; ` ` `  `    ``// Sum of any sub-array cannot be ` `    ``// a floating point value ` `    ``if` `((totalSum - k) % ``2` `== ``1``) ` `        ``return` `false``; ` ` `  `    ``// Required sub-array sum ` `    ``int` `S = (totalSum - k) / ``2``; ` ` `  `    ``int` `sum = ``0``; ` `    ``for` `(``int` `i = ``0``; i < size; i++)  ` `    ``{ ` `        ``sum += array[i]; ` `        ``if` `(sum == S) ` `            ``return` `true``; ` `    ``} ` `    ``return` `false``; ` `} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `main (String[] args) ` `    ``{ ` `        ``int` `array[] = { ``2``, ``4``, ``1``, ``5` `}; ` `        ``int` `k = ``2``; ` `        ``int` `size = array.length; ` `         `  `        ``if` `(solve(array, size, k)) ` `            ``System.out.println (``"Yes"``); ` `        ``else` `            ``System.out.println (``"No"` `); ` `    ``} ` `} ` ` `  `// This Code is contributed by akt_mit  `

 `# Function that return true if it is possible ` `# to divide the array into sub-arrays ` `# that satisfy the given condition ` `def` `solve(array,size,k): ` `    ``# To store the sum of all the elements ` `    ``# of the array ` `    ``totalSum ``=` `0` `    ``for` `i ``in` `range` `(``0``,size): ` `        ``totalSum ``+``=` `array[i] ` ` `  `    ``# Sum of any sub-array cannot be ` `    ``# a floating point value ` `    ``if` `((totalSum ``-` `k) ``%` `2` `=``=` `1``): ` `        ``return` `False` ` `  `    ``# Required sub-array sum ` `    ``S ``=` `(totalSum ``-` `k) ``/` `2` ` `  `    ``sum` `=` `0``; ` `    ``for` `i ``in` `range` `(``0``,size): ` `        ``sum` `+``=` `array[i] ` `        ``if` `(``sum` `=``=` `S): ` `            ``return` `True` `     `  ` `  `    ``return` `False` ` `  ` `  `# Driver Code ` `array``=` `[``2``, ``4``, ``1``, ``5``] ` `k ``=` `2` `n ``=` `4` `if` `(solve(array, n, k)): ` `    ``print``(``"Yes"``) ` `else``: ` `    ``print``(``"No"``) ` ` `  `# This code is contributed by iAyushRaj. `

 `using` `System; ` `class` `GFG ` `{ ` ` `  `// Function that return true if it is possible ` `// to divide the array into sub-arrays ` `// that satisfy the given condition ` `public` `static` `bool` `solve(``int``[] array, ``int` `size, ``int` `k) ` `{ ` `    ``// To store the sum of all the elements ` `    ``// of the array ` `    ``int` `totalSum = 0; ` `    ``for` `(``int` `i = 0; i < size; i++) ` `        ``totalSum += array[i]; ` ` `  `    ``// Sum of any sub-array cannot be ` `    ``// a floating point value ` `    ``if` `((totalSum - k) % 2 == 1) ` `        ``return` `false``; ` ` `  `    ``// Required sub-array sum ` `    ``int` `S = (totalSum - k) / 2; ` ` `  `    ``int` `sum = 0; ` `    ``for` `(``int` `i = 0; i < size; i++)  ` `    ``{ ` `        ``sum += array[i]; ` `        ``if` `(sum == S) ` `            ``return` `true``; ` `    ``} ` ` `  `    ``return` `false``; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main() ` `{ ` `    ``int``[] array = { 2, 4, 1, 5 }; ` `    ``int` `k = 2; ` `    ``int` `size = 4; ` `     `  `    ``if` `(solve(array, size, k)) ` `        ``Console.Write(``"Yes"``); ` `    ``else` `        ``Console.Write(``"No"``); ` `} ` `} ` ` `  `// This code is contributed by iAyushRaj. `

 ` `

Output:
```No
```

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Improved By : jit_t, iAyushRaj

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