# Subarray whose absolute sum is closest to K

Given an array of n elements and an integer K, the task is to find the subarray with minimum value of ||a[i] + a[i + 1] + ……. a[j]| – K|. In other words, find the contiguous sub-array whose sum of elements shows minimum deviation from K or the subarray whose absolute sum is closest to K.

Example

Input:: a[] = {1, 3, 7, 10}, K = 15
Output: Subarray {7, 10}
The contiguous sub-array [7, 10] shows minimum deviation of 2 from 15.

Input: a[] = {1, 2, 3, 4, 5, 6}, K = 6
Output: Subarray {1, 2, 3}
The contiguous sub-array [1, 2, 3] shows minimum deviation of 0 from 6.

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

A naive approach would be to check if the sum of each contiguous sub-array and it’s difference from K.

Below is the implementation of the above approach:

 `# Python Code to find sub-array whose  ` `# sum shows the minimum deviation ` ` `  `def` `getSubArray(arr, n, K): ` `    ``i ``=` `-``1` `    ``j ``=` `-``1` `    ``currSum ``=` `0` `    ``# starting index, ending index, Deviation ` `    ``result ``=` `[i, j, ``abs``(K``-``abs``(currSum))] ` `     `  `    ``# iterate i and j to get all subarrays ` `    ``for` `i ``in` `range``(``0``, n): ` `         `  `        ``currSum ``=` `0` `         `  `        ``for` `j ``in` `range``(i, n): ` `            ``currSum ``+``=` `arr[j] ` `            ``currDev ``=` `abs``(K``-``abs``(currSum)) ` `             `  `            ``# found sub-array with less sum ` `            ``if` `(currDev < result[``2``]): ` `                ``result ``=` `[i, j, currDev] ` `                 `  `            ``# exactly same sum ` `            ``if` `(currDev ``=``=` `0``): ` `                ``return` `result ` `    ``return` `result ` `     `  `# Driver Code ` `def` `main(): ` `    ``arr ``=` `[``15``, ``-``3``, ``5``, ``2``, ``7``, ``6``, ``34``, ``-``6``] ` `     `  `    ``n ``=` `len``(arr) ` `     `  `    ``K ``=` `50` `     `  `    ``[i, j, minDev] ``=` `getSubArray(arr, n, K) ` `     `  `    ``if``(i ``=``=``-``1``): ` `        ``print``(``"The empty array shows minimum Deviation"``) ` `        ``return` `0` `     `  `    ``for` `i ``in` `range``(i, j ``+` `1``):  ` `        ``print` `arr[i], ` `     `  `     `  `main() `

Output:

```-3 5 2 7 6 34
```

Time Complexity: O(N^2)

Efficient Approach: If the array only consists of non-negative integers, use the sliding window technique to improve the calculation time for sum in each iteration. The sliding window technique reduces the complexity by calculating the new sub-array sum using the previous sub-array sum. Increase the right index till the difference (K-sum) is greater than zero. The first sub-array with negative (K-sum) is considered, and the next sub-array is with left index = i+1(where i is the current right index).

Below is the implementation of the above approach:

 `# Python Code to find non-negative  ` `# sub-array whose sum shows minimum deviation ` `# This works only if all elements ` `# in array are non-negative ` ` `  ` `  `# function to return the index  ` `def` `getSubArray(arr, n, K): ` `    ``currSum ``=` `0` `    ``prevDif ``=` `0` `    ``currDif ``=` `0` `    ``result ``=` `[``-``1``, ``-``1``, ``abs``(K``-``abs``(currSum))] ` `    ``resultTmp ``=` `result ` `    ``i ``=` `0` `    ``j ``=` `0` `     `  `    ``while``(i<``=` `j ``and` `j

Output:

```-3 5 2 7 6 34
```

Time Complexity: O(N)

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