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Minimum Subarray With Required Sum

Last Updated: 7 Sep, 2020
Difficulty: Moderate


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You have been given an array(ARR) of positive integers and an integer X. You have to find the minimum length subarray such that the sum of all of its elements is strictly greater than the given integer X.

A subarray is a contiguous block of elements that can be formed by deleting some (possibly zero) elements from the beginning or the end of the original array. 
For example :
If the given array is [1, 2, 3, 4, 5], then [2, 3, 4], [1, 2], [5] are some subarrays while [1, 3], [2, 3, 5] are not.

If there are multiple subarrays with minimum length, find one which appears earlier in the array (i.e. subarray that starts with lower index).

If there is no such subarray, print an empty line.
Input Format:
The first line of input contains two integers 'N' and 'X' separated by a single space. 'N' represents the size of the given array/list and 'X' represents the given integer.

The second line of input contains 'N' single space-separated integers representing the elements of the array/list.
Output Format :
The only line of output contains single space-separated elements of the minimum length subarray.

You do not need to print anything explicitly, it has already been taken care of.
Constraints :
1 <= N <= 5 * 10^5
1 <= X <= 10^9
1 <= ARR[i] <= 10^9

Time Limit: 1 sec
Follow Up :
Try to solve in O(N) Time Complexity and O(1) Space Complexity.

Approach 1

We can check every subarray of the array/list if it’s sum is greater than X(given integer) or not. To do this, we traverse for every possible start and endpoint of the subarray using two nested loops. We will keep updating the ‘sum’ while expanding our endpoint. Out of all the valid(sum greater than X) subarrays, we pick the minimum length subarray.

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