Google Interview: Find all contiguous subsequence in a given array of integers, whose sum falls in the given range. Can we do better than O(n^2)?

Question

Given an array of Integers, and a range (low, high), find all contiguous subsequence in the array which have sum in the range.

Is there a solution b

Answer 1

Here is way you can get O(nlogn) if there are only positive numbers :-

1. Evaluate cumulative sum of array
2. for i  find total sum[j] in (sum[i]+low,sum[i]+high) using binary search
3. Total = Total + count
4. do 3 to 5 for all i

Time complexity:-

Cumulative sum is O(N)
Finding sums in range is O(logN) using binary search
Total Time complexity is O(NlogN)