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Let say x1 is zero and x2 is length of array, is there any way to get the sum without going through all elements? Probaby not, hence it cannot be O(n).
- castro October 30, 2015However if x1 and x2 are fixed within range of the array, we can achieve x2-x1 which is a constant irrespective of the size of the array. This only work if preprocessing is done as suggested by Naor