Is it possible to build a Fenwick tree in O(n)?

Question

Fenwick tree is a data structure which allows two kind of operations (you can augment it with more operations):

• point update update(index, value)<

Answer 1

Here's the Java implementation:

public BIT(long[] nums) {
        bit = new long[nums.length + 1]; //one-indexed
        for (int i = 1; i <= nums.length; i++) {
            bit[i] += nums[i - 1]; //update node
            if (i + (i & -i) <= nums.length) {
                bit[i + (i & -i)] += bit[i]; //update parent
            }
        }
    }

Same general idea as j_random_hacker's post: we update the current node and the next higher parent node, using the property that all children nodes will always be visited before their respective parent nodes