Tree Group Tree Group

According to Peter M. Fenwick, as all integers can be represented as a power of 2, we can also represent a sequence of sequences as a sum of a series of sub-sequences. Using this idea, we can classify a prefix and divide it into multiple sub-sequences, and divide the method with the power of the number 2 and have a very similar way. On the one hand, the number of subsequence is the number of the second binary representation of 1, on the other hand, the number of sub-series represented by F[i] is also the power of 2.

Three Concepts

1. Lowest bit number = Lowestbitnum (x)

= X&-x

or = x & (x^ (x-1))

2. Subsequent

Successor of i = i + lowestbitnum (i)

3. Precursor

Precursor of i = I-lowestbitnum (i)

two implementations

Sum (i) = all precursor nodes of I node + i

Update (i) = updates the I node and all subsequent nodes