Introduction - If you have any usage issues, please Google them yourself
Many improved versions of binary indexed tree. Which can be used to do these kinds of work in a 1D array:
Change one point+k and get the prefixsum
Change a range+k and get value of one point
Change a range+k and get the prefixsum
RMQ(Range max/minimum question)
An offline balanced tree
2D extend and 2+D is similar