Someone can help me to solve this problem, I try Quad-tree but i got TLE. Update Sub-Matrix & Query Sub-Matrix
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Two dimensional lazy-loading tree (segment tree with lazy propagation) can be used.
Firstly you should try to solve simpler task, with two-dimensional segment tree: - Update one element of matrix - Query sum of sub-matrix
Then you can change segment tree to lazy-loading tree.
how to make lazy tags when dealing with two dimensional seg-tree,I used to think that it is impossible....
Yeah, you' re right — it won't work.
It's a straightforward Fenwick-tree problem in two dimensions. If you don't have any idea on how to solve this, it would be better to begin with a one-dimensional version like PYRSUM
Sketch of the idea behind both questions: Topcoder thread, Petr's blog
You are wrong. Both queries asks about sub-matrix.
Using quad tree you can reach O(N * K) ~ 10^8 with a big constant factor, i think it is not very easy to pass 1 sec TL using quad-tree.
At least one Fenwick-tree based approach works; as proof you can see that I solved the problem using this sort of technique already: http://www.spoj.com/status/USUBQSUB,hex539/
Actually your comment seems a bit out-of-place- was it supposed to be directed at me?
can you please explain me, or give me a code with 2d fenwick-tree, or 2d lazy propagation? I think it should be O(n) for query.
Here's one implementation. (It's XOR-sum, but the idea is the same and the implementation of ordinary sum is easier.) http://codeforces.me/contest/341/submission/4391440
And a simple linear version, without context: http://pastebin.com/CuuRyRZw
This is a new technique for me, i think is really interesting and useful. I used it in Pyramid Sum 2(SPOJ), yesterday.
hex539 wrote a very good article in topcoder. Range BIT updates