MATSUM  Matrix Summation
A N × N matrix is filled with numbers. BuggyD is analyzing the matrix, and he wants the sum of certain submatrices every now and then, so he wants a system where he can get his results from a query. Also, the matrix is dynamic, and the value of any cell can be changed with a command in such a system.
Assume that initially, all the cells of the matrix are filled with 0. Design such a system for BuggyD. Read the input format for further details.
Input
The first line of the input contains an integer t, the number of test cases. t test cases follow.
The first line of each test case contains a single integer N (1 <= N <= 1024), denoting the size of the matrix.
A list of commands follows, which will be in one of the following three formats (quotes are for clarity):
 "SET x y num"  Set the value at cell (x, y) to num (0 <= x, y < N).
 "SUM x1 y1 x2 y2"  Find and print the sum of the values in the rectangle from (x1, y1) to (x2, y2), inclusive. You may assume that x1 <= x2 and y1 <= y2, and that the result will fit in a signed 32bit integer.
 "END"  Indicates the end of the test case.
Output
For each test case, output one line for the answer to each "SUM" command. Print a blank line after each test case.
Example
Input: 1 4 SET 0 0 1 SUM 0 0 3 3 SET 2 2 12 SUM 2 2 2 2 SUM 2 2 3 3 SUM 0 0 2 2 END Output: 1 12 12 13
hide comments
flareneos:
20120112 17:51:51
Guys, I used 2D BIT and I still get TLE. Anyone has an idea why ? 

bristy:
20120111 21:04:46
@admin:


Krzysztof Lewko:
20110617 17:56:03
@aayush yes 

aayush:
20110615 08:33:18
can this solved by Binary indexed tree 2D??? 

Hermano:
20110523 16:17:12
Too slow. How can I sum all elements of a matrix faster? I'm using Java. It looks like no one has solved this using java. 

Ðộc cô cầu bại:
20110514 15:16:18
@Avinash: Because you can't sum one square twice :)) 

Avinash:
20110325 04:04:33
why second line of output is not 24??


biQar:
20101005 17:27:36
@ Hy Trường Sơn & paddyHOD  u can use 2D bit for this problem !! ;) 

paddyHOD:
20100927 15:48:57
my algo is very slow,some please tell me which data structure should i take. Last edit: 20100927 15:49:22 

Hy Trường Sơn:
20090613 09:34:40
my algorithm is very slow. I use segment tree 
Added by:  Matthew Reeder 
Date:  20061029 
Time limit:  1.029s 
Source limit:  30000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  AlKhawarizm 2006 