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
anuragkanwar:
20231003 14:54:37
Guys please always use that algorithm which is faster and easier to code.


dil_shad22:
20221004 22:52:56
Thanks @arunjain9988 !


hv22:
20220803 19:05:59
good problem to learn 2d BIT


minhnguyent546:
20220513 16:21:07
SET not add :))). Caution ! 

amisin3:
20210707 20:53:26
Getting TLE even the algorithm is running for O(nlogn). Used Fenwick Trees


arunjain9988:
20210313 11:35:00
Learned: never use endl :) 

manuver:
20201019 09:13:00
things to keep in mind


nemesys:
20200819 22:08:29
Iterative 2D segment tree passed without problems.


pareksha:
20200429 12:59:42
No matter how much optimisation is done, 2D segment tree isn't working. Time Limit is too strict for it. 

sachit9_:
20200204 16:02:33
getting tle after using int ,scanf,printf,fastio,BIT , plz someone help 
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 