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.
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 32-bit integer.
- "END" - Indicates the end of the test case.
For each test case, output one line for the answer to each "SUM" command. Print a blank line after each test case.
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
Guys, I used 2D BIT and I still get TLE. Anyone has an idea why ?
can this solved by Binary indexed tree 2-D???
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:
@Avinash: Because you can't sum one square twice :))
why second line of output is not 24??
@ Hy Trường Sơn & paddyHOD - u can use 2D bit for this problem !! ;)
my algo is very slow,some please tell me which data structure should i take.Last edit: 2010-09-27 15:49:22
Hy Trường Sơn:
my algorithm is very slow. I use segment tree