## Checkerboard Summation (Easy)

You are given a checkerboard with M rows and N columns (1 ≤ M,N ≤ 3000). Up to 100000 of these cells have specified values written in them, and the rest are zeroes. For top-secret strategic reasons which are given out on a need-to-know basis only (and you do not, at the present moment, need to know) you must write a program that will answer up to 100000 queries of the form:

Given the coordinates of two squares on the checkerboard, find the alternating sum of all of the numbers within the rectangle delimited by those two squares. By alternating sum what is meant is that we add all numbers in squares with the same colour as the first square given, and subtract all numbers with the opposite colour.

Input
The first line of the input file contains the integers M and N.
A number of input lines then follow. Each line contains three space-separated integers R, C, and X (1 ≤ R ≤ M, 1 ≤ C ≤ N, -1000 ≤ X ≤ 1000), indicating that the value X is written in row R and column C. No cell will be given twice in the input. The last line is followed by a line containing three zeroes, signifying the end of this section of input.
Following this are a number of lines containing queries. Each line contains four space-separated integers: R1, C1, R2, and C2 (1 ≤ R1 ≤ R2 ≤ M, 1 ≤ C1 ≤ C2 ≤ N). Output the alternating sum of all squares contained within the box [R1,R2] × [C1,C2], as described.

Output
Print the answer to each query on its own line, in order.

Sample Input
3 3
1 2 5
3 1 -2
2 3 11
0 0 0
2 1 3 3
0 0 0 0

Sample Output
13

Explanation
The checkerboard is three cells by three cells. Here's what it looks like:
``` 0  5  0
0  0 11
-2  0  0```

We are asked to find the alternating sum of the second and third rows. The 11 is in a square of the same colour as (2,1), so it is added; -2 is on a square of opposite colour, so it is subtracted. 11-(-2) = 13.

Point Value: 12 (partial)
Time Limit: 2.00s
Memory Limit: 256M
Author: bbi5291

Languages Allowed:
C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, PHP, SCM, CAML, PERL, C#, C++11, PYTH3

• (0/0)
Hi, I realise this problem is quite old but I'm just working on it now.

I have got it going, and get the correct result when submitting for the first 4 set of tests. But then run out of time after that.

I am using Python 3 and have a DP approach (can't be sure it's the optimal one, but it seems fairly sensible to me).

I have looked through the accepted solutions and they are all in C, C++ or Java. I don't see any Python solutions.

So my question is, can Python be used? Or is it just too slow?

• (0/0)
I recoded this in C++ and it solved no problem.

Same strategy as Python, but of course it runs so much faster.

• (0/0)
You can divide the squares into two types: those for which x+y is even, and those for which x+y is odd. Also, this is a DP problem - see if you can figure out how to compute, for a given (x,y) the sum of the rectangle with its upper left corner at the upper left corner of the board and its lower right corner at (x,y).

• (0/0)
"The last line is followed by a line containing three zeroes, signifying the end of this section of input."

Four?

• (1/0)
3 3
1 2 5
3 1 -2
2 3 11

This is the checkerboard values.

0 0 0

This tells you the checkerboard values are finished inputting.

2 1 3 3
0 0 0 0

The first line is input for which you have to output an answer, and the 0 0 0 0 tells you it is done inputting.

• (0/0)
oh okay ty

• (2/0)
There are no update operations in this problem - you know the entire grid and it will not be modified.
How does this make the problem easier?