Forces in the crystal

Problem code: HX

All submissions for this problem are available.

The time limit for the large test cases for this problem has been upped to 15 seconds.

Suppose that we have a crystalline triangular grid of atoms. Atoms are arranged on a regular grid, and each atom has six neighbors (unless it lies on the boundary of crystal). Each atom has an electric charge of q, and can be polarized in only one of two directions: up or down (the laws of physics in Byteland are somewhat surprising!). If two atoms are neighbors and share the same polarization, then a destructive force against the crystal occurs, whose value is equal to q1*q2. We can choose the polarization for each atom, and we would like to minimize total force working against the crystal, i.e., the sum of values of all the individual forces.

Input

First, 1000 <= n <= 2000, the size of input. Then n lines with n numbers in each follow. In the x-th line, 1 <=  x <= n, the y-th number, 1 <=  y <= n, is the charge of the atom with coordinates in the crystal equal to (x,y) if x is odd, (x,y+1/2) otherwise. For any atom at coordinates (x,y), the coordinates of the neighbors are assumed to be the following (as long as they appear in the crystal): (x-1,y-1/2),(x-1,y+1/2),(x,y-1),(x,y+1),(x+1,y-1/2),(x+1,y+1/2). Each charge q is in the range 0.1 <= q <= 1.

Output

For each atom given at input, output 0 or 1 depending on whether the polarization of the atom should be directed up or down.

Score

The score of your program is equal to the value of the force acting on the crystal. The program is tested multiple times for different data sets, and the results are averaged.

Example

Input:
3
1 2 3
4 5 6
7 8 9

Output:
0 0 0
0 0 0
0 0 1

Score:
269 = (1*2+1*4+2*3+2*5+2*4+3*6+3*5+4*5+4*7+4*8+5*6+5*8+7*8)

Author: admin
Date Added: 22-09-2009
Time Limit: 10 - 15 sec
Source Limit: 50000 Bytes
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Comments

the output doesn't look

manish2382 @ 27 Oct 2009 11:51 AM

the output doesn't look right.....if cordinate (3,1) is 1 then the score would be even less

The output provided doesn't

triplem @ 27 Oct 2009 03:07 PM

The output provided doesn't give the optimal answer. But it is a valid output.

I see successful submissions

mtutnid @ 7 Apr 2012 03:23 PM
I see successful submissions that take up to 147.27 s to complete. The time limit here is shown to be 10s and then the upper bound was raised to 15 s. So how long can my program take 150s?

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