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### 11460 - Balance

Posted: **Wed Jun 25, 2008 10:58 am**

by **kalyon**

do i have to implement centroid of a polygon algorithm from formula like in

http://en.wikipedia.org/wiki/Centroid
or is there a simple way that i couldnt figure it out yet

...any idea?

### Re: 11460 - Balance

Posted: **Wed Jun 25, 2008 8:15 pm**

by **kalyon**

i figured out as:

**first** make two polygon set as above and below the x-axis.

**second** add the points to these polygons at which points original big polygon crosses the x-axis.

**third** find the centroids of these polygons.

**finally** find the diff. between x coordinates of two centroids.

the important step is second step. when you adding this points to the polygons you have to be careful about the order of the points.

all i need now is to express this as a code.

### Re: 11460 - Balance

Posted: **Thu Jun 26, 2008 12:03 pm**

by **Chirag Chheda**

Well in test case given in the problem

first polygon->(0 1) (2 3) (4 1) ..Its centroid(2,5/3)

second polygon->(4 -3) (2 -3) (2 -1) (0 -1)..Its centroid (2,-2)

Hence the difference between the X co-ordinate is 0.

then how come the answer is 0.5??

Can u plz xplain

### Re: 11460 - Balance

Posted: **Thu Jun 26, 2008 12:24 pm**

by **kalyon**

as i wrote before since there are two polygon sets we have to add extra points (on wich points the x-axis crossed) to these two polygons.

so the polygons must be:

CE: **(0, 0)**, (0, 1), (2, 3), (4, 1), **(4, 0) ** x-coord of centroid is 2

CLR: **(4, 0)**, (4, -3), (2, -3), (2, -1), (0, -1), **(0, 0)** x-coord of centroid is 2.5

so the difference is 0.5

### Re: 11460 - Balance

Posted: **Thu Jun 26, 2008 1:29 pm**

by **Chirag Chheda**

the x co-ordinate of CLR shud be 2 I think.

How come its 2.5

### Re: 11460 - Balance

Posted: **Thu Jun 26, 2008 2:10 pm**

by **kalyon**

in this page:

http://local.wasp.uwa.edu.au/~pbourke/g ... /polyarea/
you can find some sample codes.

according to my calculations test case is correct.

### Re: 11460 - Balance

Posted: **Fri Jun 27, 2008 7:16 am**

by **Chirag Chheda**

Thnx got it.Now i will try 2 solve it

Keep posting..

### 11460 - Balance

Posted: **Mon Jun 30, 2008 3:46 pm**

by **hasib_bd**

I'm getting wa.

For the below Inputs my code generates following outputs.

**Input:**Code: Select all

```
15
5
0 3
4 1
3 -1
-3 -1
-4 1
5
-3 -1
3 -1
4 1
0 3
-4 1
8
0 0
0 1
2 3
4 1
4 -3
2 -3
2 -1
0 -1
7
0 1
0 -1
2 -1
2 -3
4 -3
4 1
2 3
7
0 1
2 3
4 1
4 -3
2 -3
2 -1
0 -1
7
0 -1
2 -1
2 -3
4 -3
4 1
2 3
0 1
7
4 -3
4 1
2 3
0 1
0 -1
2 -1
2 -3
7
-4 -3
-4 1
-2 3
0 1
0 -1
-2 -1
-2 -3
7
0 1
0 -1
-2 -1
-2 -3
-4 -3
-4 1
-2 3
9
-3 0
-3 3
0 3
0 0
1 0
2 0
2 -3
-1 -3
-1 0
9
-3 0
-1 0
-1 -3
2 -3
2 0
1 0
0 0
0 3
-3 3
10
0 3
-300 3
-3 0
-1 0
-1 -3
2 -3
2 0
4 0
301 3
0 3
3
-1 2
-4 -1
2 -1
3
-1 2
-4 -1
2 1
3
-1 2
-4 1
2 -1
```

**Output:**Code: Select all

```
Balanced.
Balanced.
CE is aft of CLR by 0.50 units.
CE is aft of CLR by 0.50 units.
CE is aft of CLR by 0.50 units.
CE is aft of CLR by 0.50 units.
CE is aft of CLR by 0.50 units.
CE is forward of CLR by 0.50 units.
CE is forward of CLR by 0.50 units.
CE is aft of CLR by 2.00 units.
CE is aft of CLR by 2.00 units.
Balanced.
Balanced.
CE is forward of CLR by 2.00 units.
CE is aft of CLR by 2.00 units.
```

Can anyone who solved this problem can provide more input/output? I'm not getting any reason for WA.

### Re: 11460 - Balance

Posted: **Tue Jul 01, 2008 6:00 am**

by **hasib_bd**

Can there be any inputs like below?

The problem description doesn't clarify this...

**Input:**
Code: Select all

```
2
5
-3 2
0 -1
3 2
3 -2
-3 -2
6
-3 2
-1 0
1 0
3 2
3 -2
-3 -2
```

### Re: 11460 - Balance

Posted: **Wed Jul 09, 2008 10:54 am**

by **kalyon**

Problem definition says:

"The first line of input will contain a single integer n specifying the number of points along the outline of the side view of the boat. The following n lines will each contain two integers: the x and y coordinate of a point along the outline.

**The points will be given in order along the outline**. The x axis (i.e. the line y = 0) represents the waterline. Assume that the boat faces in the direction of increasing x coordinates."

from this i understand:

1. points are in clockwise order or counter-clockwise order along the coordinate system. (but when you are solving it must be clockwise order. i dont know why i just saw this in some document about polygon centroids. )

2. x coordinates can be negative. (i dont see any statement about it in the problem.)

according to these your inputs seems correct to me.

but i really wonder the judge's test case because i get WA too