JOIN
 Problem Statement
Contest: 2018 TCO Marathon Round 4
Problem: CakeSharing

### Problem Statement

You are given a rectangular cake divided in H x W squares. Some of the squares have cream roses in the middle of them. You want to cut the cake into NP pieces to share with your friends, and you want the pieces to be as similar as possible, i.e., to have similar areas and similar numbers of roses on them. You also want the pieces to look neat, so you will do the cutting as follows:
• You will do exactly NP-1 cuts, each cut dividing one of the pieces in two pieces of non-zero areas.
• Each cut will be a line segment with end points in integer coordinates, on the border of one of the previously cut pieces.
• The cuts will not intersect, except in points which are end points of one or several cuts.
• If the center of a rose is exactly on the cut, it is destroyed and is not counted towards either of the pieces the cut separates. If the rose is close to the cut but its center is not exactly on the cut, the rose is not damaged.
Here is an example of a perfectly cut cake for example 0 (seed = 1). There are five pieces, each has area 20.0 (one fifth of the total area of the cake), and each has one rose on it. The sixth rose present on the cake initially has been destroyed by one of the cuts.

### Implementation

Your code should implement a single method cut. It gives you the following information about the problem:
• String[] roses gives you the dimensions of the cake and the placement of roses on it. roses[R][C] indicates whether there is a rose in a square of the cake in row r and column c: '.' denotes an empty square, and 'R' denotes a square with a rose on it.
• int NP gives you the number of pieces to cut the cake into.
The return from this method will describe the cuts you want to do. The return must have exactly NP-1 elements. Each element of the return must be formatted as "X1 Y1 X2 Y2", and will give the x and y coordinates of the end points of the next cut. x and y coordinates correspond to column and row dimensions, respectively. X1 and X2 must be between 0 and W, inclusive, and Y1 and Y2 must be between 0 and H, inclusive.

### Scoring

Your raw score for a test case will be calculated as (1.0 + stdDevArea) * (1.0 + stdDevRoses), where stdDevArea and stdDevRoses are standard deviation of the area of the piece and the number of roses on it, respectively. If your return was invalid (had incorrect number of elements, was formatted incorrectly, attempted an invalid cut, etc.), the raw score for this test case will be -1.

Your normalized score for each test case (except the ones on which your raw score was -1) is MIN/YOUR, where YOUR is your raw score, and MIN is the smallest positive raw score currently obtained on this test case (considering only the last submission from each competitor).

Finally, your total score is equal to the arithmetic average of normalized scores on all test cases, multiplied by 1,000,000.

### Tools

An offline tester is available here. You can use it to test/debug your solution locally. You can also check its source code for exact implementation of test case generation and score calculation. That page also contains links to useful information and sample solutions in several languages.

### Definition

 Class: CakeSharing Method: cut Parameters: String[], int Returns: String[] Method signature: String[] cut(String[] roses, int NP) (be sure your method is public)

### Notes

-The time limit is 10 seconds per test case (this includes only the time spent in your code). The memory limit is 1024 megabytes.
-There is no explicit code size limit. The implicit source code size limit is around 1 MB (it is not advisable to submit codes of size close to that or larger). Once your code is compiled, the binary size should not exceed 1 MB.
-The compilation time limit is 30 seconds. You can find information about compilers that we use and compilation options here.
-There are 10 example test cases and 100 full submission (provisional) test cases. There will be 2000 test cases in the final testing.
-The match is rated.

### Constraints

-Both dimensions of the board H and W will be between 10 and 80, inclusive.
-The probability of each square of the cake having a rose is between 10% and 90%.
-The number of pieces into which you want to cut the cake will be between 5 and 2 * (H + W), inclusive.

### Examples

0)

```seed = 1
H = 10
W = 10
Number of pieces N = 5
Probability of a rose = 7
Number of roses = 6
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```
1)

```seed = 2
H = 45
W = 45
Number of pieces N = 10
Probability of a rose = 75
Number of roses = 1539
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2)

```seed = 3
H = 80
W = 80
Number of pieces N = 320
Probability of a rose = 50
Number of roses = 3195
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3)

```seed = 4
H = 53
W = 78
Number of pieces N = 222
Probability of a rose = 21
Number of roses = 879
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..R..R..R....RR....R.R.RR.............R.........RR........R.R......R....RR.R.R
............R....RRR...........R..R.R..R.....RR...........RRR.........RR......
....R.R.......R.............RR.RR........R..R...R..R.R..RR...RR.R..........RRR
```
4)

```seed = 5
H = 66
W = 58
Number of pieces N = 90
Probability of a rose = 15
Number of roses = 543
...................R..R...................RR..R...R.....R.
....R.......................R..........R......R...........
....R.R...R..R.R........R...R......R..R..........R....R...
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...R............R.......R......R.....R.......R..R.......R.
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....................................R...........R...R...R.
..RR..........RR..R.................R............R......R.
```
5)

```seed = 6
H = 43
W = 42
Number of pieces N = 111
Probability of a rose = 74
Number of roses = 1368
R..RRRR.RRRR.R.RRRRR.RRRRRRRRRRRRRR...RR.R
RRR...RRRR..R.RRRRRRRR.RRRRR.R.RR.R.RRRRR.
RRRRRR.RRR.R..RRRRRR.R...R.R.RRRRRRRRRRRR.
RR.R.RR..RRR..RR..R.R.RRRRRRR...RRRRRRRRRR
.RRRRR.RRRR...RRRRRRRR.RRRRRRR.RRRRRRRR.R.
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R.RRRRRRRRRR.R.RR.RRRR.RR.RRRRRRRR.RR.RRR.
.RR.RRRRRR..RRR.R.RRRR.R.RRRRRRR..RRRRRRRR
RRR.RRRR..R.RR.RRRR.R.RR..RRRRR.RRRRRRRRRR
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RRRRRR..RRRRRR..RRRRRRRRRR..RRRRRRRRRRRRRR
.RR..RRRRRRRRRRR.RRRRR.RRRR.RRR.RRRRRRRRRR
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RRR.R.RRRRRRR.R.RRR.R.RRRR.RRRR.RR.RRRRRRR
RRRRR.RRRRRRRRRRRRRRRRRRRRR.RRRRRR.RRRRRRR
.R..RRR..R.RR.RR..R..RRRRRR..R.RR.RR.RR.RR
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.RR.RRRR...RRR..RRRRRRR.RRRRRRRRRR..RRRRR.
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.RR.R.R.RRRRRR.RRRRRRR.RRRRRRRR.RRRRR.RR.R
.R.RRRR.RR.RR.RR.RR.RR.R...R..RRRR.RRR.RRR
R.RRRRRRR.R.R.RRRRRRRR..R.RRR.RRR.RR.RRRRR
R.R.RR.RR.RRR..RR..R.RRR..R.RRRRRRR.R.RRRR
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.RRRRRRR.R.RRR.RRRRRR.R.R.RR.R.R.R.RR.RRRR
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.RR...R.RRRR..RRRRRR.RR.RRRRRR.R.RRRRR.RRR
RRR..R.RR.RRR.RR..R.R..RRRRRR.RRR..R.RR.RR
RRRRRRRRR..RRRRRR.R..RR.R...R.RRRR.RR.R.RR
R.RRR...RRR.RR.R.RRR..RR.R.RRRRRR.RRRRRRRR
.RRRRRRRRRR.RRRR.RRRRRR.RRR.R..RRRRRRRRRR.
RRR.R.RRRRRRRRR..R..R.RRRRRRR.R..RRRRRRRRR
.R.RR.RRR.RR.R.RRRR.RR.RR.RRR.RRR.R.RRRR.R
```
6)

```seed = 7
H = 44
W = 31
Number of pieces N = 40
Probability of a rose = 25
Number of roses = 339
R.....R......R.RR.R...RRR......
.......R.RR.RR.RR...RRR...R..RR
R.R......R...R..R........R.....
R........R....R....R.......R..R
.R....R....R.............R...RR
.....RR...R.R...RRRR.........R.
.R............R...R.R.....RRR.R
R.RRR...........R.RR....RR.R...
R.......R..R.......RRR..R....R.
....R..R.R..RRR..R.RR.....R.R..
.R..R.R........R.R..R.....R....
.......R.R..R....RR......R..R..
.R......R..R......R.R.R..R..R.R
...R...........R..........R.R..
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......R...R.R.......R.....R...R
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.......R.RRR....RRRR..R.R.RR.R.
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...R.R...R...R....R.......R..R.
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RR.RR...RR..R..RRR.....R....R..
..........R......R.RR.RRRRR....
.R...RR.....R...R.......R...R.R
....R........R.........R.......
```
7)

```seed = 8
H = 73
W = 60
Number of pieces N = 96
Probability of a rose = 64
Number of roses = 2779
R.RR.RRRRRRRR...RRR.RRRRR.RRR..RRRRRRR.RRRR....RRRRR..RRRR.R
RR..R.R.RR.RR.RR.R..R.R.RR.R.R.RRR.R.RR..RR.RRRR..R.RRRRR.RR
.RR.RR.RRR..R.RRRR....RRR.RRR..R..RR.R.R.RR.RRR.RRR...RRR.RR
RR.R.RRR....R.R.R.R.R.RRRRRRR.R......R.RRRRR.R..RR.RRRRRRR..
.R...RR..RRRRR.RRRRR.R.RR.RRRRRR.RRRRRRRRR.R..RRRRRRRR..RRR.
RR.RRRRRRRR.R.RRRRRR.R...R..R.R..R.RR.RR.RRRRRRR..RRRR.RRRR.
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RRR.RRR.RRRRRRR.R..RRRR.R.R..R.RRRRR.RRRRR.RRR.R.R...RRR..R.
R.RRRRRR..RRRRRRR.R.RRRRR.RRRRR.R....R.R..R.R...RR.RR.RRRRRR
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RRR.R..R.RR.R.RRR.RRRRRRRR.RRRR.RR....RRRRRR.R.RR..R.RR..R..
.RRRR.RR..R.R.RR..RRRRRR.RR..R.R.R..RR.RR...RRRRR.R.RRR..R.R
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.R.RRRRRRRRRR.....R..R..RR..RRRR..RRR..R.RR.RRR.RRRRRRRR....
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RR.RRRRRR.....RR...RRRRRRR.RR.RR.R..R..RRRRRR..R.RRRRRRR....
R.RRR.R.RR..R.RRRR.RRRRR...R.R.R.R.RRRR.RRRRR.RR.RR..RRRRR.R
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R.R.R....R..R.......R.RRR...RRRRR.R.RRR..RRRRRR.R..R.R..RRR.
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R....RR.RRRR.R.RRRRRR..RRRR.RR.RR.RR.RR..R..RRRRR.R.R.RR.R.R
RRRRR.RRRR..RRRR.RRR...R.RRRRR...R..RR.RRRR..R.RR..RR.R.R...
.RRR..R.RRR..R.RR.RRRRR..RRRRRRRRR..RR.RRRRR.R.RRRR..R.RR.R.
RRR.R.R..R.RRR.RRRR.RRR..R.RRRRRR...RR...RRRRRR..R.RRRRRRRRR
.RR.RR.R.RR.R..RR.R.R.R....R.RRRR..R...R.....R...RRRRRRRR.R.
R.RRRR.RRR.RRR..RR....RRRRRRR..RRRR....RRRRRR.RRR.R.R.R.R.RR
RRRR..RRRRRRRRR.R.RR..R.R.R..R.RRRR.R.RR..RRRR.RRRRRR....RR.
.R.R...RR.R.RRRR.RR.R.R..RR..RR.RRRRR.RR.R..R..RRRRRRR.RRRRR
.RRRR.R....RRRRRR...R.R.R.R....RR....R.RR.RR.RRRRRRRR.R..R..
RRRRRRR.RRR.R.RR.RRRRRRRRRRRRRR.RRR.RR.RR.RR.RRRR.RRR.RRR.RR
R.RRRRRRRRR..RRRRRRRR.RRR..RRR.RR.RR.R...R.RRRRRR.RR.RR.R.R.
RRRRRRRR.RRRRRRRRRRRRRRR.......RRRRR.R.R..RR.RR..RRRR.RRRRRR
..RRRRRR.RR.R..R.RRRRR..RR.R....R.R.RRRR.RRRR..R.RRRRRRR..RR
RR.RRR.RR..R.R.RR..RRRRR.RRRR.RRRRRRRRRR..RR..R.RRRR.R.R.RRR
RRRR.R.RR.RRRR.R.RR.RRR..R.RRRRR.RR.R.RR.RRRRR...R..R.R..RR.
...RR.RRR.RR.R..RRRRRRR.R...RRRR.R.RRRRRRRRRR.R.RR.RR.R..R.R
.R.RRR...RRR..R..RR.R....RR..RRRR.R.RRRRRR..R..R.RRRRR.RRRR.
.RRRR.RR.RRRRRR.RRRRR.R.RR.RR.R..RRRR.RR...R.RR.R..RRRRRRRR.
RRR..RR.R.RR.RRRR.RRRRRRRRRRRRR.RRRRRR.RR.RRRR....RR.RRRRRRR
RR.R..RRR.R.RR.RR.RRR.R..RRRR.R.R.R.RR.RR.R.RRRR.R.RR...R..R
..RRRR....R.R.R..RR.RRR..RR...RRR.R..R.R.RR.RRRRR..RRRR.RRRR
```
8)

```seed = 9
H = 76
W = 40
Number of pieces N = 146
Probability of a rose = 32
Number of roses = 998
R...R.....R......RR.R..R.RR....R.R.R....
..RRR.R..R....RR.RR...R.R..RRR..........
...R...R...R.......RRRR...R.R....R..R.R.
R..R.RRR..R.R........RR.RR..RR...RR...R.
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...R.R...R....R..R........R.....R.....R.
.R..RRR.R.....R...R.R.......R.R.RR......
RR.RRR.R.R...........RR.R..RR......RRRR.
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.....R..RR....RR...R...R..R...R.RR..R..R
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..RR..RR........RR..RR..R...R..R.R......
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....RR.R.R..R.RR.R..........R..RRR....R.
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.....R....R.R.RR..RR..R.......R..R.R..R.
R.....RRR.......RR....RRR...R.R..RRR....
.R..RR..RR..R....RRRR...R.R............R
R......................R..R.....R.RR.RRR
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R.R..............RRRR..R......RRR..RRRR.
....RR.R..R....RR.R.R...R..RR.RRR.......
.R..R.RR..RRR..R..........RRR..RRR..RRR.
....RR....RR.....R.R.RRR..R....RR.RR....
.R........RR...RRRRR.R.RR.RRRR.R.RRR.RR.
.RR...R..R...R.....R..R.RR...R..RRRRR..R
...R..R..R..R...RR....RR.....R......R.R.
.R......R.....R.....R.R.....R....R.R....
..R...RR....RR..R.R...R......RR.R.R..R..
.....R.....RR...RR.RR.R....R.........R..
..............R...R....RRR...RR.....RR..
...R......R.R...R..R..RR....RRR......RR.
.........R.RR...R.RR..R.R.......RR.R.R..
..RRRRRR.R.R.......R...RR..R.....RRR....
...RR..........R.R........RR.RR..RR...R.
RR.R...R.RRRRRR.RRR.R....R...R.......R..
....RR..R..RR.R..R....R.R.R......R...R.R
...R............RRR...R....R.RR...R.....
....R...R..RR.R...R.R..R.......R.R.RR...
.....RRRRRR...RRRRRR.......R..R..RR.R.RR
...R.R.R.RR..R......R.R.RR...RR.........
..R.R....R..R.....RR..R.R.....R..RR...R.
R.R..RR..R..R.R..RR......RRRRR....RR.R..
R........RR..R.R....R...RR.....RRRRR.R.R
R.RR......RR.RR.....RR.R.R...RR.RR.R..R.
..R.R..R..R..RR..R.R.RRRR.....R..RRRRR..
..RR.....R.R....RRRR...RR.RR.....R....R.
R.......R......RRR.....R...R.RR.R.....RR
R.......RR...R.R........R.R..RR.....R.R.
.R...R...R.R..R.R...R..RRR....R.R.......
...R..R....R...RRR...R...RR..R.R..R.R.RR
.R.....RRR..R...R.....RRRR..R.....R...R.
RR.R.....R...R.....RR.R...RR...R..RR..R.
.RR.......R.RR..RRR..R...R....R.......RR
.RR......RR..RR..R..R......R...RR.......
......R...R.R....RR......R.......RR.....
.R...R.R...R..RR.R....R.......R.R.......
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RR.R.R.R..R.RR...RR..RR.R.....R...RRRRR.
.R....R....R...RR..R..R...RR.R.......RR.
```
9)

```seed = 10
H = 14
W = 63
Number of pieces N = 95
Probability of a rose = 73
Number of roses = 650
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