Task 2 was revealed 1.4.2025 at 18:00 CET
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Available from 01.04.2025 18:00 CET until 02.04.2025 17:59 CET - You can get 2 points
There is a two-dimensional array with N rows and M columns. The array defines a surface of sphere, so the [0] column is next to the [1] and the [M-1] columns, like the rows also (the [0] row is next to the [1] and the [N-1] rows). This array defines the Universe. Values at the array are separated with SPACE (what else could be the separator, then the SPACE character ) and 0 <= values < 10.
Calculate the stability of the Universe like this:
- search for local maximum points, where the local maximum is the P point, because the value at the P point is bigger than every other 16 values around the P point based on the next pattern. A gravitational center will be the P point. The other 8 values around the P point will be 0.
|
x2’ |
0 |
a2 |
0 |
y2 |
|
0 |
x1’ |
a1 |
y1 |
0 |
|
b2’ |
b1’ |
P |
b1 |
b2 |
|
0 |
y1’ |
a1’ |
x1 |
0 |
|
y2’ |
0 |
a2’ |
0 |
x2 |
- each center of gravity is clearly separated from the others
- the value of P will be bigger, not bigger or equal, than the other 16 values
- calculate the stability of each gravitational center, where the P point (as a gravitational center) is in stability when numbers are in balance around the P point:
- the values on the [a,b,x,y] axes are located symmetrically around the point P exactly at the center (a: vertical, b: horizontal, x: diagonal, y: the other diagonal)
- values are symmetrical when the st values are equal with the st’ values, where s∈a,b,x,y
and t ∈{1,2}
(fe.: a1=a1’ and a2=a2’ and … y2=y2’) - stability needs to be checked on all axes [a,b,x,y]
- the numbers can be (most of the time will be) different on any two axes
- in case of Example #1: around the value 8: axis a has value 3 and 1; axis y has value 4 and 1, and the numbers are in symmetry around the value 8
- a gravitational center (P point) is unstable when any proper pair of the numbers on any axis from [a,b,x,y] are not equal around the P point (fe.: a1!=a1’ or a2!=a2’ or … y2!=y2’)
- count the stable and unstable gravitational centers: after you found all gravitational centers, and you decided about a gravitational center is in balance or not, the questions are:
- How many gravitational centers are stable, and
- How many gravitational centers are unstable
- stability of the Universe can be described with the numbers of stable and unstable gravitational centers
Input: a file with a grid representing a Universe. At the first line two numbers will be separated with a SPACE, as the dimension of grid. Fe.: “200 200” or like the example file below, “8 12”. After that as many rows and columns as defined, values separated with SPACE also. The Universe is zero filled. The file doesn’t contain empty lines between two lines of the universe and no empty line after the definition of the grid size.
Example input file:
8 12
4 0 0 3 0 2 0 3 0 0 4 3
0 2 0 0 5 3 5 0 0 1 0 1
0 0 0 1 2 7 2 1 0 0 0 0
0 0 0 0 5 3 5 0 0 0 0 0
0 0 0 3 0 2 0 3 0 0 0 0
0 1 0 0 0 0 0 0 0 2 0 1
4 0 0 0 0 0 0 0 0 0 4 3
6 3 0 0 0 0 0 0 0 3 6 8
Output: Two separated (with a SPACE) numbers. The first is the number of stable center points and the second is the amount of unstable center points.
Example #1: this universe has two gravitational centers, and both are stable. The brown 7 and the blue 8 are the local maximums according to the pattern above with the four axes. Numbers around the center points are the same on any axes and any in any distance.
|
4 |
0 |
0 |
3 |
0 |
2 |
0 |
3 |
0 |
0 |
4 |
3 |
|
0 |
2 |
0 |
0 |
5 |
3 |
5 |
0 |
0 |
1 |
0 |
1 |
|
0 |
0 |
0 |
1 |
2 |
7 |
2 |
1 |
0 |
0 |
0 |
0 |
|
0 |
0 |
0 |
0 |
5 |
3 |
5 |
0 |
0 |
0 |
0 |
0 |
|
0 |
0 |
0 |
3 |
0 |
2 |
0 |
3 |
0 |
0 |
0 |
0 |
|
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2 |
0 |
1 |
|
4 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
4 |
3 |
|
6 |
3 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
3 |
6 |
8 |
The result should like: 2 0
Example #2: this universe has two gravitational centers also, one stable and one unstable center point.
|
4 |
0 |
0 |
3 |
0 |
2 |
0 |
3 |
0 |
0 |
4 |
3 |
|
0 |
2 |
0 |
0 |
5 |
3 |
5 |
0 |
0 |
1 |
0 |
1 |
|
0 |
0 |
0 |
1 |
2 |
7 |
2 |
1 |
0 |
0 |
0 |
0 |
|
0 |
0 |
0 |
0 |
5 |
3 |
5 |
0 |
0 |
0 |
0 |
0 |
|
0 |
0 |
0 |
1 |
0 |
2 |
0 |
3 |
0 |
0 |
0 |
0 |
|
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2 |
0 |
1 |
|
4 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
4 |
3 |
|
6 |
3 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
3 |
6 |
8 |
The diagonal line with red values is not in balance around this center point. Red values are not equal, this diagonal axis is not in balance, so the center point (with value 7) is not in balance.
The result should like: 1 1
There is 1 input file. The grid size is 200x200. It will contain some gravity centers. The separator is the SPACE, and the grid is zero filled.
Your task:
Read input file and into the field with the answer, enter:
- the resulting values
- at the end paste the source code of your program.
Click here to download CGW Task 2 Input file
! You only have one chance to submit your answer, resubmission is not possible.
Answer:
Click here to download Answer to Task 2
Scoring system:
|
Points for |
Correct answer |
Country |
Source Code |
|
Round 1 |
1 |
1 |
1 |
|
Round 2 |
2 |
1 |
1 |
|
Round 3 |
3 |
1 |
1 |
|
Round 4 |
4 |
1 |
1 |
|
Round 5 |
5 |
1 |
1 |
|
Bonus points for |
Quick and correct answer |
||||||||
|
Round 1 |
5 |
4 |
3 |
2 |
1 |
||||
|
Round 2 |
6 |
5 |
4 |
3 |
2 |
1 |
|||
|
Round 3 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
||
|
Round 4 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
|
|
Round 5 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |