"Informatics Stars" Online Contests - 2011-2014 |
Start: Oct.20.2012 at 10:00:00 AM
Finish: Oct.20.2012 at 03:00:00 PM
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Time limit 2000/4000/4000/4000 ms. Memory limit 65000/65000/65000/65000 Kb.
Prepared by Ibrahim Mesecan.
Min Max Normalization
Shqip
In a usage in statistics, when having data examples coming from different sources, in order to be able compare them,
they are needed to be normalized . This opeation refers to putting all the data to a common scale in
order to negate that variable's effect on the resulting data, thus allowing underlying characteristics of the data
sets to be compared. This allows data on different scales to be compared, by bringing them all to a common scale.
There are various normalization methods in statistics: Standard score normalization, Student's t-statistic,
nondimensional ratios of errors, residuals, means and standard deviations, etc.
The Min Max normalization is also used frequently. In this method min and max of every sample are found first, then, that sample
is scaled with the new range according to the following formula:
(b-a)*(x - min)
f(x) = -------------- + a
max - min
where a and b are the min and max of the new range; x is the current value of
the data set which is going to be converted to; min and max are the min
and max of this data set.
e.g. If we have the data: 5 3 9 7; and we want it to normalize it
to the new range 1...4.
min of the sample data is 3
max of the sample data is 9
a (min of the new range) is 1
b (max of the new range) is 4
The element value that we will convert: x (the first element of data series) is 5
Then 5 (the first element of the data series) can be converted with the following formula:
(4-1)*(5 - 3)
f(5) = -------------- + 1 = 2
9 - 3
After normalizing all the elements the new data series will be: 2 1 4 3;
Question
Write a program that is going to read a two dimensinal array, and it will normalize all data to the given scale.
(All the rows will be normalized independently to the given scale.)
Input specification
The first line contains four numbers m, n, a, b.
m is (integer) the length of the input array where 1 ≤ m ≤ 25,
n is (integer) the height of the input array where 1 ≤ n ≤ 3000,
a, b are (floating point numbers) the min and max of the new range where -10000 ≤ a, b ≤ 10000)).
Starting from the second line, we will have m numbers in the following n lines representing the input data.
The values stored in the input array A[n][m] will be integers in the range from -150000 to +150000,
Output specification
Give the normalized array m numbers in n lines in the same order as the input data. Each number in the line will be separated
by a space. Output numbers' data type will be double with at most 3 digit precision.
When calculating the 3 digit precision, the 4th digit will be rounded (up or down) to the third digit.
Sample Run
Sample Input 1
| Sample Output 1
| |
4 5 1 10
1 0 2 3
8 4 7 5
2 0 3 2
5 5 3 2
5 4 5 5
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4 1 7 10
10 1 7.75 3.25
7 1 10 7
10 10 4 1
10 1 10 10
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Sample Input 2
Sample Output 2
3 6 0 1
5 4 1
5 9 6
-3 -3 0
8 3 6
13 11 12
4 6 10
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1 0.75 0
0 1 0.25
0 0 1
1 0 0.6
1 0 0.5
0 0.333 1
| | |
Для отправки решений необходимо выполнить вход.
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