A wondrous square is an n by n grid which fulfills the following conditions:
(i) It contains integers from 1 to n2, where each integer appears only once.
(ii) The sum of integers in any row or column must add up to 0.5 x n x (n2 + 1).
For example the following grid is a wondrous square where the sum of each row or column is 65 when n = 5:
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9
Write a program to read n (2 < n < 10) and the values stored in these n by n cells and output if the grid represents a wondrous square or not.
Also output all the prime numbers in the grid along with their row index and column index as shown in the output. A natural number is said to be prime if it has exactly two divisors. E.g. 2,3,5,7,11 ………..
The first element of the given grid i.e 17 is stored at row index 0 and column index 0 and the next element in the row i.e. 24 is stored at row index 0 and column index 1.
Test your program for the following data and some random data.
SAMPLE DATA:
INPUT:
N = 4
16 15 1 2
6 4 10 14
9 8 12 5
3 7 11 13
OUTPUT:
YES IT REPRESENTS A WONDROUS SQUARE.
PRIME ROW INDEX COLUMN INDEX
2 0 3
3 3 0
5 2 3
7 3 1
11 3 2
13 3 3
15 0 1
INPUT:
N = 3
1 2 4
3 7 5
8 9 6
OUTPUT:
NOT A WONDROUS SQUARE.
PRIME ROW INDEX COLUMN INDEX
2 0 1
3 1 0
5 1 2
7 1 1
INPUT:
N = 2
2 3
3 2
OUTPUT:
NOT A WONDROUS SQUARE.
PRIME ROW INDEX COLUMN INDEX
2 0 0
2 1 1
import java.io.*;
public class wondrous
{
public static void main()throws IOException
{
BufferedReader br=new BufferedReader(new
InputStreamReader(System.in));
System.out.println("enter the number of rows and colomn");
int n=Integer.parseInt(br.readLine());
System.out.println("enter the numbers");
int arr[][]=new int[n][n];
for(int i=0;i<n;i++)
{
for(int j=0;j<n;j++)
{
arr[i][j]=Integer.parseInt(br.readLine());
}
}
int r[]=new int[n];
int c[]=new int[n];
int co=0;
int x=(n/2)*((n*n)+1);
for(int i=0;i<n;i++)
{
for(int j=0;j<n;j++)
{
r[j]=arr[i][j];
c[j]=arr[j][i];
}
if(sumr(r)!=x && sumc(c)!=x)
{
System.out.println("not wondrous");
break;
}
co++;
}
if(co==n)
{
System.out.println("wondrous");
}
System.out.println("prime \t row \t column");
for(int i=0;i<n;i++)
{
for(int j=0;j<n;j++)
{
if(prime(arr[i][j])==1)
{
System.out.println(arr[i][j]+"\t"+i+"\t"+j+"\t");
}
}
}
}
public static int sumr(int arr[])
{
int s=0;
for(int i=0;i<arr.length;i++)
{
s+=arr[i];
}
return s;
}
public static int sumc(int arr[])
{
int s=0;
for(int i=0;i<arr.length;i++)
{
s+=arr[i];
}
return s;
}
public static int prime(int n)
{
int h=0;
for(int i=1;i<=n;i++)
{
if(n%i==0)
{
h++;
}
}
if(h==2)
{
return 1;
}
else
{
return 0;
}
}
}
