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Test For Wondrous Square (Magic Square)

ISC 2005 Computer Science Practical, Question 2 · Arrays and matrices

The question

A wondrous square is an n by n grid which fulfills the following conditions: (i) It contains integers from 1 to n^2, where each integer appears only once. (ii) The sum of integers in any row or column must add up to 0.5 * n * (n^2 + 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 <-- 15 is not a prime

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
3       0               1
3       1               0
2       1               1

Question: ISC 2005 Computer Science Paper 2 (Practical), Question 2, set by the Council for the Indian School Certificate Examinations (CISCE). Solution and video: Vinay Singh.

Java solution

ISC2005Q2.java Download GitHub

import java.util.*;

class Square {
    private int a[][], N, sum;

    public Square(int a[][]) {
        this.a = a;
        this.N = a.length;
        sum = (int)(0.5 * N * (N*N+1));
    }
    public boolean isWondrousSquare(){
        boolean flag[] = new boolean[N*N];
        int sumOfRows, sumOfCols;
        for (int row = 0; row < N; row++) {
            sumOfRows= sumOfCols=0;
            for (int col = 0; col < N; col++) {
                sumOfRows += a[row][col];
                sumOfCols += a[col][row];
                if( flag[a[row][col] -1 ] ) return false;
                flag[a[row][col] -1 ] = true;
            }
            if( sumOfRows!=sum || sumOfCols!=sum) return false;
        }
        return true;
    }
    public String toString(){
        String output="PRIME\tROW INDEX\tCOLUMN INDEX\n";
        for (int row = 0; row < N; row++) {
            for (int col = 0; col < N; col++) {
                if(isPrime(a[row][col])){
                    output+=a[row][col]+"\t"+row+"\t\t"+col+"\n";
                }
            }
        }
        return output;
    }
    private static boolean isPrime(int n){
        if(n<2) return false;
        else if(n==2) return true;
        else if(n%2==0) return false;
        else{
            int limit=(int)Math.sqrt(n);
            for( int i = 3; i<=limit; i+=2){
                if(n%i==0) return false;
            }
        }
        return true;
    }
}

public class ISC2005Q2 {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        System.out.print("INPUT:\nN = ");
        int N = in.nextInt();
        int a[][] = new int[N][N];
        for (int row = 0; row < N; row++) {
            for (int col = 0; col < N; col++) {
                a[row][col] = in.nextInt();
            }
        }
        Square sq = new Square(a);

        System.out.println("OUPUT:");
        if (sq.isWondrousSquare()) {
            System.out.println("YES IT REPRESENTS A WONDROUS SQUARE.");
        } else {
            System.out.println("NOT A WONDROUS SQUARE.");
        }
        System.out.println(sq);
        in.close();
    }
}

Test For Wondrous Square (Magic Square)

The question

Java solution

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