Array2D - MagicSquare
A magic square is an arrangement of numbers (usually integers)
in a square grid, where the numbers in each row, and in each
column, and the numbers in the forward and backward main
diagonals, all add up to the same number. A magic square has
the same number of rows as it has columns.
You will need to complete the class MagicSquare below to
determine if a grid of numbers satisfies the conditions of a magic
square.
/***
* Determines if an arrangement of numbers in a square grid is a magic square.
* The numbers in each row, and in each column, and the numbers in the forward
* and backward main diagonals, all add up to the same number.
***/
public class MagicSquare
{
private int[][] grid;
public MagicSquare(int[][] g) {
grid = g;
}
/**
* find the sum of a given row
*/
public int rowSum(int row) {
// <<< Complete the code >>>
}
/**
* find the sum of a given column
*/
public int colSum(int col) {
// <<< Complete the code >>>
}
/**
* returns the sum in the "up" diagonal (from the lower left to the upper right)
*/
public int upDiagSum() {
// <<< Complete the code >>>
}
/**
* returns the sum in the "down" diagonal (from the upper left to the lower right)
*/
public int downDiagSum() {
// <<< Complete the code >>>
}
/**
* determines if the sum all rows, columns, and main diagonals are equal
*/
public boolean isMagicSquare() {
// <<< Complete the code >>>
}
/***
* prints the grid - this method is complete
*/
public void printGrid() {
for (int row = 0; row < grid.length; row++) {
for(int col = 0; col < grid[0].length; col++) {
System.out.print(grid[row][col] + "\t");
}
System.out.println("");
}
}
/***
* The main method is complete - it tests out the above methods.
*
* expected output:
*
*8 1
6
*3 5
7
*4 9
2
* Magic Square: true
*
*2 1
6
*3 5
7
*4 9
8
* Magic Square: false
*
*1 2
3
4
*5 6
7
8
* 9 10
11
12
* 13 14
15
16
* Magic Square: false
*
* 7 12
1
14
* 2 13
8
11
* 16 3
10
5
*9 6
15
4
* Magic Square: true
*
* 6 32
3
34
35
1
* 7 11
27
28
8
30
* 19 14
16
15
23
24
* 18 20
22
21
17
13
* 25 29
10
9
26
12
* 36 5
33
4
2
31
* Magic Square: true
*
* 6 32
2
34
35
1
* 7 11
27
28
8
30
* 19 14
16
15
23
24
* 18 20
22
21
17
13
* 25 29
10
9
26
12
* 36 5
33
4
3
31
* Magic Square: false
*
* 8 58
59
5
4
62
63
1
* 49 15
14
52
53
11
10
56
* 41 23
22
44
45
19
18
48
* 32 34
35
29
28
38
39
25
* 40 26
27
37
36
30
31
33
* 17 47
46
20
21
43
42
24
* 9 55
54
12
13
51
50
16
* 64 2
3
61
60
6
7
57
* Magic Square: true
*
* 8 58
59
5
4
62
63
1
* 49 15
14
52
53
11
10
56
* 41 23
22
44
45
19
18
48
* 32 34
35
29
28
38
39
25
* 40 26
27
37
36
30
31
33
* 17 47
46
20
21
43
42
57
* 9 55
54
12
13
51
50
16
* 64 2
3
61
60
6
7
24
* Magic Square: false
*
*/
public static void main(String[] args) {
MagicSquare m0 = new MagicSquare( new int[][] {{8,1,6},{3,5,7},{4,9,2}});
m0.printGrid();
System.out.println("Magic Square: " + m0.isMagicSquare() + "\n");
MagicSquare m1 = new MagicSquare( new int[][] {{2,1,6},{3,5,7},{4,9,8}});
m1.printGrid();
System.out.println("Magic Square: " + m1.isMagicSquare() + "\n");
MagicSquare m2 = new MagicSquare( new int[][] {{1,2,3,4},{5,6,7,8},{9,10,11,12},{13,14,15,16}});
m2.printGrid();
System.out.println("Magic Square: " + m2.isMagicSquare() + "\n");
MagicSquare m3 = new MagicSquare( new int[][] {{7,12,1,14},{2,13,8,11},{16,3,10,5},{9,6,15,4}});
m3.printGrid();
System.out.println("Magic Square: " + m3.isMagicSquare() + "\n");
MagicSquare m4 = new MagicSquare( new int[][] {{6,32,3,34,35,1}, {7,11,27,28,8,30},
{19,14,16,15,23,24},
{18,20,22,21,17,13}, {25,29,10,9,26,12}, {36,5,33,4,2,31}});
m4.printGrid();
System.out.println("Magic Square: " + m4.isMagicSquare() + "\n");
MagicSquare m5 = new MagicSquare( new int[][] {{6,32,2,34,35,1}, {7,11,27,28,8,30},
{19,14,16,15,23,24},
{18,20,22,21,17,13}, {25,29,10,9,26,12}, {36,5,33,4,3,31}});
m5.printGrid();
System.out.println("Magic Square: " + m5.isMagicSquare() + "\n");
MagicSquare m6 = new MagicSquare( new int[][] {{8,58,59,5,4,62,63,1}, {49, 15, 14, 52, 53, 11, 10,
56},
{41, 23, 22, 44, 45, 19, 18, 48}, {32, 34, 35, 29, 28, 38, 39, 25},
{40, 26, 27, 37, 36, 30, 31, 33}, {17, 47, 46, 20, 21, 43, 42, 24},
{9, 55, 54, 12, 13, 51, 50, 16}, {64, 2, 3, 61, 60, 6, 7, 57 }});
m6.printGrid();
System.out.println("Magic Square: " + m6.isMagicSquare() + "\n");
MagicSquare m7 = new MagicSquare( new int[][] {{8,58,59,5,4,62,63,1}, {49, 15, 14, 52, 53, 11, 10,
56},
{41, 23, 22, 44, 45, 19, 18, 48}, {32, 34, 35, 29, 28, 38, 39, 25},
{40, 26, 27, 37, 36, 30, 31, 33}, {17, 47, 46, 20, 21, 43, 42, 57},
{9, 55, 54, 12, 13, 51, 50, 16}, {64, 2, 3, 61, 60, 6, 7, 24 }});
m7.printGrid();
System.out.println("Magic Square: " + m7.isMagicSquare() + "\n");
}
}