Magic square java source code
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We have i as the counter for the outer loop and jas the counter for the inner loop. I find it simplest to never use them rather than to find the narrow circumstances where it will work. Here is the 5x5 square that you get if you follow this method: 11 18 25 2 9 10 12 19 21 3 4 6 13 20 22 23 5 7 14 16 17 24 1 8 15 Write a program whose input is the number n and whose output is the magic square of order n if n is odd. This method can be extended to 3 dimension to construct magic cubes. Doubly Even Magic Cube The logic to create magic cube can be extended from following magic square 1 15 14 4 12 6 7 9 8 10 11 5 13 3 2 16 The above magic square can be created in following manner.

Using the above magic square as an example, we can say that number 2 is on row 0 column 0, and number 3 is on row 2 column 1. Notice that we use a nested for loop to do this. We use a boolean variable called magic as a flag and set its initial value to true On line 7, we declare a 2D array called square, and allocate spaces for 3 rows and 3 columns in it. So with the current input, the statements on lines 41-49, 54-60, and 65-72 are skipped. I could have the magic square full of 5's, and that would pass. .

And of course, the sum of numbers in these cells equals to 15, and therefore, line 71 is skipped, and the value of magic remains the same. Start filling the square from top left hand corner. A magic square adds up the values in each vertical, horizontal, and diagonal row to the same value. Not every square grid of numbers is a magic square, only when it satisfies this rule. Lets trace this block using the first input and start with the first outer cycle, which is when i is 0. Therefore, the next statement is executed, and the value of magic now is false.

Regarding magic squares, you have to validate that the elements are distinct. Obviously, lines 64-73 contain statements that calculate the sum of numbers on the second diagonal. A magic square is an NxN square matrix whose numbers usually integers consist of consecutive numbers arranged so that the sum of each row and column, and both long main diagonals are equal to the same sum which is called the magic number or magic constant. A magic square can be composed of 9 numbers 3 by 3 grid , 16 numbers 4 by 4 , and so on, as long as they form a square, obviously! Have a look at the link and see if anything leaps out at you. Since 15 is not equal to 6, the value of this condition is true. } This is just the high-level code.

One thing do is reformat your code so that it's properly aligned and indented. Keep it short if sum! I prefer to put the { on the same line as its control statement. Use MathJax to format equations. If not possible, follow these steps. See last column of version before moved to the top row. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. The same process goes on until both iand j reached the value of 2.

The next block of statements lines 29-37 is where we calculate the sum of each of the rest of the rows, and check whether the result is the same as the reference value, which is 6. For example, if I put in the number 3 as the odd number, my output is: 6 1 0 3 4 5 9 7 8 0 isn't supposed to be there but the number two is. Any move will be wrapped around like pac man or train tunnel in Matrix. On line 76 when the value is tested again, line 79 is executed to display the conclusion, that is, these numbers do not form a magic square. At the end of the nested loop, the contents of the square array is illustrated as below: On lines 25 and 26, the sum of the numbers in the first row is calculated. Please use code tags when posting code:. Notice that the sum of row index and column index of each of these cells are the same, which is 2? The same goes for the sum of each column, 2+9+4, 7+5+3, and 6+1+8 , and each diagonal 2+5+8 and 6+5+4.

Creating methods helps to isolate logic, which hopefully makes things clearer for you and also makes things easier to test. This is shown in Figure 7-32. The position of next number is calculated by decrementing row number of previous number by 1, and incrementing the column number of previous number by 1. In order to determine whether it is a magic square, we need to calculate the sum of each row, column, and diagonal, and check whether they are all the same. And here's the code that does it. This time however, we use the column index as the counter for the outer loop, and the row index as the counter for the inner loop.

It is then later overwritten by the value 5. So, good luck on your problem. Place an order with our service and get qualified help as soon as needed. Remember that we set the initial value of magic to true, and so far this value has not changed. A magic square whose rows and columns add up to a magic number but whose main diagonals do not, is known as a semimagic square.