(Apr 23, 2015) /questions/80674/better-method-to-swap-the-values-of-two-2-d-arrays/80680#80680. begingroup An algorithm for generating even-order magic squares due to Collison is presented here if you have MATLAB, you can try to find the file magic.m. An n-by-n magic square is an array containing the integers from 1 to n2, arranged so that each of the rows, each of the columns, and the two principal diagonals have the same sum. "Answer to 'Better Method to Swap the Values of Two 2-D Arrays'." Mathematica Stack Exchange. Moler, Experiments with MATLAB, MathWorks, Inc., 2011 pp. Swap the values of at and with the corresponding values of. Then the block matrix (with the first swap colored) isġ. Swap the values of at with the corresponding values of. Swap the values of at, , and with the corresponding values of. Where is a magic square of order, ,, and. If N is the order, then N x N different numbers are used to. The ‘order’ is the number of rows and columns, so a magic square of order 4 means it has 4 rows and 4 columns.
includeIf is singly even, then is odd, and a magic square of order can be constructed from four copies of the magic square of order. A magic square is a square array of numbers with the property that the sum of the numbers in each row, column and diagonal is the same, known as the magic sum. Description A 3x3 magic square is a 3x3 grid of the numbers 1-9 such that. The elements in where is True are reversed that is, at such a position with value, the new value is. One way to generate a magic square when n is odd is to assign the integers 1 to n2 in ascending order, starting at the bottom, middle cell. The elements in where is False are left alone. A magic squares is an n-by-n matrix of the integers 1 to n2, such that all row, column, and diagonal sums are equal. Given, convert it into a magic square at minimal cost. We can convert any digit to any other digit in the range at cost of.
You will be given a matrix of integers in the inclusive range. The elements in where is False are left alone, and the elements in where is True are reversed that is, the value at a True position is replaced with. We define a magic square to be an matrix of distinct positive integers from to where the sum of any row, column, or diagonal of length is always equal to the same number: the magic constant. here, " " is the equal operation yielding True or False component-wise, so that is a matrix of Boolean values.ĭefine to be a matrix of the integers from 1 to, stored sequentially in rows.
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