Merge pull request algorithm-visualizer#198 from archie94/magic-square

Implementation of Magic Square

Author: Raghav Dua

algorithm/category.json

@@ -106,8 +106,9 @@
    "etc": {
       "list": {
          "flood_fill": "Flood Fill",
-	 "cellular_automata": "Cellular Automata",
-         "create_maze": "Create Maze"
+         "cellular_automata": "Cellular Automata",
+         "create_maze": "Create Maze",
+         "magic_square": "Magic Square"
       },
       "name": "Uncategorized"
    }

algorithm/etc/magic_square/basic/code.js

@@ -0,0 +1,41 @@
+var i = Math.floor (n/2);
+var j = n-1;
+
+for ( var num = 1; num <= n*n; ) {
+	logTracer._print ( 'i = ' + i );
+	logTracer._print ( 'j = ' + j );
+
+	if( i == -1 && j == n ) {
+		j = n - 2;
+		i = 0;
+
+		logTracer._print ( 'Changing : ' );
+		logTracer._print ( 'i = ' + i );
+		logTracer._print ( 'j = ' + j );
+	} else {
+		if ( j == n ) {
+			j = 0;
+			logTracer._print ( 'Changing : ' + 'j = ' + j);
+		}
+		if ( i < 0 ) {
+			i = n-1;
+			logTracer._print ( 'Changing : ' + 'i = ' + i );
+		}
+	}
+
+	if ( A[i][j] > 0 ) {
+		logTracer._print ( ' Cell already filled : Changing ' + ' i = ' + i + ' j = ' + j );
+		j -= 2;
+		i++;
+		continue;
+	} else {
+		A[i][j] = num++;
+		tracer._notify( i, j, A[i][j] )._wait ();
+		tracer._denotify ( i, j );
+		tracer._select ( i, j )._wait ();
+	}
+	j++;
+	i--;
+}
+
+logTracer._print ( 'Magic Constant is ' + n*(n*n+1)/2 );

algorithm/etc/magic_square/basic/data.js

@@ -0,0 +1,14 @@
+var n = 7;
+var A = new Array (n);
+for (var i = n - 1; i >= 0; i--) {
+	A[i] = new Array (n);
+}
+
+for ( var i = n -1; i >= 0; i-- ) {
+	for ( var j = n - 1; j >= 0; j-- ) {
+		A[i][j] = 0;
+	}
+}
+
+var tracer = new Array2DTracer ('Magic Square')._setData(A);
+var logTracer = new LogTracer ( 'Console' );

algorithm/etc/magic_square/desc.json

@@ -0,0 +1,13 @@
+{
+  "Magic Square": "In recreational mathematics, a magic square is an arrangement of distinct numbers (i.e., each number is used once), usually integers, in a square grid, where the numbers in each row, and in each column, and the numbers in the main and secondary diagonals, all add up to the same number, called the magic constant. A magic square has the same number of rows as it has columns, and in conventional math notation, 'n' stands for the number of rows (and columns) it has. Thus, a magic square always contains n2 numbers, and its size (the number of rows [and columns] it has) is described as being of order n. A magic square that contains the integers from 1 to n2 is called a normal magic square. (The term magic square is also sometimes used to refer to any of various types of word squares.)",
+  "Complexity": {
+    "time": " O(N<sup>2</sup>)",
+    "space": "O(N<sup>2</sup>)"
+  },
+  "References": [
+    "<a href='https://en.wikipedia.org/wiki/Magic_square'>Wikipedia</a>"
+  ],
+  "files": {
+    "basic": "Magic Square"
+  }
+}