Added N-Queens solution (#63)

* Add N-Queens solution

* Update N_Queens.input

---------

Co-authored-by: Kostis Sagonas <kostis@cs.ntua.gr>

Author: marwterzi

dana/programs/N_Queens.dana

@@ -0,0 +1,101 @@
+def main
+
+    def printBoard: board as byte[][], n as int
+        var i j is int
+        i := 0
+        loop:
+            if i >= n : 
+                break
+            j := 0
+            loop:
+                if j >= n :  
+                    break
+                if board[i][j] = 1 :  
+                    writeString: "Q "
+                else :
+                    writeString: ". "
+                j := j + 1
+            writeString: "\n"
+            i := i + 1
+        writeString: "\n"
+
+    def isSafe is byte: board as byte[][], row col n as int
+        var i j is int
+
+        # check columns
+        i := 0
+        loop:
+            if i >= row :  
+                break
+            if board[i][col] = 1 :  
+                return : 0  
+            i := i + 1
+
+        # check left diagonal
+        i := row - 1
+        j := col - 1
+        loop:
+            if i < 0 or j < 0 :  
+                break
+            if board[i][j] = 1 :  
+                return : 0
+            i := i - 1
+            j := j - 1
+
+        # check right diagonal
+        i := row - 1
+        j := col + 1
+        loop:
+            if i < 0 or j >= n :  
+                break
+            if board[i][j] = 1 :  
+                return : 0
+            i := i - 1
+            j := j + 1
+
+        return : 1  
+
+    def solveNQueensUtil is byte: board as byte[][], row n as int
+        if row = n :  
+            printBoard: board, n
+            return : 1   
+
+        var col is int
+        col := 0
+        loop:
+            if col >= n :  
+                break
+            if isSafe: board, row, col, n :  
+                board[row][col] := 1  
+                if solveNQueensUtil: board, row + 1, n :  
+                    return : 1  
+                board[row][col] := 0  
+            col := col + 1  
+
+        return : 0   
+
+    def solveNQueens: n as int
+        var board is byte[n][n]
+        var i j is int
+
+        i := 0
+        loop:
+            if i >= n :  
+                break
+            j := 0
+            loop:
+                if j >= n :  
+                    break
+                board[i][j] := 0  
+                j := j + 1  
+            i := i + 1  
+
+        if solveNQueensUtil: board, 0, n :  
+            writeString: "Solution found.\n"
+        else :
+            writeString: "No solution exists.\n"
+
+    var size is int
+    writeString: "Enter board size: "
+    size := readInteger()  
+    solveNQueens: size  

dana/programs/N_Queens.input

@@ -0,0 +1 @@
+8

dana/programs/N_Queens.result

@@ -0,0 +1,10 @@
+Q . . . . . . .
+. . . . . . Q .
+. . . . Q . . .
+. . . Q . . . .
+. . Q . . . . .
+. Q . . . . . .
+. . . . . Q . .
+. . . . . . . Q
+
+Solution found.