Merge pull request #684 from Ananya-Misra/knight

knight tour's problem added

Author: smv1999

Backtracking/Knight's_Tour.java

@@ -0,0 +1,65 @@
+/*Moving according to the rules of chess knight must visit each square exactly once. Print the order of each the cell in which they are visited.*/
+import java.util.*;
+public class MyClass {
+    public static void main(String args[]) {
+        Scanner sc = new Scanner(System.in);
+        int n = sc.nextInt();
+        // provide start position
+        int r = sc.nextInt();
+        int c = sc.nextInt();
+        int board[][] = new int[n][n];
+        // The 8 possible moves where a knight can move from its current position
+        int posx[] = {-1,-1,1,1,-2,-2,2,2};
+        int posy[] = {-2,2,-2,2,-1,1,-1,1};
+        path(board, r, c, 1, posx, posy);
+    }
+    public static boolean path(int board[][], int row, int col, int move, int posx[], int posy[]) {
+        board[row][col] = move;
+        // if all the positions are visited then print the result
+        if (move == board.length*board.length) {
+            // printing result in matrix form
+            for (int i = 0; i < board.length; i++) {
+                for (int j = 0; j < board.length; j++)
+                    if (board[i][j] < 10)
+                        System.out.print("0" + board[i][j] + " ");
+                    else
+                        System.out.print(board[i][j] + " ");
+                System.out.println();
+            }
+            return true;
+        }
+        for (int i = 0; i < 8; i++) {
+            int newx = row + posx[i];
+            int newy = col + posy[i];
+            // checking if the new position is a valid move and not visited yet
+            if (validmove(newx, newy, board) && board[newx][newy] == 0) {
+                if (path(board, newx, newy, move + 1, posx, posy)) {
+                    return true;
+                }
+            }
+        }
+        // if position is not valid mark position as unvisited in the matrix
+        board[row][col] = 0;
+        return false;
+    }
+    // checks that the new position is not outside the matrix of n*n
+    static boolean validmove(int newx, int newy, int board[][]) {
+        if (newx >= 0 && newx < board.length && newy >= 0 && newy < board.length)
+            return true;
+        return false;
+    }
+}
+
+/*Input
+8
+0 
+0
+Output
+01 08 15 22 03 10 19 64 
+16 23 02 09 18 21 04 11 
+07 14 17 24 05 12 63 20 
+34 25 06 13 44 27 52 61 
+55 46 33 26 53 62 43 28 
+32 35 54 45 40 29 60 51 
+47 56 37 30 49 58 39 42 
+36 31 48 57 38 41 50 59 */