From 5a29a9bd63445f9e472f8d90b48af5772a23aa50 Mon Sep 17 00:00:00 2001
From: Megha1209 <51127835+Megha1209@users.noreply.github.com>
Date: Mon, 14 Oct 2019 11:59:28 +0530
Subject: [PATCH 1/3] Rat Chases Cheese Question

---
 Ratchasesitscheese.java | 73 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 73 insertions(+)
 create mode 100644 Ratchasesitscheese.java

diff --git a/Ratchasesitscheese.java b/Ratchasesitscheese.java
new file mode 100644
index 0000000..9f2866a
--- /dev/null
+++ b/Ratchasesitscheese.java
@@ -0,0 +1,73 @@
+package lect12backtracking;
+
+import java.util.Scanner;
+
+public class Ratchasesitscheese {
+	static Scanner x = new Scanner(System.in);
+
+	public static void main(String[] args) {
+
+		char[][] maze = takeInput();
+		int[][] AuxiMaze = new int[maze.length][maze[0].length];
+		//int[][] temp = new int[maze.length][maze[0].length];
+		paths(maze, 0, 0, AuxiMaze);
+		if (c == 0) {
+			System.out.println("NO PATH FOUND");
+		}
+
+	}
+
+	static int c = 0;
+
+	public static void paths(char[][] maze, int row, int col, int[][] Auxi) {
+		if (row == maze.length - 1 && col == maze[0].length - 1) {
+			Auxi[row][col] = 1;
+			//for(int i=0;i<Auxi.length;i++){
+            //for(int j=0;j<Auxi[0].length;j++){
+            //    temp[i][j]=Auxi[i][j];
+			//display(temp);
+
+			display(Auxi);
+			c = 1;
+			return;
+		}
+		if (row == maze.length || col == maze[0].length || row < 0 || col < 0 || maze[row][col] == 'X'
+				|| Auxi[row][col] == 1) {
+			return;
+		}
+
+		Auxi[row][col] = 1;
+
+		paths(maze, row + 1, col, Auxi);
+
+		paths(maze, row, col + 1, Auxi);
+
+		paths(maze, row - 1, col, Auxi);
+
+		paths(maze, row, col - 1, Auxi);
+		Auxi[row][col] = 0;
+
+	}
+
+	public static char[][] takeInput() {
+		int n = x.nextInt();
+		int m = x.nextInt();
+		char[][] maze = new char[n][m];
+		for (int i = 0; i < n; i++) {
+			String a = x.next();
+			for (int j = 0; j < m; j++) {
+				maze[i][j] = a.charAt(j);
+			}
+		}
+		return maze;
+	}
+
+	public static void display(int[][] maze) {
+		for (int i = 0; i < maze.length; i++) {
+			for (int j = 0; j < maze[0].length; j++) {
+				System.out.print(maze[i][j] + " ");
+			}
+			System.out.println();
+		}
+	}
+}

From c5548cedec534b31971a49992f7b05f098e25017 Mon Sep 17 00:00:00 2001
From: Megha1209 <51127835+Megha1209@users.noreply.github.com>
Date: Mon, 14 Oct 2019 22:58:00 +0530
Subject: [PATCH 2/3] Add files via upload

---
 Backtracking/Ratchasesitscheese.java | 73 ++++++++++++++++++++++++++++
 1 file changed, 73 insertions(+)
 create mode 100644 Backtracking/Ratchasesitscheese.java

diff --git a/Backtracking/Ratchasesitscheese.java b/Backtracking/Ratchasesitscheese.java
new file mode 100644
index 0000000..9f2866a
--- /dev/null
+++ b/Backtracking/Ratchasesitscheese.java
@@ -0,0 +1,73 @@
+package lect12backtracking;
+
+import java.util.Scanner;
+
+public class Ratchasesitscheese {
+	static Scanner x = new Scanner(System.in);
+
+	public static void main(String[] args) {
+
+		char[][] maze = takeInput();
+		int[][] AuxiMaze = new int[maze.length][maze[0].length];
+		//int[][] temp = new int[maze.length][maze[0].length];
+		paths(maze, 0, 0, AuxiMaze);
+		if (c == 0) {
+			System.out.println("NO PATH FOUND");
+		}
+
+	}
+
+	static int c = 0;
+
+	public static void paths(char[][] maze, int row, int col, int[][] Auxi) {
+		if (row == maze.length - 1 && col == maze[0].length - 1) {
+			Auxi[row][col] = 1;
+			//for(int i=0;i<Auxi.length;i++){
+            //for(int j=0;j<Auxi[0].length;j++){
+            //    temp[i][j]=Auxi[i][j];
+			//display(temp);
+
+			display(Auxi);
+			c = 1;
+			return;
+		}
+		if (row == maze.length || col == maze[0].length || row < 0 || col < 0 || maze[row][col] == 'X'
+				|| Auxi[row][col] == 1) {
+			return;
+		}
+
+		Auxi[row][col] = 1;
+
+		paths(maze, row + 1, col, Auxi);
+
+		paths(maze, row, col + 1, Auxi);
+
+		paths(maze, row - 1, col, Auxi);
+
+		paths(maze, row, col - 1, Auxi);
+		Auxi[row][col] = 0;
+
+	}
+
+	public static char[][] takeInput() {
+		int n = x.nextInt();
+		int m = x.nextInt();
+		char[][] maze = new char[n][m];
+		for (int i = 0; i < n; i++) {
+			String a = x.next();
+			for (int j = 0; j < m; j++) {
+				maze[i][j] = a.charAt(j);
+			}
+		}
+		return maze;
+	}
+
+	public static void display(int[][] maze) {
+		for (int i = 0; i < maze.length; i++) {
+			for (int j = 0; j < maze[0].length; j++) {
+				System.out.print(maze[i][j] + " ");
+			}
+			System.out.println();
+		}
+	}
+}

From f0d25a7717e8d0ee3264ae18cd44c6bd53a6a1f4 Mon Sep 17 00:00:00 2001
From: Megha1209 <51127835+Megha1209@users.noreply.github.com>
Date: Mon, 14 Oct 2019 22:59:56 +0530
Subject: [PATCH 3/3] ChessBoard Problem

---
 Backtracking/Chessboard2.java | 80 +++++++++++++++++++++++++++++++++++
 1 file changed, 80 insertions(+)
 create mode 100644 Backtracking/Chessboard2.java

diff --git a/Backtracking/Chessboard2.java b/Backtracking/Chessboard2.java
new file mode 100644
index 0000000..0718405
--- /dev/null
+++ b/Backtracking/Chessboard2.java
@@ -0,0 +1,80 @@
+package lect12backtracking;
+
+import java.util.Scanner;
+
+public class Chessboard2 {
+static int count =0;
+	public static void main(String[] args) {
+		Scanner scn = new Scanner(System.in);
+		int n = scn.nextInt();
+		boolean[][] arr = new boolean[n][n];
+		int[] mp = Makemines(n*n);
+		Chessboard2(arr,0,0,"",mp);
+		System.out.println();
+		System.out.println(count);
+		
+	}
+	public static void Chessboard2(boolean[][] board, int row, int col, String ans,int[] mp) {
+		if (row == board.length - 1 && col == board[0].length - 1) {
+			System.out.print("{0-0}" + ans+" ");
+			count++;
+			return;
+		}
+		if (row >= board.length || col >= board[0].length || board[row][col])
+			return;
+		board[row][col] = true;
+		
+		int cell = row * (board[0].length) + col + 1;
+
+		if (mp[cell] == 1) {
+			return ;
+		} else if (mp[cell] == 2) {
+			Chessboard2(board,board.length-1,board[0].length-1, ans + "P{" + (board.length - 1) + "-" + (board[0].length-1) + "}", mp);
+		}
+
+		
+				Chessboard2(board, row + 2, col + 1, ans + "K" + "{" + (row + 2) + "-" +( col + 1 )+ "}",mp);
+		Chessboard2(board, row + 1, col + 2, ans + "K" + "{" + (row + 1) + "-" + (col + 2) + "}",mp);
+		if (row == 0 || col == 0 || col == board[0].length - 1 || row == board.length - 1) {
+		for(int i =1;i<board.length;i++)
+		Chessboard2(board, row , col+i, ans + "R" + "{" + (row ) + "-" + (col+i)+ "}",mp);
+		for(int i =1;i<board.length;i++)
+		Chessboard2(board, row+i, col , ans + "R" + "{" + (row+i) + "-" + (col ) + "}",mp);}
+		if (row == col|| row + col == board.length - 1 ) {
+		for(int i =1;i<board.length;i++)
+		Chessboard2(board, row + i, col + i, ans + "B" + "{" + (row + i) + "-" + (col + i) + "}",mp);}
+		board[row][col] = false;
+	}
+	public static int[] Makemines(int n)
+	{ int arr[] = new int[n+1];
+	 int c=1;
+	 for(int i=2;i<arr.length;i++)
+	 { if(isPrime(i))
+	 {if(c%2==1)
+		 arr[i] = 1;
+	 else
+		 arr[i] = 2;
+	 c++;
+		 
+	 }
+	}
+	 return arr;
+
+}
+	public static boolean isPrime(int n)
+	{
+	for(int i =2;i<n;i++)
+		{if(n%i==0)
+			return false;}
+	return true;
+	}
+}
+	
+	
+	
+	
+	
+	
+	
+	
+